BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| APPLIED MATHEMATICS (TURKISH, THESIS) | |||||
| Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT5012 | Numerical Solutions to Differential Equations I | Fall Spring |
3 | 0 | 3 | 8 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Basic information
| Language of instruction: | Turkish |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
| Recommended Optional Program Components: | None |
| Course Objectives: | This course focus on numerical techniques for finding solutions to ordinary differential equations by examining the error analysis and efficiencies of the methods. |
Learning Outcomes
|
The students who have succeeded in this course; The students who succeeded in this course; o will be able to understand basic methods for ordinary differential equations. o will be able to solve numerically any given linear or nonlinear ordinary differential equation. o will be able to understand the concepts of consistency, stability, and convergence. o will be able to solve ordinary differential equations by using a computer program (C, C+ , Fortran, Matlab). o will be able to discuss the consistency, convergence and stability for schemes. o will be able to do error analysis. |
Course Content
| This course focuses on the fundamentals of modern and classical numerical techniques for linear and nonlinear ordinary differential equations, with application to a wide variety of problems in science, engineering and other fields. The course covers the basic theory of scheme consistency, convergence and stability and various numerical methods. |
Weekly Detailed Course Contents
| Week | Subject | Related Preparation |
| 1) | Existence, Uniqueness, and Stability Theory | |
| 2) | Consistency, Stability, and Convergence | |
| 3) | Euler’s Method and Its Error Analysis | |
| 4) | Multistep Methods | |
| 5) | Midpoint and Trapezoidal Methods | |
| 6) | A Low-Order Predictor-Corrector Algorithm | |
| 7) | A Low-Order Predictor-Corrector Algorithm (continued) | |
| 8) | Derivation of Higher-Order Multistep Methods | |
| 9) | Derivation of Higher-Order Multistep Methods (continued) | |
| 10) | Convergence and Stability Theory for Multistep Methods | |
| 11) | Stiff Differential Equations and The Method of Lines | |
| 12) | Single-Step Methods | |
| 13) | Single steps and Runge-Kutta Methods (continued) | |
| 14) | Boundary Value Problems |
Sources
| Course Notes / Textbooks: | An Introduction to Numerical Analysis (2nd edition), Kendall E. Atkinson, John Wiley and Sons, Inc. |
| References: | . |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Homework Assignments | 7 | % 30 |
| Presentation | 1 | % 30 |
| Final | 1 | % 40 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Presentations / Seminar | 1 | 40 | 40 |
| Homework Assignments | 7 | 10 | 70 |
| Final | 1 | 46 | 46 |
| Total Workload | 198 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |