BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT4064 | Partial Differential Equations I | Fall | 3 | 0 | 3 | 6 |
Basic information
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor TOFIGH ALLAHVIRANLOO |
| Recommended Optional Program Components: | None |
| 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. |
Learning Outcomes
|
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 |
Course Content
| 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. |
Weekly Detailed Course Contents
| 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. |
Sources
| Course Notes / Textbooks: | 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: |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Homework Assignments | 3 | % 10 |
| Midterms | 1 | % 40 |
| Final | 1 | % 50 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 14 | 2 | 28 |
| Homework Assignments | 3 | 10 | 30 |
| Midterms | 1 | 10 | 10 |
| Final | 1 | 15 | 15 |
| Total Workload | 125 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |