Course Description

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<td><strong>Course Description</strong></td>
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<td><strong>Course Code: MAT 2250</strong></td>
<td><strong>Course Title: </strong>Linear Algebra- I</td>
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<td><strong>Credit Hours:</strong>3(3,1,0)</td>
<td><strong>Level:</strong>Fourth</td>
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<td><strong>Prerequisites: </strong>MAT 2240</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Matrix Definition – Matrix Operations – Symmetric Matrices – Transpose and Inverse of a Matrix – Hermitian Matrices – Markov Matrices – Factorization – Positive definite Matrix – Row Operations – Row Reduced Echelon Form – Linear system of Equations – Solving Ax=0 and Ax = b – Vector Spaces and Subspaces – Basis and Dimension – Orthogonality – Similar Matrices – Singular Value Decomposition – Least Squares Approximations – Determinants – Properties of Determinants – Applications of Determinants – Cramer’s Rule – Gauss elimination rule – Gauss Jordan Elimination – Eigenvalues and Eigenvectors – Diagonalization – Linear Transformation – Matrices with MATLAB.</td>
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<td>Course Code:  MAT2301</td>
<td>Course Title: Visual Programming of Mathematical  Problems</td>
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<td>Course hours: 3 (3, 0,1)</td>
<td>Level: Third </td>
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<td>Pre-requisite: 1400 TC</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">The course covers the basic programming principles  focusing on  graphical user interfaces and structured programming  techniques. The topics include design interfaces for mathematical applications, using variables and constants to store information, input/output operations, arithmetic operations, arithmetic expressions, sequential,  selection, and repetition programming structure, arrays implementation. ,function implementation and other related topics. Upon completion, students should be able to design, code, test, and debug Visual programs.</td>
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<td><strong>Course Code: MAT 2<span dir="RTL">31</span>1</strong></td>
<td><strong>Course Title: </strong>Infinite Series and Calculus Applications</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: Third </strong></td>
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<td><strong>Prerequisites:</strong>  MAT 10<span dir="RTL">6</span>0</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Sequences and Series – sequence of real number- Bounded and monotonic sequences- Geometric sequences-infinite series- Convergence and Divergence of Infinite Series - Integral Test - Ratio Test- Root Test and Comparison Test.  Conditional Convergence and Absolute Convergence - Alternating Series Test- Power Series – Differentiation and integration of power series - Taylor and Maclaurin series- The centroid of a plane region- Moments and center of mass – Work- Power –Energy-Fluid pressure and force- Newton's Method- Linearization and Differentials- Optimization.</td>
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<td><strong>Course Code: MAT 2240</strong></td>
<td><strong>Course Title: </strong>Algebra and Analytic Geometry</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: Third </strong></td>
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<td><strong>Prerequisites:</strong>  MAT 10<span dir="RTL">6</span>0</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Analytic Geometry: the straight line-circle, Conic sections General theory of second order curves – Simplifying the general second order equation by Translation and Rotation – systems of coordinates –Introduction to mathematical logic: Statement – Conjunction – Disconjunction – Conditional and bi-conditional statements – Existential and universal quantifiers – Negation- Converse – Inverse and contrapositive–  Truth tables – Methods of proof. Sets theory: Concept De Morgan's laws– power set – Cartesian product – ordered pairs and triples. Relations: domain and range of relation notions of reflexive – symmetric – transitive relation – Equivalence relations – equivalence class – partition– quotient set. Orderings: partial and total orderings – Mapping and Functions – Different types of mapping domain and range of a function – composition of functions – Inverse of mapping – Composition of mapping– Countable set – Equivalent sets – Cardinal Number – Finite and infinite sets.</td>
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<td><strong>Course Code: MAT 2321</strong></td>
<td><strong>Course Title: Actuarial mathematics-I</strong></td>
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<td><strong>Credit Hours: </strong>3(3,0,0)</td>
<td><strong>Level:  </strong>Fourth</td>
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<td><strong>Prerequisites:</strong>  MAT 10<span dir="RTL">6</span>0</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Introduction and definitions - the general law of simple interest –true and commercial interest – present value and discount-the sum of annuities-certain using fixed and variable simple interest rates- some practical applications on simple interest including methods of redemption of short term loans, modification of  loans and saving accounts. The general law of compound interest: the sum, present values and discount –the nominal rate of compound interest – the calculation of the sum and present value of annuities –certain with fixed and variable compound rates of interest-some practical applications on compound interest including methods of redemption of long term loans, modification of loans and redeemable securities - investment using software and spread sheets  - insurance-Investment using Excel.</td>
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<td><strong>Course Code: MAT 3260</strong></td>
<td><strong>Course Title: </strong>Mathematical Programming</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Elective</td>
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<td><strong>Prerequisites:</strong> MAT 2250, MAT 2311</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Polyhedra – Extreme Points – Optimality Conditions – The Simplex Method – Separating Hyperplanes and Duality – Sensitivity Analysis – Parametric Programming – Interior Point Methods – Affine Scaling – Network Problems and the Simplex Method – Duality in Networks – Shortest Path Problem – Integer Programming Formulations – Integer Programming Duality.</td>
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<td><strong>Course Code: MAT 3270</strong></td>
<td><strong>Course Title: </strong>Number Theory</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Elective</td>
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<td><strong>Prerequisites: </strong>MAT 2240</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Divisibility – Greatest Common Divisor – Division Algorithm – Prime Factorization and Binomial – Binomial Theorem and Congruencies – Congruencies – Residue Systems – Fermat's Little Theorem – Euler's Theorem – Wilson's Theorem – Diophantine Equations – Chinese Remainder Theorem – RSA Cryptography - Hensel's Lemma – Solving Equations Modulo Primes – Quadratic Residue Symbol - Quadratic Reciprocity – Continued Fractions – Curves in Projective Space –  Statement of Falting's Theorem – (Mordell Conjecture) – Singular Points and Smoothness – Elliptic Curves – Abelian Groups – Torsion Points and Finite Generation of Group of Torsion Points – Mazur's Theorem and Calculating the Torsion Subgroup.</td>
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<td><strong>Course Code: MAT 3280</strong></td>
<td><strong>Course Title: </strong>Linear Algebra<span dir="RTL">-</span>II</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Fifth</td>
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<td><strong>Prerequisites: </strong>MAT 2250</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Vector Spaces: Vector space axioms – Subspace and Span – Linear Combination – Linear independence – Generators – Basis and Dimension – Coordinate and Change of Basis – Rank of a Matrix – Linear Transformations – Kernel and range – Isomorphism – Matrix of a Linear transformation – Similarity and change of basis – Trace – Determinants and Permutations – Odd and even permutations – Computation by row and column operations – Cofactor expansion – Eigenvalues and Eigenvectors – Diagonalization – Characteristic Polynomial – Cayley Hamilton theorem – Jordan canonical form I& II – Symmetric Matrices – Inner Product – Norm – orthogonal transformations – Congruence – orthogonal basis – orthogonal Projections – Isometrics – Spectral theorem – Hermitian Products – Cauchy- Schwarz inequality – Angle between vectors – Gram–Schmidt processes – Applications of Linear Algebra: Graph Theory – Cryptography – Finding The Equation of a Curve Passing through a Point – Computer Graphics.</td>
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<td><strong>Course Code: MAT <span dir="RTL">2</span>290</strong></td>
<td><strong>Course Title: </strong>Mechanics</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Fourth</td>
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<td><strong>Prerequisites: </strong>MAT 1060</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Static: Force as a vector – Vector Algebra – Free-body Diagrams – Coplanar Forces – Couples. Dynamics: Kinematics – RectiLinear Motion – Position Vector – Velocity and Acceleration – Graphical Methods – Relative Motion – CurviLinear Motion – Position Vector -  Velocity and Acceleration in 2- D and 3- D – Relative Motion – Applications on CurviLinear Motion. Kinetics: Newton's 2nd Law – Principle of Work and Kinetic Energy – Principle of Impulse and Momentum – Central Force – Impact – Vibrations.</td>
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<td><strong>Course Code: </strong>MAT 3320</td>
<td><strong>Course Title: </strong> Multivariable Calculus</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:  </strong>Fifth</td>
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<td><strong>Prerequisites:  </strong>MAT 2311</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Coordinate Systems – Multivariable Functions – Partial derivatives - Critical Points of Multivariable Functions - Maxima and Minima of the Functions of Two Variables –SP -  Lagrange Multipliers – Double Integrals in Rectangular  Coordinates – Double Integrals in Polar Coordinates –Triple Integrals in Rectangular and Cylindrical Coordinates – Spherical Coordinates – Centre of Mass - Moment of Inertia - Gradient Fields and Path Independence – Divergence and Curl.</td>
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<td><strong>Course Code: MAT 3330</strong></td>
<td><strong>Course Title: </strong>Ordinary Differential Equations<span dir="RTL">-</span>I</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Fifth</td>
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<td><strong>Prerequisites:</strong>MAT 2250, MAT 2311</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">First Order Equations:  Non-Linear Separable – Homogeneous – Exact Equation – Linear Bernoulli’s Equation – Direction Fields. Second Order Linear Equations with Constant Coefficients – Homogeneous case – Non-homogeneous Equations via Method of Undetermined Coefficients – Non-homogeneous Equations via Method of Variation of Parameters  – Remarks on Higher Order Equations – Linear Independence  and the Wronskian – Applications to Forced Oscillation Problems – Effect of Resonances – Laplace Transform Application to Constant Coefficient Linear Equations<span dir="RTL"> -  </span> Fourier Series.</td>
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<td><strong>Course Code: MAT 3340</strong></td>
<td><strong>Course Title: </strong>Ordinary Differential Equations- II</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:  </strong>Sixth</td>
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<td><strong>Prerequisites:</strong>MAT 3320, MAT 3330</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">First Order Systems – Conversion of Second and Higher Order Equations to First Order Systems – Differentiation of Vector and Matrix Functions – Solution of Linear Constant Coefficient Systems – Two Dimensional Systems and Phase Plane – Classification of Equilibria for Linear Systems – Qualitative behavior of Nonlinear <span dir="RTL">ٍٍٍ</span>Systems: Classification of Equilibria – Stability – Applications - Examples to the Pendulum and Population Models – Singular Points of Linear Second Order ODEs with Variable Coefficients – Frobenius Method – Bessel Functions – Properties of Bessel Functions – Modified Bessel Functions – Differential Equations Satisfied by Bessel Functions – Introduction to Boundary- Value Problems – Eigenvalues – EigenFunctions – Orthogonality of EigenFunctions – Sturm-Liouville Problem – Fourier Series – Fourier Sine and Cosine Series – Complete Fourier Series.</td>
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<td><strong>Course Code: </strong>MAT 3350</td>
<td><strong>Course Title: Vector Analysis</strong></td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:  </strong>Sixth</td>
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<td><strong>Prerequisites:  </strong>MAT 3320</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Vectors – Dot Product – Cross Product – Parametric Curves – Velocity – Acceleration – arc length – Curvature – Torsion – Level Curves – Partial Derivatives – Tangent Plane – Scalar Field and the Gradient – Directional Derivative – Lagrange Multipliers – Double and Iterated Integrals – Double Integrals in Polar Coordinates – Applications – Change of Variables – Triple Integrals in Rectangular and Cylindrical Coordinates – Spherical Coordinates – Gradient Fields and Path Independence – Conservative Fields and Potential Functions – Green's Theorem – two dimensional Curl (Vorticity) – Simply connected Regions – Flux Form of Green's Theorem – Vector Fields in 3- D- space – Surface Integrals and Flux – Divergence Theorem – Line Integrals in Space – Exactness – Potential – Stokes' Theorem – Conservation Laws – Heat/Diffusion Equation – Maxwell's Equations.</td>
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<td><strong>Course Code: MAT 3370</strong></td>
<td><strong>Course Title: </strong>Numerical Analysis</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:  </strong>Fifth</td>
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<td><strong>Prerequisites: </strong>MAT 2250, MAT 2311</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Types of Errors – Interpolation – Numerical Differentiation – Numerical Integration – Solving Algebraic Systems of Equations by Iterations – Root Finding – Solving System of Nonlinear Equations – Methods of Solving First Order Initial Value Ordinary Differential Equations – Converting Higher Order Ordinary Differential Equations to First Order Ones – Solving Systems of First Order Initial Value Ordinary Differential Equations – Finite Differences – Solving Two Point Boundary Value Problems by Finite Differences.</td>
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<td><strong>Course Code: MAT <span dir="RTL">2</span>4<span dir="RTL">5</span>0</strong></td>
<td><strong>Course Title:</strong> Abstract Algebra -I</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Fourth</td>
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<td><strong>Prerequisites:  </strong>MAT 2240</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Binary Operation – Associative – Commutative – Identity element v Inverse of an element – Fundamental Properties of Groups - Subgroups – Cyclic Groups – Permutation Groups – Symmetry Groups – Group Homeomorphisms and Cayley Theorem – Cosets and Lagrange's Theorem – Quotient Groups – Finite Groups – Discrete Groups – Finite Rotation Groups – Normal and Factor Groups – BiLinear Forms – Symmetric Forms – Hermitian Forms –The Rotation Group – Abelian Groups – Finitely Generated Abelian Groups – P Group - The Isomorphism - Theorems of Groups – Simple Group – Group Representation –Normal and Subnormal Series – Composition Series – Soluble Groups – Nilpotent Groups.</td>
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<td><strong>Course Code: MAT 3460</strong></td>
<td><strong>Course Title: </strong>Real Analysis- I</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:  </strong>Sixth</td>
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<td><strong>Prerequisites:</strong> MAT 2240, MAT 3320, MAT 3330</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Sets and Fields – The Real Numbers – Countability – Metric Spaces – Closed Sets – Compact Spaces – Compact Subsets of Euclidean Space – Completeness – Sequences and Series – Continuity – Continuity and Compactness – Differentiability – Mean Value Theorem – Taylor Series – Riemann- Stieltjes Integral – Integrability – Fundamental Theorem of Calculus – Sequences of Functions – Uniform Convergence – Equicontinuity – Power Series – Fundamental Theorem of Algebra.</td>
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<td><strong>Course Code: MAT 3510</strong></td>
<td><strong>Course Title: </strong>Mathematical Packages</td>
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<td><strong>Credit Hours: </strong>3(2,1,0)</td>
<td><strong>Level:  </strong>Sixth</td>
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<td><strong>Prerequisites:</strong> MAT 2301, MAT 3330</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Introduction: Problem Formulation – Algorithm Development. FORTRAN 95: Program Creation – Compilation and Linking Variables and Parameters – Flow Control – Subroutines and Functions – Use of Libraries.  C++ for Scientific Uses –  Mathematica® : Vectors and Matrices – Numerical Calculations – Symbolic Calculations – Graphics.  MATLAB®"Matrix Laboratory": MATLAB® Vectors and Matrices – Numerical Calculation. Applications: Polynomials – Interpolation – Integration – Differentiation – ODE – Graphics – 2- D and 3- D. Graphics: Review of Common Graphics Program – Graphics with Spreadsheets – Kaleidagraph – SigmaPlot – TecPlot, etc.</td>
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<td><strong>Course Code: MAT 4350</strong></td>
<td><strong>Course Title: </strong>Complex Analysis</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: Eigth </strong></td>
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<td><strong>Prerequisites</strong>:  MAT 3320, MAT 3330</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Complex Algebra and Functions – Algebra of Complex Numbers – Complex Plane – Polar Form – Geometric Series – Functions of Complex Variable – Analyticity – Cauchy- Riemann Conditions – Harmonic Functions – Complex Exponential – Complex Trigonometric and Hyperbolic Functions – Complex Logarithm – Complex Powers – Inverse Trig. Functions – Complex Integration – Contour Integration – Path Independence – Cauchy's Integral Theorem – Cauchy's Integral Formula – Higher Derivatives – Bounds – Liouville's Theorem – Maximum Modulus Principle – Mean value Theorems – Fundamental Theorem of Algebra – Radius of Convergence of Taylor Series – Residue Calculus – Laurent Series – Poles – Essential Singularities – Point at Infinity – Residue Theorem – Integrals around Unit Circle – Real Integrals From - ∞ to +∞. Contours. Singularity on Path of Integration – Principal Values – Integrals involving Multivalued Functions – Conformal Mapping – Inversion Mappings – BiLinear/Mobius Transformations.</td>
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<td><strong>Course Code: MAT 4360</strong></td>
<td><strong>Course Title: </strong>Introduction to Partial Differential                               Equations</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Seventh</td>
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<td><strong>Prerequisites:  </strong>MAT 2311</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2"> </td>
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<td><strong>Course Code: </strong>MAT 3320</td>
<td><strong>Course Title: </strong> Multivariable Calculus</td>
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<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:  </strong>Fifth</td>
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<td><strong>Prerequisites:  </strong>MAT 2311</td>
<td><strong>Co-requisites</strong></td>
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<td colspan="2">Introduction and Basic Facts about PDE's  –  Types of PDE’s  –   Derivation of the Heat and Wave Equations from physics – Solution of boundary problems (Dirichlet, Neumann, Robin) by Fourier series – Eigenvalues  –   EigenFunctions – Orthogonality of EigenFunctions – Sturm–Liouville Problem  –  Separation of Variables: The Heat Equation in 1D – The Wave Equation in 1D.Laplace’s Equation in Rectangles, Circles - Inhomogeneous PDEs and the (Generalized) Fourier series – Fourier Transform – Solutions of PDE's by Fourier Transform – Heat and Wave Equations in Half Space – Solving Simple Equations by Characteristics.</td>
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<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4380</strong></td>
<td><strong>Course Title: </strong>Nonlinear Dynamics</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Elective</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong>MAT 2250, MAT 3330</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Pendulum – Free Oscillator – Energy in the Plane Pendulum – Stability of Solutions to ODEs – Linear Systems – Nonlinear Systems – Conservation of Volume in Phase Space – Damped Oscillators and Dissipative Systems – Phase Portrait of Damped Pendulum – Forced Oscillators and Limit Cycles – Van der Pol Equation – Parametric Oscillator – Mathieu’s Equation – Elements of Floquet Theory – Stability of the Parametric Pendulum – Damping. Fourier Transforms: Continuous Fourier Transform – Discrete Fourier Transform – Inverse DFT – Autocorrelations – Power Spectra – Poincaré Sections – Periodic – Quasiperiodic Flows – Aperiodic Flows – 1– D Flows – Rössler Attractor – Fluid Dynamics and Rayleigh– Bénard Convection – The Concept of a Continuum – Mass Conservation – Momentum Conservation – Substantial Derivative – Forces on Fluid Particle – Nondimensionalization of Navier–Stokes Equations –  Bifurcation Diagram – Pattern Formation – Convection in the Earth – Introduction to Strange Attractors – Dissipation and Attraction – Attractors with 2D – Aperiodic Attractors – Rössler Attractor – Lorenz Equations – Physical Problem and Parametrization – Equations of Motion – Momentum Equation – Temperature Equation – Dimensionless Equations – Stability –   Diverging Trajectories –  Lyaponov Exponents.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4390</strong></td>
<td><strong>Course Title: </strong>Differential Geometry</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Elective</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong>MAT 2250, MAT 3320, MAT 3330</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Geometry of Curves in the Plane – Arc Length – Tangential and Normal Vectors – (signed) Curvature – Reconstruction of a Curve with given Curvature and Arc Length – Evolutes and Involutes – the Isoperimetric Inequality and Hopf’s Theorem on the Tangential Degree of an Embedded Closed Curve – Geometry of Curves in the Space – Arc length – Curvature – Torsion – The Frenet– Serret Equations – Reconstruction of a curve with given curvature and torsion – Generalized helices – Evolutes and involutes. Surfaces in Space: The first and second fundamental forms – Area and the Gauss and Codazzi Equations – Gaussian curvature – developable surfaces – principal curvature – Meunier’s Theorem – surfaces of constant Gaussian curvature – mean curvature – minimal surfaces – Intrinsic Geometry of Surfaces – Geodesic curvature of curves on surfaces – First variation of arc length – The Gauss–  Bonnet Theorem and applications.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4400</strong></td>
<td><strong>Course Title: </strong>Advanced Fluid Mechanics</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:  </strong>Elective</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong>MAT <span dir="RTL">2</span>290, MAT 4360 </td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Continuum Viewpoint and the Equation of Motion – Static Fluids – Mass Conservation – Inviscid Flow (Differential Approach) –   Euler's Equation – Bernoulli's Integral – The Effects of Streamline Curvature – Control Volume Theorems (Integral Approach) –  Linear Momentum Theorem – Angular Momentum Theorem – First and Second Laws of Thermodynamics – Navier– Stokes Equation and Viscous Flow – Boundary Layers – Separation and the Effect on Drag and Lift – Vorticity and Circulation – Potential Flow –  Lift – Drag  and Thrust – Surface Tension and its Effect on Flows.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4410</strong></td>
<td><strong>Course Title: </strong>Classical Mechanics</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong> Elective</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 2290, MAT 4360</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Principle of Stationary Action – Lagrange Equations – Hamilton's Principle – Coordinate Transformations and Rigid Constraints – Total time Derivatives and the Euler–  Lagrange Operator – State and Evolution – Chaos – Conserved Quantities – Rigid Bodies – Kinematics of Rigid Bodies – Moments of Inertia – Generalized Coordinates for Rigid Bodies – Motion of a Free Rigid Body – Axisymmetric Top – Spin–  Orbit Coupling – Euler's Equations – Hamilton's Equations – Legendre Transformation – Hamiltonian Action and Poisson Brackets – Phase Space Reduction – Phase Space Evolution – Surfaces of Section – Autonomous Systems: Henon–  Heiles – Exponential Divergence – Solar System – Liouville Theorem – Phase Space Structure – Linear Stability – Homoclinic Tangle – Integrable Systems – Poincare–  Birkhoff Theorem – Invariant Curves – KAM Theorem – Canonical Transformations – Integral Invariants – Extended Phase Space – Generating Functions – Time Evolution in Canonical  Hamilton–  Jacobi Equation – Lie Transforms – Perturbation Theory – Perturbation Theory with Lie Series.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4420</strong></td>
<td><strong>Course Title: </strong>Introduction to Functional Analysis</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong> Elective</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 3280, MAT 3460</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Normed Vector Spaces – Completeness – Functionals – Hilbert spaces – Isomorphism – Cardinality – Aleph   Null – Invariant Subspace – Basic theory of Banach Spaces –  Lebesgue Measure – Measurable Functions – Completeness of L–  p spaces – Dual Space " The space of all Continuous Linear Functionals" – Frechet spaces - Frechet  Urysohn Space as a type of Sequential Space –  Major and Foundational results –  The Uniform Boundedness Principle or (Banach–Steinhous Theorem) – Spectral Theorems - Integral Formula for the Normal Operators on a Hilbert Space – Hahn–  Banach Theorem – extends Functionals from a subspace to the full space – Open Mapping Theorem – Closed Graph Theorem –  Theory of Compact Operators – Hilbert–Schmidt and Trace Class Operators.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4430</strong></td>
<td><strong>Course Title: </strong>Introduction to Topology</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level : </strong>Seventh</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong>MAT 3460</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Logic and Foundations – Relations – Cardinality – Axiom of Choice – Topologies – Closed Sets – Continuous Functions – Arbitrary Products – Metric Topologies – Quotient Topology – Connected Spaces – Compact Spaces – Well–  Ordered Sets – Maximum Principle – Countability and Separation Axioms – Urysohn Lemma – Metrization – Tietze Theorem – Tychonoff Theorem – Stone–Cech Compactification – Baire Spaces – Dimension – Imbedding in Euclidean Space.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4450</strong></td>
<td><strong>Course Title: </strong>Abstract Algebra-II</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Seventh</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong>MAT 2450</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Rings: Definitions – Basic Properties of Rings – Subring – Fields – Division Ring – Integral Domain – Characteristic of the Rings – Right and Left Ideal of the Ring – Quotient Rings – Principlal Ideal Domains – Unique Factorization – Gauss' Lemma – Explicit Factorization – Maximal Ideals – Gauss Primes – Quadratic Integers – Ideal Fractions – Ideal Classes – Relations in a Ring – Adjoining Elements – Polynomial Rings – Euclidean Rings – Ring Homomorphism – Ring Endomorphism – Fields: Algebraic Elements – Modules over rings – Submodules – quotient modulas.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4470</strong></td>
<td><strong>Course Title: </strong>Real Analysis–II</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Elective</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 3320, MAT 3460, MAT 3280 </td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Metric Spaces – Continuity – Limit Points – Compactness – Connectedness – Differentiation in n Dimensions – Conditions for Differentiability – Mean Value Theorem – Chain Rule – Mean  Value Theorem in n Dimensions – Inverse Function Theorem – Reimann Integrals of Several Variables – Conditions for Integrability – Measure Zero – Fubini Theorem – Properties of Reimann Integrals – Integration Over More General Regions – Rectifiable Sets – Volume – Improper Integrals – Exhaustions – Compact Support – Partitions of Unity –  Dual Spaces – Tensors – Pullback Operators – Alternating Tensors – Redundant Tensors – Wedge Product – Determinant – Orientations of Vector Spaces – Tangent Spaces and k– Forms – The d Operator – Pullback Operator on Exterior Forms – Integration with Differential Forms – Change of Variables Theorem – Sard's Theorem Poincare Theorem – Generalization of Poincare Lemma – Proper Maps and Degree – Regular Values – Degree Formula – Topological Invariance of Degree – Canonical Submersion and Immersion Theorems – Manifolds – Tangent Spaces of Manifolds – Differential Forms on Manifolds – Orientations of Manifolds – Integration on Manifolds – Degree on Manifolds – Hopf Theorem – Integration on Smooth Domains  – Stokes’ Theorem.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4480</strong></td>
<td><strong>Course Title: </strong>Principles of Automatic Control</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Elective</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 2250, MAT 3320, MAT 3330</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Closed– loop control systems – Open– loop control systems – The Laplace Transform  –  Mathematical Modeling of Dynamic Systems – Transient response Analysis – Basic Control Actions and Response of Control Systems – Root Locus Analysis – Frequency– Response Analysis – Analysis of Control System in State Space – Liapunov Stability Analysis and Quadratic Optimal.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4490</strong></td>
<td><strong>Course Title: </strong>Applications of Continuum Mechanics to Earth, Atmospheric, and Planetary Sciences</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Elective</td>
</tr>
<tr>
<td><strong>Prerequisites</strong>: MAT 2250, MAT 4360</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Tractions – Stress Tensor – Stress Tensor in Different Coordinate Systems – Pore Fluid Pressure – Newton's Second Law – Stress in the Earth – Stress Rotation – Sandbox Tectonics – Displacement Gradients – Measurement of Displacement Gradient Tensor – Finite Strain – Elasticity – Dislocation in Elastic Half space Model of the Earthquake Cycle – Stress and Strain from a Screw Dislocation  Plates – Navier Stokes Equation – Growth and Decay of Boundary undulations – Flow in Porous Media.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4500</strong></td>
<td><strong>Course Title: </strong>Numerical Methods for Partial            Differential Equations</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Elective</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong>MAT 3370. MAT 4360</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Finite Differences: Elliptic Problems – Parabolic Problems – 2D Problems – Solution Methods –   Iterative Methods – Multigrid Methods – Hyperbolic Problems – Finite Volumes: Linear Problems – Conservation Laws.Nonlinear Problems. Finite Elements: Variational Formulation – General Elliptic Problems – Overview –Parabolic Problems – Eigenvalue Problems. Integral Equations: Collocation and Galerkin Methods – Fast Solvers.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4520</strong></td>
<td><strong>Course Title: </strong> Multivariable Calculus</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Selective </td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 3320, MAT 3330</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Review of Vector Spaces – Functional – The Geodesics Problems – Brachistochrone – Linear Functional – Properties of Functional – Local Maximum – Local Minimum – Extremum Value – Extremal with Corners – Euler’s Necessary Condition – Constant End Points Problems – Minimal Time Curve Problem – Functional of Several Variables – Canonical Euler – Lagrange Equations – Hamilton’s Principle – Functional of Higher Derivatives – Euler–  Poisson Differential Equation – Functional with Multiple integrals – Minimal Surface Plateau’s Problem and Applications – Schrödinger’s Equations – Inverse Problem – Moving End Points Problems – Transversality Conditions – Hamilton–  Jacobi Equation – Extremals With Corners – Reflection of Extremals – Refraction of Extremals – Corners Conditions – Necessary and Sufficient Conditions of Extremals – Legendre Condition – Jacobi Conditions – Weierstrass Condition – Optimal Control – Optimality Principle – Bellman’s Equation – Maximum Principle and Its Applications.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4530</strong></td>
<td><strong>Course Title: </strong>Optimization</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Elective</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 2250, MAT 3320</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Linear Optimization – Introduction – The Geometry of Linear Optimization – The Simplex Method – Duality Theory I – Duality Theory II – Sensitivity Analysis – Robust Optimization – Large Scale Optimization – Network Flows – Network Optimization – Introduction and Applications – Network Optimization – The Network Simplex Algorithm – Discrete Optimization – Exact Methods for IP – Lagrangian Methods – Heuristic Methods – Dynamic Optimization – Dynamic Programming – Nonlinear Optimization – Applications of Nonlinear Optimization – Optimality Conditions and Gradient Methods for Unconstrained Optimization – Line Searches and Newton's Method – The Conjugate Gradient Algorithm Optimality Conditions for Constrained Optimization – The Affine Scaling Algorithm – Barrier Interior Point Algorithms – Semidefinite Optimization</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4540</strong></td>
<td><strong>Course Title: </strong>Computational Geometry</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: Elective</strong></td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 2250, MAT 3330, MAT 3370</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Classification of Geometric Modeling Forms – Differential Geometry of Curves – Differential Geometry of Surfaces – Introduction to Spline Curves – B– splines (Uniform and Non– uniform) – Spline Surfaces – Physically– Based Deformable Surfaces – Fairing – Generalized Cylinders – Blending Surfaces – Surface Intersections – Nonlinear Solvers – Interval Methods – Robustness – Offset Curves and Surfaces – Advanced Topics in Differential Geometry (Geodesics – Developable Surfaces – Umbilics – Parabolic Line – Ridge Line – Sub– Parabolic Line) – Localization  – Discrete Differential Geometry.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4550</strong></td>
<td><strong>Course Title: </strong>Wavelets and Modern Signal Processing</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:</strong> Elective</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong>MAT 4470</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">The Continuous Fourier Transform – The Discrete Fourier Transform – FFT –  Time Frequency Analysis –Short time Fourier transform – The Wavelet Transform –The Continuous Wavelet Transform – Discrete Wavelet Transforms – Orthogonal Basis of Wavelets – Statistical Estimation – Denoising by Linear Filtering – Inverse Problems – Approximation Theory: Linear/Nonlinear Approximation and Applications to Data Compression. – Wavelets and Algorithms– Fast Wavelet Transforms – Avelet Packets – Cosine Packets – Basis Pursuit – Data Compression – Nonlinear Estimation – Topics in Stochastic Processes– Topics in Numerical Analysis – Multigrids and Fast Solvers.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4560</strong></td>
<td><strong>Course Title: </strong>Rigid Body Dynamics</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:</strong> Elective</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT <span dir="RTL">2</span>290, MAT 3330</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">CurviLinear Motion – Cartesian Coordinates – Equations of Motion in Cartesian Coordinates – Intrinsic Coordinates – Other Coordinate Systems – Application Examples – Work and Energy – Conservative Forces – Potential Energy – Linear Impulse and Momentum – Angular Impulse and Momentum – Relative Motion – Translating Axes – Relative Motion Rotating/Translating Axes – Newton's Second Law for Non–  Inertial Observers – Inertial Forces – Newtonian Relativity – Gravitational Attraction – The Earth as a Non–  Inertial – Reference Frame – 2D Rigid Body Kinematics – Conservation Laws for Systems of Particles. 2D Rigid Body Dynamics: Equations of Motion – Work and Energy – Impulse and Momentum – Pendulums. 3D Rigid Body Kinematics.   3D Rigid Body Dynamics: Inertia Tensor – Equations of Motion – Gyroscopic Motion – Torque–  Free Motion – Spin Stabilization. Variable Mass Systems: The Rocket Equation – Central Force Motion – Keppler's Laws – Orbits – Orbit Transfer.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT <span dir="RTL">3</span>240</strong></td>
<td><strong>Course Title: Actuarial mathematics-II</strong></td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:</strong> Elective</td>
</tr>
<tr>
<td><strong>Prerequisites:   </strong>MAT 2321</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Review of financial models - portfolio selection <span dir="RTL">- </span>taxation - Monte-Carlo simulation and option pricing - measurement and assessment of financial performance - risk management - financial analysis and planning - Finite Difference methods for partial differential equations in finance - Time series analysis and parameter estimation - Applications.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4620</strong></td>
<td><strong>Course Title: </strong>Ethics of Mathematicians</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>1(1,0,0)</td>
<td><strong>Level:  </strong>Eigth</td>
</tr>
<tr>
<td><strong>Prerequisites:   </strong>MAT 3460</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Concept of Ethics in Islam – Manners of Mathematicians  -  Difference between Mathematical Ethics and Manners – Ethics and General Welfare – Ethics in General jobs – Duties in General job -  Manners of the Mathematical  Employee – Illegal Manners of the Mathematical  Employee – Deviation of Authority or job – Bribery – Gifts and Tips -  Favoritism – Embezzlement – Forgery – Using the Authority or job.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 4820</strong></td>
<td><strong>Course Title: </strong>Graduation Project</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(2,1,0)</td>
<td><strong>Level:  </strong>Eigth</td>
</tr>
<tr>
<td><strong>Prerequisites:   </strong>MAT 4430</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">As a partial fulfillment for the award of degree of Bachelor of Science in Mathematics, students are required to complete a graduation project during the course of study. At the beginning of the last semester of the program the student will have to select a topic for the project in consultation with the project supervisor allotted to them from the department. The student will have to do a detailed study of the selected topic under the guidance of the supervisor and submit a report by the end of the semester. The project report will be examined by an examiner appointed by the Head of the Department and proper grade will be awarded for the project.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 1050</strong></td>
<td><strong>Course Title: </strong>Differential Calculus</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>First</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong></td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Real numbers, polynomials , Functions, Limits and Continuity: Algebraic Functions – Exponential Functions – Logarithmic Functions – Trigonometric Functions – Limits – Continuity. Derivatives: Techniques of Differentiation – Derivatives of Algebraic Functions – Derivatives of Exponential Functions – Derivatives of Logarithmic Functions – Derivatives of Trigonometric Functions – Equations of the Tangent and Normal – The Chain Rule – Inverse Trigonometric Functions – Hyperbolic Function and Inverse Hyperbolic Functions – Inverse Trigonometric Functions – Derivatives of Inverse Trigonometric Functions – Derivatives of Hyperbolic Functions – Inverse Hyperbolic Functions – Derivatives of Inverse Hyperbolic Functions- Calculation of the nth  Derivatives – Differentiation of a composite Functions – Differentiation of Implicit Functions Applications to Calculus: Function graph – Rolle’s Theorem- mean value theorem - Differentials L'Hospital Theorem -maxima and minim- Related Rates -horizontal and vertical asymptotes.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 1060</strong></td>
<td><strong>Course Title: </strong>Integral Calculus</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Second</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong></td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Integration:  Indefinite Integrals – Techniques of Integration: Trigonometric Integrals – Integration by Inverse Substitution – Completing the Square – Partial Fractions – Integration by Parts – Reduction Formulas –  Definite Integrals – Arc length – Surface Area- Areas between Curves -Volumes of Revolution– Numerical Integration - Parametric Equations –– Polar Coordinates – Area in Polar Coordinates - Indeterminate Forms – Improper Integrals.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 2230</strong></td>
<td><strong>Course Title: </strong>Algebra and Analytic Geometry  for Physics and Statistics Students</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Third</td>
</tr>
<tr>
<td><strong>Prerequisites:  </strong>MAT 10<span dir="RTL">5</span>0</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Analytic Geometry: General theory of second order curves – Simplifying the general second order Equation by Translation and Rotation – Intersection of a straight line and a curve – tangents – systems of coordinates – The plane and the straight line in space – second order surfaces – Conic sections in plane. 2- Linear Algebra:Matrix Definition – Matrix operations – Symmetric Matrices – Transpose and Inverse of a Matrix – Hermitian Matrices.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: </strong>MAT 3320</td>
<td><strong>Course Title:</strong>, Multivariable Calculus</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level:  </strong>Fourth</td>
</tr>
<tr>
<td><strong>Prerequisites:  </strong>MAT 1060</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Coordinate Systems – Multivariable Functions – Partial Derivatives - Critical Points of Multivariable Functions - Maxima and Minima of the Functions of Two Variables –SP -  Lagrange Multipliers – Double Integrals in Rectangular  Coordinates – Double Integrals in Polar Coordinates –Triple Integrals in Rectangular and Cylindrical Coordinates – Spherical Coordinates – Mass Center _ Moment of Inertia - Gradient Fields and Path Independence – Divergence and Curl.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 3410</strong></td>
<td><strong>Course Title: </strong>Differential Equations for Physics and ChemistryStudents</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Fifth</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong>MAT 1060</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">First order Equations: Nonlinear separable – homogeneous – exact Equation – Linear Bernoulli’s Equation – direction fields. Second order Linear Equations with constant coefficients – homogeneous case – inhomogeneous Equations via method of undetermined coefficients – inhomogeneous Equations via method of variation of parameters – Laplace transform – Introduction to Boundary Value Problems: Eigenvalues – EigenFunctions – Orthogonality of EigenFunctions – Sturm Liouville Problem - Types of PDEs – Separation of Variables – The Heat Equation – The Wave Equation.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 1420</strong></td>
<td><strong>Course Title: </strong>Mathematics<span dir="RTL">-</span>I for Students of BA</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>First</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong></td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Properties of Real Numbers – Fractions – Solutions to Algebraic Equations and Inequalities – Quadratic Equations – Functions and their Graphs – Trigonometric Functions – Matrices and Systems of Algebraic Equations.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 1430</strong></td>
<td><strong>Course Title: </strong>Mathematics- II for Students of BA</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Second</td>
</tr>
<tr>
<td><strong>Prerequisites: </strong>MAT 1420</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Limits – Continuity – Asymptotic Lines – Derivatives – Implicit Differentiaions – Applications to Calculus – Mean Value Theorem – Rolle's Theorem – L'Hospital rule – Maxima and Minima – Points of Inflection – Curvature – Function  Graph.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 1070</strong></td>
<td><strong>Course Title: </strong>Algebra & Analytic Geometry</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Third</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 1050</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Vectors in Two and Three Dimensions - Scalar and Vector Products - Equations of Lines and Planes in Space -  Surfaces - Cylindrical and Spherical Coordinates - Vector valued Functions - Limits and Continuity - Derivatives and Integrals. Motion of a particle in space - Tangential and Normal components of Acceleration - Functions in two or three variables – Lmits – Continuity - Partial Derivatives – Differentials - Chain Rule - Directional Derivatives - Tangent Planes and Normal Lines to Surfaces - Extrema of Functions of Several Variables - Lagrange Multipliers - Systems of Linear Equations – Matrices – Determinants - Inverse of a Matrix - Cramer’s Rule.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 2030</strong></td>
<td><strong>Course Title: </strong>Differential and Integral Calculus</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Fourth </td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 1060, MAT 1070</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Infinite Series - Convergence and Divergence of Infinite Series - Integral Test - Ratio Test, Root Test and Comparison Test.  Conditional Convergence and Absolute Convergence - Alternating Series Test - Power Series - Taylor and Maclaurin series - Double Integral and its Applications to Area, Volume, Moments and Center of Mass - Double Integrals in Polar Coordinates - Triple Integral in Rectangular, Cylindrical and Spherical Coordinates and Applications to Volume, Moment and Center of Mass - Vector Fields - Line Integrals - Surface Integrals - Green’s Theorem - The Divergence Theorem - Stoke’s Theorem..</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 2040</strong></td>
<td><strong>Course Title: </strong>Differential Equations</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Fifth</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 2030</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Introduction to Differential Equations - Equations with separable variables - Homogeneous Equations - Exact Equation - The Linear Equation of First Order - Linear Equation of Second Order - Direct Deduction - Comparison Theorems - Linear Equations with Constant Coefficients - Inhomogeneous case - Methods of undetermined Coefficients and Variations - Variation of Parameters - Systems of Differential Equations - Odd & Even Fourier Series - Fourier Integral.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 2440</strong></td>
<td><strong>Course Title: </strong>Linear Algebra</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Fourth</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 1060, MAT 1070</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Column and Row Vectors - Product of Vectors - Matrices and their combination with vectors - Addition and Multiplication of Matrices.  Solution of Linear Equations - Inverse of Square Matrix - Permutation Matrices. Systems of Equations and inequalities - Matrix Algebra – Determinants - Linear Dependence and Linear Independence - Properties of Matrices - Adjoint Matrix – Matrix Inverse - Matrix Functions of  Single Variables - Solution of Systems of Linear Equations - Solution of Linear systems by elimination -  Rank of Matrices - Eignvalues and Eignvectors – Introduction - Properties of Eignvalues and Eignvectors – Applications - Diagonalizable Matrices - Block Diagonal and Jordan Forms - Review and Miscellaneous Exercises.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 2540</strong></td>
<td><strong>Course Title: </strong>Numerical Methods</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong>Fifth</td>
</tr>
<tr>
<td><strong>Prerequisites:</strong> MAT 1070</td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Linear and Quadratic Equations - Functions of a Single Variable - Solution of Systems of Linear Equations - Solution of Linear Systems by Elimination - Elementary Introduction to Linear Programming - Convex Sets - Maxima and Minima of Linear Functions  - Problems of Maximizing or Minimizing a Linear Function to Linear Contraints - Linear Programming Problems - Numerical Solution of Differential Equations - Mathematical Preliminaries - Simple Difference Equations - Euler Method - Runge-Kutta Methods - Systems of Linear Equations – Introduction - Properties of Matrices - Diagonal and Triangular Matrices - Numerical Solution of Linear systems - The Pivoting Strategy - Introduction, Properties and the Numerical Methods.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 2220</strong></td>
<td><strong>Course Title: </strong>Linear Algebra for  Computer Students</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong></td>
</tr>
<tr>
<td><strong>Prerequisites:</strong></td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Matrix Definition – Matrix Operations – Symmetric Matrices – Transpose and Inverse of a Matrix – Hermitian Matrices – Markov Matrices – Factorization – Positive Definite Matrix – Row Operations – Row Reduced Echelon Form – Linear system of Equations – Solving Equation of the form <img alt height="19" src="file:///C:/Users/user/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" style="border-style: none; border-color: rgb(204, 204, 204);" width="47" loading="lazy"> and<img alt height="19" src="file:///C:/Users/user/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" style="border-style: none; border-color: rgb(204, 204, 204);" width="47" loading="lazy">.<br>
<br>
<br>
<br>
 Vector Spaces and Subspaces – Basis and Dimension – Orthogonality – Similar Matrices – Singular Value Decomposition – Least Squares Approximations – Determinants – Properties of Determinants – Applications of Determinants – Cramer’s Rule – Gauss Elimination Rule – Gauss Jordan Elimination – Eigenvalues and Eigenvectors – Diagonalization – Linear Transformation – Matrices with MATLAB.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 2350</strong></td>
<td><strong>Course Title: </strong>Calculus for  Computer Students</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong></td>
</tr>
<tr>
<td><strong>Prerequisites:</strong></td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Differentiation: Graphing – Derivatives – Slope – Velocity – Rate of Change – Limits – Continuity – Trigonometric Limits – Derivatives of Products – Quotients – Derivatives of Trigonometric Functions – Chain Rule – Higher Derivatives – Implicit Differentiation – Inverses- Exponential and Log – Logarithmic Differentiation – Hyperbolic Functions.
<p>Applications of Differentiation:  Linear and Quadratic Approximations – Function Graph – Maxima and Minima – Related Rates – Newton's Method and Other Applications – Mean Value Theorem</p>
<p>Integration:  Indefinite Integrals – Techniques of Integration: Trigonometric Integrals – Integration by Inverse Substitution – Completing the Square – Partial Fractions – Integration by Parts – Reduction Formulas – Definite Integrals – Areas between Curves – Volumes by Slicing - Volumes by Disks – Work – Average Value – Numerical Integration - Parametric Equations – Arc length – Surface Area – Polar Coordinates – Area in Polar Coordinates - Indeterminate Forms – L'Hospital's Rule – Improper Integrals – Infinite Series – Convergence Tests – Taylor Series.</p>
</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 3310</strong></td>
<td><strong>Course Title: </strong>Differential Equations for Computer Students</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong></td>
</tr>
<tr>
<td><strong>Prerequisites:</strong></td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">First order Equations: Nonlinear Separable – Homogeneous – Exact Equation – Linear Bernoulli’s Equation – Direction fields - Second Order Linear Equations with Constant Coefficients – Homogeneous Case – Inhomogeneous Equations via Method of Undetermined Coefficients – Inhomogeneous Equations via Method of Variation of Parameters  – Remarks on Higher Order Equations – Linear Independence  and the Wronskian – Applications to Forced Oscillation Problems – Effect of Resonances – Laplace Transform – Application to Constant Coefficient Linear Equations -   Fourier Series.</td>
</tr>
</tbody>
</table>
<p style="font-size: 13.0080003738403px; line-height: 20.0063037872314px;"> </p>
<table border="1" cellpadding="1" cellspacing="1" style="width: 710px; line-height: 24px !important;" width="200">
<tbody>
<tr>
<td><strong>Course Code: MAT 1090</strong></td>
<td><strong>Course Title: </strong>Mathematics for Pharmacy</td>
</tr>
<tr>
<td><strong>Credit Hours: </strong>3(3,1,0)</td>
<td><strong>Level: </strong></td>
</tr>
<tr>
<td><strong>Prerequisites:</strong></td>
<td><strong>Co-requisites</strong></td>
</tr>
<tr>
<td colspan="2">Real numbers- solutions of equlities and inequalties-Roots of quadratic equations-Trigonemitric functions– Limits – Continuity – Derivatives – Rule of differentiation – Partial Derivatives –Integration – Techniques of Integration: Partial Fractions – Integration by Parts –Introduction to differential equations.<br>
 </td>
</tr>
</tbody>
</table>
<p> </p>

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