Digital Methods

Syllabus [Numerical Methods]

[2nd Semester , 2018/2019]

Instructor Information

Instructor

Email

Office Location & Hours

Ismail Hamdan

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.

Language(s) of Instruction:         English                   Textbook(s) Language(s) Arabic, English

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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