COURSE SYLLABUS
FACULY OF SCIENCE
MATHEMATICS DEPARTMENT
COURSE NAME: Numerical treatment of ordinary differential equations
COURSE NUMBER: M A T H 6 2 2
SEMESTER/YEAR: 1
stsemester 2020
DATE: 1/9/2020
Instructor Information
Name of the instructor: Dr. Rania Alharbey
Office location: Room:156 c Building: 7
Office hours:
Sun Mon Tue Wed Thu
Time
Contact number(s): 63635
E-mail address(s): [email protected]
Course Information
Course name: Differential Equations (1) Course number: 622
Course meeting times:
Sun Mon Tue Wed Thu
Time 11-1 11-1
Place: Room:19C Building:7
Course website address: http://rallehabi.kau.edu.sa Course prerequisites and requirements:
Course name Course number
Numerical analysis1 423
Contents: • Initial value problem for ordinary differential equations 1. Euler’s method
2. Higher order Taylor methods 3. Runge-Kutta methods
• Higher order equations and systems of differential equations
• Multistep methods 1. Runge-Kutta
2. Multi step and prediction and corrector
• Numerical analysis including stability
• Convergence
• Error analysis
• Boundary value problem
• Integral equations
Important Dates: Project1 Lab exam Final exam
Homework discussion
Course Objectives
By the end of the course the student will be able to:
• To provide the students with the required computational knowledge to study and evaluate the solution of the differential equations (initial and boundary value problem-IVP and BVP).
• Knowledge of the integral equation. The relation between Mathematics and other fields of science .
• Solve important classes of ordinary differential equations of the first ,second and higher orders
> Model some real life problems using differential equations and interpret the solution
> Apply numerical methods to solve IVP, BVP
> Use mathematical software to solve and plot differential equations numerically
> Use reasoning and critical thinking to solve problems
.
Learning Resources
Textbooks:
Main References:
[1] Numerical Analysis, Richard L. Burden and J. Douglas Faires, Brooks/Cole Thomson Learning (8th or 9th Eds.).
[2] A first Course in Integral Equations, Abdul-Majid Wazwaz, World Scientific, USA.
Lab references
[3] Dynamic Systems with Applications using Maple, Stephen Lynch, Birkhäuser Boston 2001.
[4] Differential Equations with Maple, Kevin R. Coombes, Brian R. Hunt, Ronald L.
Lipsman, John E. Osborn and Garrett J. Stuck, University of Maryland at College Park, John Wiley & Sons, Inc
Further Reading:
[1] E. Hairer, S.P. Norsett, and G. Wanner, Solving Ordinary Differential Equa- tions I: Nonstiff Problems. Springer-Verlag, Berlin, 1987.
[2] P. Henrici, Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York, 1962.
[3] K.W. Morton, Numerical Solution of Ordinary Differential Equations. Oxford University Computing Laboratory, 1987.
Course Requirements and Grading
Student assessment:
(A clear rationale and policy on grading)
HW 20%
Seminar 5%
Lab 20%
Project 10%
Mid Exam 15%
Final 30%
No makeup tests will be given. If a student misses a test with my approval, the score on the final exam will be used to replace the missing test score. In the event that a student misses a test without my approval, a zero will be assigned for that test score. Approval must be obtained in advance if at all possible
Expectations from students:
(Attitudes, involvement, behaviors, skills, and ethics) I aim to treat all student with respect and fairness. Since I expect the same consideration, please observe the following courtesies:
Attendance at each scheduled class meeting is expected. A DN will be given if the student misses 20% of the classes
All assignments must be handed in on time. No late assignment will be allowed
Arrive for class on time. Late class arrivals are disruptive and inconsiderate; moreover, they may be regarded as absences. Students who frequently arrive late may be asked not to return to class.
Silence cell phones. Use of cell phones in the class room will not be permitted; you should not bring one into the classroom unless the ringer is turned OFF. Students in violation of this policy may be asked to leave class.
Math 622 Syllabus
Textbook: (1) Numerical Analysis, Richard L. Burden and J. Douglas Faires, Brooks/Cole Thomson Learning (8th or 9th Eds.).(Chs5 &11) (2) A first Course in Integral Equations, Abdul-Majid Wazwaz, World Scientific, USA (Ch2 &3).
Chapter Title Section
Ch5: Initial value problems for ordinary differential equations
5.1 Elementary Theory of Initial-Value Problems
5.2 Euler’s Method
5.3 Higher-Order Taylor Methods
5.4 Runge-Kutta Methods
5.6 multistep methods
5.9 Higher-Order Equations and Systems of Differential Equations
5.10 Stability
Ch11: Boundary-value problems for ordinary differential equations
11.1 The linear shooting method 11.3 Finite-Difference methods for linear problems
Chapter Title (book2) Section
Ch2: Introductory concepts of integral equations
2.1 Classification of integral equations
2.2 Classification of integro-DE
2.3 linearity and homogeneity
Chapter Title Section
Ch3: Voltera Integral equations
3.1 Introduction
3.2 Voltera integral equations of the second kind
3.3 Voltera integral equations of the first kind
