MM401 : Partial Differential Equations

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

03

Prerequisite

MM215MM311

Overview

This course introduces students to the concept of partial differential equations, linear and nonlinear first order partial differential equations, and methods for their solution. It also deals with the Pfaff differential equation and its solutions, partial differential equations of the second order, and various methods for its solution. The course focuses on solving partial differential equations and determining the appropriate method for each case.

Intended learning outcomes

By the end of the course, the student should be able to:

1. Learn about the origin of the partial differential equation by deleting the optional functions and constants.

2. List the different ways to solve the linear partial differential equation.

3. Compare the different ways to solve the Pfaff equation.

4. Distinguish between the special solution and the homogeneous solution of the partial differential equation

5. Explain the method of reducing the partial differential equation to the legal form.

6. Mention the basic steps of the method of separating variables.

7. Explain Fourier series.

8. Explain the origin of the partial differential equation.

9. Compare the different methods for solving the linear partial differential equation.

10. Deduce the methods of solving Pfaff's equation

11. Discuss the solution of partial differential equations of the first order.

12. Classify the type of partial differential equation of the second order and methods of reducing it to the legal form

13. Explore the solution of boundary values problems using the separation of variables method.

14. Justify the use of Fourier series in solving the partial differential equation.

15. Find a partial differential equation from an ordinary equation.

16. Use the appropriate method to solve the linear partial differential equation

17. Use the appropriate method to solve Pfaff's equation

18. There is the special solution and the homogeneous solution for the partial differential equation of the second order, students should know this.

19. Solve the partial differential equation of the second order.

20. Used Fourier series to solve the partial differential equation

21. There is a solution to the boundary values problems by separating the variables, the students should know this.

Teaching and learning methods

1. Theoretical lectures

2. Discussion and dialogue

3. Brainstorm

4. Using mathematical proof methods

5. Exercises and multi-idea problem solving.

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 left to the course instructor.

3. Written final exam (essay + objective) = 60 marks.

Course content:

Week	Scientific Subject	Hours	Lecture	Exercises
1	The origin of the partial differential equation by deleting the optional functions and constants	3	ü	ü
2	Linear differential equation and ways to solve it	3	ü	ü
3 - 4	Pfaff equation and ways to solve it	6	ü	ü
5	First Midterm Exam (2 Hours)
5 - 6	Solve the linear differential equation of the first order	4	ü	ü
7 - 8	Partial differential equation of the second order and methods of finding the special and homogeneous solution	6	ü	ü
9 - 10	Partial differential equations of the second order and their reduction to the legal form	4	ü	ü
10	Second Midterm Exam (2 Hours(
11 - 12	Method of separation of variables to find the solution to the initial value of the second order	6	ü	ü
13 - 14	Solutions using Fourier series	6	ü	ü
15 - 16	Final Exam
	Total	56

References

Reference	Publisher	Release	Author
Partial differential equations	Publications Management	1998	Dr.. Zawam Dallah

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