### Digital Methods

Syllabus [Numerical Methods]

[2nd Semester , 2018/2019]

# Instructor Information

 Instructor Email Office Location & Hours Ismailhamdan56@gmail.com [AL-Layeek School, 13:00-15:00, Saturday]

# General Information

## Description

The course includes: Numerical Methods in general, Numerical Methods in Linear Algebra, Numerical Methods for Differential Equations.

## Expectations and Goals

Enabling students to:

1-    Understanding the approximate solutions for equations.

2-    Understanding the computing values of a polynomials. Horner’s Scheme.

3-    Finding the numerical solution of linear system, Jacobi’s and Gauss – Seidel Method.

4-    Finding the numerical solution of ODEs.

# ourse Materials

## Required Text

-         Numerical Methods ,Soft Copy, P.KANDASAMY, K.THILAGAVATHY, K.GUNAVATHI.

-         Differential Equations with Boundary- Value Problems, Soft Copy, Dennis G.Zill, Michael R.Cullen.

-         الرياضيات الحسابية، ديميدوفيتش ومارون، مطبعة جامعة دمشق 1980.

-         Lectures notes .

# Course Schedule

 The subject Week Introduction: Approximate Numbers, Polynomials 1 Computing the values of a polynomials. Horner’s Scheme. 2 Solution of equation by Iteration: Isolation of roots, Graphical Solution of Equation. 3 Solution of equation by Iteration: Bisection Method, Newton – Raphson Method, Iteration method. 4 Interpolation: Lagrange Interpolating Polynomial 5 Interpolation Formulas by use of Differences 6 Approximate Integration of functions, Trapezoidal Rule. 7 Approximate Integration of functions, Simpson’s General Formula. 8 Direct Methods for Solving Linear System: Gauss and Gauss – Jordan Method. 9 Direct Methods for Solving Linear System: LU – Factorization. 10 Iterative Methods for Solving Linear Systems: Jacobi’s Method 11 Iterative Methods for Solving Linear Systems: Gauss – Seidel Method 12 Numerical Solution of ODEs: Taylor Series Method, Picard’s Method. 13 Numerical Solution of ODEs: Runge – Kutta Methods 14 Solution of PDEs: Laplace Equation, Heat Equation. 15

# Testing Schedule

 test Date Subject Type language % of final grade Quizz 1 16/03/2019 The 1st six topics written English 10 Quizz 2 27/04/2019 The 2nd six topics written English 10 Final exam 25/05/2019 All of topics written English 75

# General notes:

-       Specifying 5% for Activity and participation

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