APPLIED MATHEMATICS (TURKISH, NON-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 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: Must Course
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
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 apply mathematical principles to real world problems.
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.