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Description of Individual Course Units
| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits |
|---|---|---|---|---|---|
| MAT748 | APPLIED MATHEMATICS I | 3 | 5 | 5,00 |
Level of Course Unit
Lisans
Language of Instruction
Turkish
Objectives of the Course
To study concepts of Fourier series and integral transformations and their applications to some problems of theory of differential equations and mathematical physics.
Name of Lecturer(s)
Learning Outcomes
| 1 | Scientific, mathematical thinking skill |
| 2 | Capable of doing research in areas of theoretical and applied mathematics |
| 3 | Fundamental mathematical skills (problem solving, reasoning, relation, generalization) |
| 4 | Following development in science and technology and skill for modernize herself / himself consistently |
| 5 | Skill for access information and capable of making research, using databases and other information sources |
Mode of Delivery
Formal Education
Prerequisities and Co-Requisities
None
Recommended Optional Programme Components
None
Content of the Course
Fourier series: ortogonal systems of functions ,trigonometric systems and Fourier series,expansion of functions to Fourier series,properties of Fourier coefficients ,sufficient conditions for expanding to Fourier series,examples,Fourier series in complex form Fourier integral and transformations :definitions ,properties of Fourier integral ,sine and cosine Fourier integrals ,Fourier transformation and properties,examples Laplace transformations: definitions and properties of Laplace transfomations,examples,expansion theorems for inverse transfomation,convolutions,applications to linear differential equations with constant coefficients. Mathematical models of some bvp for PDE: physical interpretation of some boundary value problems for diffusion and wave equations,Fourier and Laplace methods for solving of bvp for PDE,D’richlet and Neumann problems for Laplace equation.
Weekly Detailed Course Contents
| Week | Subjects (Theoretical) | Teaching Methods | Preparatory |
|---|---|---|---|
| 1 | Fourier series: ortogonal systems of functions ,trigonometric systems and Fourier series | ||
| 2 | expansion of functions to Fourier series,properties of Fourier coefficients | ||
| 3 | sufficient conditions for expanding to Fourier series, | ||
| 4 | sine and cosine Fourier integrals | ||
| 5 | sine and cosine Fourier integrals | ||
| 6 | Examples | ||
| 7 | examples Laplace transformations: definitions and properties of Laplace transfomations,examples | ||
| 8 | examples Laplace transformations: definitions and properties of Laplace transfomations,examples | ||
| 9 | expansion theorems for inverse transfomation,convolutions, applications to linear differential equations with constant coefficients | ||
| 10 | Laplace transform solution of ordinary differential equations with variable coefficients | ||
| 11 | Solutions of ordinary differential equation systems with Laplace transform | ||
| 12 | Mathematical models of some bvp for PDE | ||
| 13 | physical interpretation of some boundary value problems for diffusion and wave equations | ||
| 14 | Fourier and Laplace methods for solving of bvp for PDE,D’richlet and Neumann problems for Laplace equation. |
Text Book / Material / Recommended Resources
Krikoroff,A.M; Shabunin,M.I Course of mathematical analysis. “Nauka”,Moscow 1988 Cevdet Koçak Higher Mathematics . İTÜ Vakfı,İstanbul 1996 Alekseev,V.M ; Tikhomirov,V.M and Fomin, S.V Optimal control. New York and London, 1990
Assessment Methods and Criteria
| Term (or Year) Learning Activities | Quantity | Weight |
|---|---|---|
| Midterm Examination | 1 | 90 |
| Discussion | 1 | 10 |
| Total | 100 | |
| End Of Term (or Year) Learning Activities | Quantity | Weight |
| Final Examination | 1 | 100 |
| Total | 100 | |
| Term (or Year) Learning Activities | 40 | |
| End Of Term (or Year) Learning Activities | 60 | |
Work Pacement(s)
None
Workload Calculation
| Activities | Number | Time (hours) | Total Work Load (hours) |
|---|---|---|---|
| Midterm Examination | 1 | 2 | 2 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 2 | 28 |
| Problem Solving | 14 | 2 | 28 |
| Discussion | 1 | 1 | 1 |
| Self Study | 14 | 1 | 14 |
| Individual Study for Mid term Examination | 6 | 4 | 24 |
| Individual Study for Final Examination | 6 | 4 | 24 |
| Total Work Load (hours) | 123 | ||
Contribution of Learning Outcomes to Programme Outcomes
| PO 1 | PO 2 | PO 3 | PO 4 | PO 5 | PO 6 | PO 7 | PO 8 | PO 9 | PO 10 | PO 11 | PO 12 | PO 13 | PO 14 | PO 15 | |
| LO 1 | 4 | 4 | 3 | 4 | 4 | 3 | 3 | 3 | 3 | 4 | 3 | 3 | 4 | 3 | 3 |
| LO 2 | 4 | 4 | 3 | 4 | 4 | 3 | 3 | 3 | 3 | 4 | 3 | 3 | 4 | 3 | 3 |
| LO 3 | 4 | 4 | 3 | 4 | 4 | 3 | 3 | 3 | 3 | 4 | 3 | 3 | 4 | 3 | 3 |
| LO 4 | 4 | 4 | 3 | 4 | 4 | 3 | 3 | 3 | 3 | 4 | 3 | 3 | 4 | 3 | 3 |
| LO 5 | 4 | 4 | 3 | 4 | 4 | 3 | 3 | 3 | 3 | 4 | 3 | 3 | 4 | 3 | 3 |
* Contribution Level: 1 Very low 2 Low 3 Medium 4 High 5 Very High