| 1 |
Course Title: |
PHYSICAL MATHEMATICS II |
| 2 |
Course Code: |
FZK2004 |
| 3 |
Type of Course: |
Compulsory |
| 4 |
Level of Course: |
First Cycle |
| 5 |
Year of Study: |
2 |
| 6 |
Semester: |
4 |
| 7 |
ECTS Credits Allocated: |
8 |
| 8 |
Theoretical (hour/week): |
5 |
| 9 |
Practice (hour/week) : |
0 |
| 10 |
Laboratory (hour/week) : |
0 |
| 11 |
Prerequisites: |
no |
| 12 |
Recommended optional programme components: |
None |
| 13 |
Language: |
Turkish |
| 14 |
Mode of Delivery: |
Face to face |
| 15 |
Course Coordinator: |
Prof. Dr. İLHAN TAPAN |
| 16 |
Course Lecturers: |
Prof. Dr. Emin N. Özmutlu |
| 17 |
Contactinformation of the Course Coordinator: |
ilhan@uludag.edu.tr, 0 224 29 41 698, UÜ Fen Edebiyat Fakültesi, Fizik Bölümü 16059 Görükle Kampüsü Bursa |
| 18 |
Website: |
|
| 19 |
Objective of the Course: |
1. To teach the method of mathematical physics
2. To teach special mathematical methods used in physics
3. To give the ability of practical solution to the problems
4. To show the application of the mathematics to the current physics problems.
|
| 20 |
Contribution of the Course to Professional Development |
|
| Week |
Theoretical |
Practical |
| 1 |
Applications of derivative. Physical and mathematical form of the derivative. The average speed. |
|
| 2 |
Slope of the function, meaning of increase and decrease of the slope, determination of the maximum and minimum points of the function. |
|
| 3 |
Examples of bisection and Newton methods, comparison between the methods. The root of a function is found within the error limits using these methods. |
|
| 4 |
The concept of series expansions is given. Taylor and Maclaurin series expansions are explained. Series expansions of exponential and trigonometric functions are given. |
|
| 5 |
Binomial theorem is given. Application of Taylor and Maclaurin series expansions are given. |
|
| 6 |
Fourier series, Trigonometric Fourier series, harmonics, sine and cosine functions. The calculation of Fourier coefficients for the functions of 2L. Fourier transformations.
First exam
|
|
| 7 |
Complex form of Fourier series. The complex Fourier transforms. The Laplace transform. |
|
| 8 |
Dirac-delta function. Properties of the Dirac-delta function. Step functions . Step functions of Dirac-delta function. |
|
| 9 |
Indexed calculations. Expression of vector in a three-dimensional space. Kronecker delta and Levi Civita. Scalar and vector products of two vectors. Index applications. |
|
| 10 |
Tensor is given. Dyad and its properties are described. The matrix form of a tensor is given. Tensors with index expression is given. Scalar multiplication of tensors is given. |
|
| 11 |
Concepts of mass and center of gravity is given by using index operations. Center of mass problems are solved by using both index operations and integrals. Cartesian, polar, spherical and cylindrical coordinates are used in integral solution. |
|
| 12 |
Definition of torque and moment of inertia is done with indexed operations.
Second exam
|
|
| 13 |
Galilean and Lorentz transformations are given. Minkowski space is mentioned. Orthogonal tensor transformation is given. Covariant and contravariant metric tensor is given. Forms of the four vectors are defined. |
|
| 14 |
Complex numbers and their properties are given. The geometric representation of complex numbers are given. Complex numbers are given in polar form. Expression of De Moivre Formula is given. |
|
| 23 |
Textbooks, References and/or Other Materials: |
1. İleri Analiz, Prof Dr. Saffet Süray, Güven Kitabevi, 1978
2. Fizikçiler ve Mühendisler için kısmi diferansiyel denklemler, Yaşar Pala, Ahmet Cengiz, Mürsel Alper, Uludağ Üniv. Basımevi, 2000
3. Fizik ve Mühendislikte Matematik Yöntemler, Emine Öztürk, Seçkin Yayıncılık, 2011
4. Fen ve Mühendislik Bilimlerinde Matematik yöntemler, Selçuk Bayın, Ders Kitapları AŞ, 2004
|
| 24 |
Assesment |
|
