First order equations; linear, quasilinear and nonlinear equations. Classification of second order linear partial differential equations, canonical forms, Cauchy problem. The Cauchy problem for the wave equation. Dirichlet and Neumann problems for the Laplace equation, maximum principle. Heat equation on the strip.
Vertical Tabs
Course Learning Outcomes
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Learning Outcomes |
Program Learning Outcomes |
Teaching Methods |
Assessment Methods |
|
1) Understands the derivation of PDE and modelling |
1,2,3,4 |
1, 2 |
A, B |
|
2) Knows the nonlinear equations, their properties and the solution techniques |
2,3,8 |
1, 2 |
A, B |
|
3) Has a general information on higher order equations and on Cauchy problem |
3,4,6 |
1, 2 |
A, B |
|
4) Knows the properties of wave equation and the solution techniques of initial value problems |
3,4,9 |
1, 2 |
A, B |
|
5) Knows the properties of Laplace equation and the solution techniques of boundary value problems |
3,4,7,9 |
1, 2 |
A, B |
|
6) Knows the properties of heat equation and the solution techniques of initial value problems |
3,4,7,9 |
1, 2 |
A, B |
Course Flow
| Week | Topics | Study Materials |
| 1 | Introduction, First-order DE, | Relevant topics in the text book |
| 2 | Introduction, First-order DE, | Relevant topics in the text book |
| 3 | First-order nonlinear DE, Compatible systems Charpit’s method | Relevant topics in the text book |
| 4 | First-order nonlinear DE, Compatible systems Charpit’s method | Relevant topics in the text book |
| 5 | Linear second-order equations; constant coefficient and factorable operators, particular solutions. | Relevant topics in the text book |
| 6 | Linear second-order equations; constant coefficient and factorable operators, particular solutions. | Relevant topics in the text book |
| 7 | Normal forms; hyperbolic, parabolic, elliptic cases; Cauchy problem. | Relevant topics in the text book |
| 8 | Normal forms; hyperbolic, parabolic, elliptic cases; Cauchy problem. | Relevant topics in the text book |
| 9 | Elliptic equations | Relevant topics in the text book |
| 10 | Elliptic equations | Relevant topics in the text book |
| 11 | Hyperbolic equations | Relevant topics in the text book |
| 12 | Hyperbolic equations | Relevant topics in the text book |
| 13 | Parabolic equations | Relevant topics in the text book |
| 14 | Parabolic equations | Relevant topics in the text book |
Recommended Sources
| Textbook |
1. An introduction to PDE and BVP, by Rene Dennemeyer, McGraw Hill.
2. Elements of PDE, by Ian Sneddon, McGraw Hill. |
| Additional Resources |
Material Sharing
| Documents | |
| Assignments | |
| Exams |
Assessment
| ASSESSMENT | ||
| IN-TERM STUDIES | NUMBER | PERCENTAGE |
| Mid-terms | 2 | 100 |
| Quizzes | 0 | 0 |
| Assignments | 0 | 0 |
| Total | 100 | |
| CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE | 40 | |
| CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE | 60 | |
| Total | 100 | |
| COURSE CATEGORY | Expertise/Field Courses |
Course’s Contribution to Program
| No | Program Learning Outcomes | Contribution | ||||
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) | x | ||||
| 2 | Acquiring fundamental knowledge on fundamental research fields in mathematics | x | ||||
| 3 | Ability form and interpret the relations between research topics in mathematics | x | ||||
| 4 | Ability to define, formulate and solve mathematical problems | x | ||||
| 5 | Consciousness of professional ethics and responsibilty | x | ||||
| 6 | Ability to communicate actively | x | ||||
| 7 | Ability of self-development in fields of interest | x | ||||
| 8 | Ability to learn, choose and use necessary information technologies | x | ||||
| 9 | Lifelong education | x | ||||
ECTS
|
ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION |
|||
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Activities |
Quantity |
Duration |
Total |
|
Course Duration (14x Total course hours) |
14 |
4 |
56 |
|
Hours for off-the-classroom study (Pre-study, practice) |
14 |
4 |
56 |
|
Mid-terms (Including self study) |
2 |
9 |
18 |
|
Quizzes |
0 |
|
00 |
|
Assignments |
- |
- |
- |
|
Final examination (Including self study) |
1 |
20 |
20 |
|
Total Work Load |
|
|
150 |
|
Total Work Load / 25 (h) |
|
|
6 |
|
ECTS Credit of the Course |
|
|
6 |