|
PARTIAL DIFFERENTIAL EQUATIONS
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| Course Name |
Code |
Regular Semester |
ECTS Credits |
Credits |
Lecture |
3
|
| Application |
-
|
|
Partial Differential Equations
|
0252072
|
4
|
5
|
3
|
Laboratory (Hour/Week) |
-
|
|
| Course Language |
Turkish
|
| Compulsory or Elective |
Compulsory
|
| Equipment |
Board, Overhead Projector, Projector, Notebook, CD
|
| Instructor |
Department of Mathematics
|
| Course Contents |
Definition of partial differantial equation (PDE)/ Cauchy Problems/ Solution methods of some special type of PDEs/ Solution of first order linear and non-linear PDEs/ Transformation of second order linear PDEs in to canonic form. Initial and boundary value problems for second order linear PDEs. Wave equation/ Heat equation/ Laplace equation/ Fourier method/ Harmonic functions/ Green functions
|
| Course Objectives |
We can use the PDEs to explain and to solve the problems that appear in mathematical modelling of a lot of physical , chemical and biological formations. Our aims are to determine some PDEs , directly or indirectly which we can face with, in various fields , to give fundamental solution method and to inform about its mathematical theory
|
Course Outcomes
(The knowledge and the skills that the student will gain at the end of the course) |
-
To improve mathematical observation and thought
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Giving informations about some engineering systems (wave , heat , equation etc. ) whose modellings are done by using PDEs ( to understand plenty many problems in nature)
|
| Textbook |
Lecture Notes
|
| Additional References |
-
Hellewing, G. “Partial differential Equations” Blaisdell, New York, 1964
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I.N. Sneddon, Elements of Partial Differential equations (McGraw – Hill)
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“Partial Differantial Equations” , W.E. Williams, Clarendon Press, Oxford, 1980
|
|
| Prerequisite Courses |
-
|
| Prerequisite Subjects |
0251012 Analysis 2 – 0252011 Analysis 3 – 0252081 Differantial Equations 1 subjects
|
| Homework/Project |
-
|
| Laboratory |
-
|
| Computer Applications |
-
|
| Additional Practices |
-
|
|
| Course Evaluation Criteria |
|
Number |
Effective Proportion % |
| Midterm Exams |
2
|
60
|
| Quiz |
-
|
-
|
| Homework |
-
|
-
|
| Term Projects |
-
|
-
|
| Term Papers |
-
|
-
|
| Laboratory |
-
|
-
|
| Other |
-
|
-
|
| Final Exam |
1
|
40
|
|
| Division of Course Credit (%) |
Basic Sciences |
-
% |
| Basic Engineering and Departmental Core Courses |
-
% |
| Departmental Core Courses |
100
% |
| Social Sciences |
-
% |
|
|
| WEEKLY COURSE PLAN |
| Week |
Subject |
| 1 |
Definition of partial differantial equation (PDE)
|
| 2 |
Cauchy Problems. Solution methods of some special type of PDEs
|
| 3 |
Solution of first order linear and non-linear PDEs
|
| 4 |
Solution of first order linear and non-linear PDEs
|
| 5 |
Transformation of second order linear PDEs in to canonic form
|
| 6 |
Transformation of second order linear PDEs in to canonic form
|
| 7 |
Initial and boundary value problems for second order linear PDEs
|
| 8 |
1st Midterm exam; Polar Coordinates
|
| 9 |
Initial and boundary value problems for second order linear PDEs
|
| 10 |
Wave equation. Heat equation
|
| 11 |
Laplace equation
|
| 12 |
Fourier method
|
| 13 |
2nd Midterm exam; Areas of Surfaces of Revolution
|
| 14 |
Harmonic functions
|
| 15 |
Green functions
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|
|
| Prepared by |
Department of Mathematics
|
Date |
01.01.2007
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