| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT4064 | Partial Differential Equations I | Fall | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Must Course |
| Course Level: | Bachelor |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor TOFIGH ALLAHVIRANLOO |
| Course Objectives: | This course concerns with the basic analytical tools of partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. The aim of this course is to analyze fundamental concepts of PDE theory. |
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The students who have succeeded in this course; The students who succeeded in this course; will be able to classify of Partial Differential Equations will be able to anaylze solution by method of separation of variables. will be able to analyze Fourier Series for 2pi periodic functions will be able to anaylze the heat equation, wave equation and their solution by method of seperation of variables. will be able to anaylze the Laplace’s equation in rectangular coordinates and its solution. will be able to analyze the Laplace’s equation in polar and spherical coordinates and their solutions. will be able to analyze maximum principles for Laplace equation |
| In this course basic concepts and classification of partial differential equations will be discussed. The heat, wave and Laplace equation will be given and the solution methods will be taught. |
| Week | Subject | Related Preparation | |
| 1) | Introduction and basic facts about PDE's | ||
| 2) | Classification of PDE’s, First-order linear PDE's | ||
| 3) | Almost Linear and Quasi Linear PDE’s | ||
| 4) | Solution of First order PDE's by Characteristics Methods | ||
| 5) | Cauchy-Kowalewski Theorem | ||
| 6) | The wave equation. Solution by seperation of variables. Existence and Uniqueness of Solutions. | ||
| 7) | Laplace equation | ||
| 8) | Laplace equation in Cyclindrical and Sprecial Coordinates | ||
| 9) | Fundamental solution of Laplace equation. | ||
| 10) | Seperation of Variables method, Boundary value problems | ||
| 11) | Green identities and applications | ||
| 12) | Poisson equation and Poisson formula | ||
| 13) | Dirichlet and Neumann Problems | ||
| 14) | Heat equation, Maximum ve minimum principle. | ||
| Course Notes: | 1-Partial Differential Equations with Fourier Series and Boundary Value Problems” by Nakhle H. Asmar. 2nd Edition, 2005, PearsonPrentice Hall. 2-Partial Differential Equations, L.C. Evans.AMS.1998. 3-Partial Differential Equations, F. John, fourth edition, v1.1982. 4-Partial Differential Equations: An Introduction, W. A. Strauss,1992 |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | 3 | % 10 |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 1 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 50 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 2 | 28 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 3 | 10 | 30 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 1 | 10 | 10 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 15 | 15 |
| Total Workload | 125 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |