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Course Outline

The Differential Equations course (Math 484) at MTU focuses on partial differential equations (PDE), including Fourier series and transforms, and analytical methods for solving first and second order PDEs. Students will learn to apply these concepts to model physical problems and solve various equations, with assessments including mid-exams, assignments, and a final exam. Attendance and adherence to university regulations are mandatory for successful course completion.

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Assaye Eshetu
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33 views1 page

Course Outline

The Differential Equations course (Math 484) at MTU focuses on partial differential equations (PDE), including Fourier series and transforms, and analytical methods for solving first and second order PDEs. Students will learn to apply these concepts to model physical problems and solve various equations, with assessments including mid-exams, assignments, and a final exam. Attendance and adherence to university regulations are mandatory for successful course completion.

Uploaded by

Assaye Eshetu
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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University MTU College NCS Department of Mathematics

Module Name Differential Equations Module Code Math 484


Course cr.h/EtCTS 3/5
Pre-requisites Ordinary differential equation
Course Description
This course discusses basic concepts of partial differential equations (PDE), some techniques of solutions of first order PDE, Fourier
series, second order PDE and analytical methods of solutions.
Course Objectives
 On completion of the course students will be able to:  apply Fourier and Laplace transforms for solving
 define Fourier series of periodic functions, PDEs,
 expand periodic functions in terms of sine and cosine,  solve one dimensional heat flow and wave equations,
 compute Fourier series,  solve Laplace equations,
 determine the order and classification of PDEs  understand generalized functions,
 solve PDEs,  Apply generalized functions.
 model some physical problems using PDEs,
1. Fourier series and orthogonal functions
1.1 Orthogonal functions
1.2 Fourier series
1.2.1 Fourier series of functions with period 2
1.2.2 Fourier series of functions with arbitrary period
1.2.3 Fourier series of odd and even functions
1.3 Complex form of Fourier series
1.4 Fourier integrals
2: Fourier transform
4.1 Fourier transform and its inverse
4.2 Properties of Fourier transform
4.3 Fourier sine and cosine transforms
4.4 Convolution
3: Introduction to partial differential equations
2.1 Definitions and basic concepts
2.2 Classification of PDEs
2.3 Definition of initial/boundary value problems
2.4 Well-posedness of a problem
2.5 Modeling some physical problems using PDEs
4: First order partial differential equations
3.1 Solution of first order PDEs with constant coefficients
3.2 Solution of a first order PDEs with variable coefficients
3.3 Charpit’s method
3.4 Application of a first order PDEs to fluid flow problems
5: Second order partial differential equations
5.1. Definition and classification of second order PDEs
5.2 Method of separation of variables
5.3 One dimensional heat and their solutions by using methods of Fourier transform
5.3 One dimensional heat and their solutions by using methods of Fourier transform
5.6 Fourier and Laplace transforms, applied to other PDE
Mode of Assessment
1. Mid Exam …………………………………........30%
2. Assignment (1) ……………….……………..30%
3. Final Exam …………………………………...40%
Total…………………………………………...100%
Course policy
A student has to:
- Attend at least 85% of the classes.
- Take all continuous assessments.
- Take final examination.

Respect all rules & regulations of the university


Textbook: I.N. Sneddon, Elements of partial differential equations
References:
R. C. Mcowen, Partial differential equations, methods and applications, Pearson education, INC, 2003
H. M. Lieberstein, Theory of partial differential equations, Academic press, 1972
R. B. Gunther & J. W. Lee, Partial differential equations of physics, Dover, 1996

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