MATH353 COMPLEX CALCULUS
| Course Code: | 2360353 |
| METU Credit (Theoretical-Laboratory hours/week): | 4 (4.00 - 0.00) |
| ECTS Credit: | 7.5 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Prof.Dr. ALİ ULAŞ ÖZGÜR KİŞİSEL |
| Offered Semester: | Fall Semesters. |
Course Objectives
By the end of this course, a student will:
- Understand in details the complex number system and the complex plane.
- Use functions of a complex variable and explore their properties.
- Understand the concepts of the derivative of a complex function and analyticity of a function.
- Make calculations with elementary functions of a complex variable.
- Evaluate line integrals and prove results using the Cauchy theorem and the Cauchy integral formulas.
- Freely use of complex sequences and infinite series, Laurent series, residues and the residue theorem and apply them to various problems.
- Understand the concepts of conformal mappings.
Course Content
Algebra of complex numbers. Polar representation. Analyticity. Cauchy-Riemann equations. Power series. Elementary functions. Mapping by elementary functions. Linear fractional transformations. Line integral. Cauchy-Theorem. Cauchy integral formula. Taylor`s Series. Laurent series. Residues. Residue theorem. Improper integrals.
Course Learning Outcomes
Students will learn the basics of functions of a complex variable.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution