APPLIED MATHEMATICS (TURKISH, THESIS) | |||||
Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT5012 | Numerical Solutions to Differential Equations I | Spring | 3 | 0 | 3 | 8 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | Tr |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
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. |
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. |
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. |
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 |
Course Notes: | An Introduction to Numerical Analysis (2nd edition), Kendall E. Atkinson, John Wiley and Sons, Inc. |
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 | 7 | % 30 |
Presentation | 1 | % 30 |
Project | % 0 | |
Seminar | % 0 | |
Midterms | % 0 | |
Preliminary Jury | % 0 | |
Final | 1 | % 40 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
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 | 0 | 0 | 0 |
Presentations / Seminar | 1 | 40 | 40 |
Project | 0 | 0 | 0 |
Homework Assignments | 7 | 10 | 70 |
Quizzes | 0 | 0 | 0 |
Preliminary Jury | 0 | ||
Midterms | 0 | 0 | 0 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 46 | 46 |
Total Workload | 198 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | Ability to assimilate mathematic related concepts and associate these concepts with each other. | |
2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | |
3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | |
4) | Ability to make individual and team work on issues related to working and social life. | |
5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | |
6) | Ability to use mathematical knowledge in technology. | |
7) | To apply mathematical principles to real world problems. | |
8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | |
9) | Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. | |
10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | |
11) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | |
12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, |