ÇAĞ UNIVERSITY
FACULTY OF ARTS AND SCIENCES
Learning Outcomes of the
Course
Code
Course Title
Credit
ECTS
MAT 312
Partial Differential Equations
3 (3-0)
7
Prerequisites
None
Language of Instruction
Mode of Delivery
Face to face
English
Type and Level of Course
Compulsory/3.Year/Fall Semester EQF- Level 6
Lecturers
Name(s)
Contacts
Lecture Hours
Office Hours
Course Coordinator Asist. Prof..Dr. Ayfer Kurt
[email protected]
Wed:9-12
Tue:13-16
Others
Thur :13-16
Course Objective
Students will be able to solve the partial differential problems arising in science.
Relationship
Students who have completed the course successfully should
be able to
Prog. Output
Net Effect
5
1
solve linear and quasi-linear equations.
1
4, 5
2
comprehend the significance of characteristics
1, 3
3, 4, 4
3
classify the linear second order equations.
2, 3, 5
5, 5
4
solve the second order Cauchy problem.
3, 5
3, 4
5
find d’Alembert solution of the Cauchy problem.
2, 3
4, 5, 5
6
solve the wave equation on a half line.
1, 2, 3
4, 5, 5
7
solve the heat equation.
1, 2, 3
4, 5
8
prove the maximum principle.
2, 3
4, 5
9
grasp the techniques for finding solutions to Laplace’s equation
2, 3
and Dirichlet and Neumann problems
Course Description: This is an introductory Partial Differential Equations. The focus will be on the analytical
solution techniques for first and second-order linear partial differential equations. Wave equation, diffusion
equation and Laplace equation.
Course Contents:( Weekly Lecture Plan )
Weeks
Topics
Preparation
Teaching Methods
1
Lectures
Introduction
None
2
Lectures
First order equations and characteristics.
Textbook Ch. 1
3
Presentation
The quasi-linear equation.
Textbook Ch.1
4
Lectures
The hyperbolic canonical form
Textbook Ch. 2
5
Lectures
The parabolic canonical form
Textbook Ch. 2
6
Lectures
The elliptic canonical form
Textbook Ch. 2
7
Presentation
The second order Cauchy problem
Textbook Ch. 2
8
Lectures
The wave equation
Textbook Ch. 4
9
Lectures
The nonhomogeneous wave equation
Textbook Ch.4
10
Lectures
The heat equation
Textbook Ch. 5
11
Presentation
The nonhomogeneous heat equation
Textbook Ch. 5
12
Presentation
Dirichlet and Neumann problems.
Textbook Ch. 6
13
Exercises
Review
None
14
Exercises
Review continued
None
REFERENCES
Textbook
Tyn Myint-U , Lokenath Debnath;Linear Partial Differential equations for Scientists
and Engineers, Birkhauser
ISBN-10: 0-8176-4393-1 e-ISBN-10: 0-8176-4560-8
ISBN-13: 978-0-8176-4393-5 e-ISBN-13: 978-0-8176-4560-1
http://sharif.ir/~moosavi/Myint-U_DebnathRelated links
Linear_Partial_Differential_Equations_for_Scientists_and_Engineers.pdf
http://www.nu.edu.sa/userfiles/mqkhirallah/01M%20Differential%20Equations%20%20Beny%20Neta%20%20Partial%20Differential%20Equations%20Lecture%20Notes.pdf
http://www.math.umn.edu/~olver/pd_/contents.pdf
Recommended Reading
Strauss Walter A., Partial Differential Equations-2nd ed., Wiley USA,2008 ISBN-13
978-0470-05456-7
O’ Neil Peter V..; Beginning Partial differential Equations- 2nd ed., Wiley-Interscience
USA, 2008 ISBN-978-0-470-13390-3
Material Sharing
Activities
Midterm Exam
Quizzes
Number
1
ASSESSMENT METHODS
Effect
40%
Notes
Homework
Effect of The Activities
Effect of The Final Exam
Contents
Hours in Classroom
Hours out Classroom
Homeworks
Implementation
Quizzes
Midterm Exam
Final Exam
40%
60%
ECTS TABLE
Number
14
14
1
1
Hours
3
8
Total
42
112
20
30
20
30
204
204/30=6,8
7
Total
Total / 30
ECTS Credit
RECENT PERFORMANCE