Overview
This course introduces students to the
basic concepts of Taylor series, Maclaurin series, the property of convergence,
and linear interpolation. It also deals with the numerical solution of a single
equation, the numerical solution of a system of linear equations.Finally this course aims at developing the student's ability to determine
differential calculus (front differences, central differences), integral
calculus (trapezoidal rule, compound trapezoidal rule), Simpson's rule,
Simpson's compound rule, error analysis.
Intended learning outcomes
By the end of the course, the student
should be able to:
1.Learn how to
solve nonlinear equations in different numerical ways
2- Get
acquainted with the basic concepts, principles, laws and rules of completion
3- Explain
numerical integration
4- Explain the numerical differentiation
5- Distinguish how to determine the amount of
error in a particular issue
6- Discover the differences between different
methods for solving nonlinear equations
7- Discuss the basic laws and rules for completion
8- Demonstrate some properties of numerical
integration
9- Infer numerical differentiation methods
10.Explain the
meaning of the difference between the real value and the approximate value
11- Solve a number of exercises and problems
on numerical methods for solving nonlinear equations
12- Use basic rules for completion
13- Use numerical integration to find out
some difficult integrals
14- The student should apply numerical
differentiation methods to some functions
15- Give justification for the amount
Teaching and learning methods
1- Lectures (bot theoretical and
practical).
2- Discussion and dialogue
3- Brain storming
4- Working papers, case study
5- Presentations
6- Videos and e-learning
7- Use of software and computer applications
such as (MATLAB, Geogebra, Geometer,)
8- Intensifying applications, solving
problems, and linking ideas with reality and life situations
evaluation methods
Methods of assessments
1- A
written exam (essay + objective) = 25 marks, or its assessment is left to the
course instructor
.2- Short tests (written or oral),
demonstration tasks, applications, exercises, and presentation = 15 marks, or
the assessment is left to the course instructor
. 3- Written final exam (essay + objective) =
60 marks
Course Content
|
The Week
|
Scientific subject
|
The number of hours
|
a lecture
|
practical
|
|
1
|
Solving Nonlinear
Equations: The Bisection Method
|
4
|
3
|
1
|
|
2
|
Linear interpolation
methods (wrong location)
|
4
|
3
|
1
|
|
3
|
Fixed point method-
|
4
|
3
|
1
|
|
4
|
Convergence and error
analysis
|
4
|
3
|
1
|
|
5
|
First Midterm ( 2 hours)
|
|
5-6
|
Completion: Newton's
method of advanced differences - divided differences -
|
6
|
4
|
2
|
|
7
|
Lagrangian method -
error estimation.
|
4
|
3
|
1
|
|
8
|
Numerical Integration:
Trapezoidal Method - Simpson Method
|
4
|
3
|
1
|
|
9
|
Richardson's method -
Romborg's integral -
|
4
|
3
|
1
|
|
10
|
Second Midterm ( 2 hours)
|
|
10-11
|
Binary integration
error analysis.
|
6
|
4
|
2
|
|
12-13
|
Numerical
Differentiation: First and second order formulas for the first and second
derivative.
|
8
|
4
|
4
|
|
14
|
Taylor series error
analysis
|
4
|
3
|
1
|
|
15
|
Final Exam
|
|
|
Total
|
56
|
|
|
References:
Numerical Analysis / Authored by: Framsis Shedd,
Translated by: Dr. Muhammad Ali Al Samari
Numerical Analysis / Authored by: Dr. Ali Mohammed Owen
