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
MAT5014 Boundary Value Problems Spring 3 0 3 12
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: Nonclassical equations of mathematical physics. Fourier series solution. Fourier and Laplace transformations and their applications to PDE. Approximate solutions of the nonlocal boundary value problems for PDE mixed types. Difference Schemes of the nonlocal boundary value problems for PDE of mixed types. Stability of difference schemes for partial differential equations of variable types.

Learning Outcomes

The students who have succeeded in this course;
Students
1. will be able to solve partial differential equations
2. can solve engineering and physics problems
3. can analyze the stability of difference schemes for partial differential equations

Course Content

Nonclassical equations of mathematical physics.
Fourier series solution.
Fourier and Laplace transformations and their applications to PDE.
Approximate solutions of the nonlocal boundary value problems of the nonlocal boundary value problems for PDE mixed types.
Difference Schemes of the nonlocal boundary value problems for PDE of mixed types.
Stability of difference schemes for partial differential equations of variable types.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Nonclassical equations of mathematical physics.
2) Fourier series solution.
3) Fourier and Laplace transformations and their applications to PDE.
4) Fourier and Laplace transformations and their applications to PDE.
5) Approximate solutions of the nonlocal boundary value problems for PDE mixed types.
6) Approximate solutions of the nonlocal boundary value problems of the nonlocal boundary value problems for PDE mixed types.
7) Difference Schemes of the nonlocal boundary value problems for PDE of mixed types.
8) Difference Schemes of the nonlocal boundary value problems for PDE of mixed types.
9) Difference Schemes of the nonlocal boundary value problems for PDE of mixed types.
10) Stability of difference schemes for partial differential equations of variable types.
11) Stability of difference schemes for partial differential equations of variable types.
12) Stability of difference schemes for partial differential equations of variable types.
13) Stability of difference schemes for partial differential equations of variable types.
14) Stability of difference schemes for partial differential equations of variable types.

Sources

Course Notes / Textbooks: Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematic), Randall J. LeVeque, SIAM, Society for Industrial and Applied Mathematics (July 10, 2007)
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 14 98
Final 1 20 20
Total Workload 200

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. 5
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. 4
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
4) Ability to make individual and team work on issues related to working and social life. 5
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. 5
6) Ability to use mathematical knowledge in technology. 5
7) To apply mathematical principles to real world problems. 4
8) Ability to use the approaches and knowledge of other disciplines in Mathematics. 4
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. 5
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. 5
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. 4
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, 4