### Basic Information

**Course Code**: MA 205**Course Name**: COMPLEX ANALYSIS**Course Offered In**: 2022-23**Instructors**: Saikat Mazumdar**Prerequisites**: There aren’t any rigid prerequisites, but having a good grasp of concepts such as limits, continuity, and differentiation using epsilon-delta from MA 105 part 1 (MA 109) would be beneficial, so it’s recommended to review and refresh your understanding of them before taking the course.**Difficulty (on a scale of 5)**: 3

### Course Content

- Complex numbers and the complex plane, Domains in the complex plane, Convergence
- Functions on the complex plane, Continuity, Derivatives and Holomorphic functions, Cauchy-Riemann equations 3.Power Series, Exponential and Trigonometric functions, Analytic Functions
- Integration along curves, Cauchy’s theorem and its applications, Cauchy integral formula
- Harmonic functions, Analytic continuation
- Singularities, Zeros and poles, Laurent series, The residue formula
- Evaluation of Integrals

### Feedback on Lectures

The lectures were moderately paced the instructor mostly followed his slides while teaching. Weekly Tutorials were held and they also carried 10% weight of the total course.There was no strict attendance policy for the lectures but it is highly recommended to attend the lectures. The course became slightly hard in the latter half thus it is recommended to attend tutorials and solve the tutorial problems beforehand. The prof was approachable and encouraged and cleared the doubts in the class itself.

### Feedback on Evaluations

Similar to other Maths Courses MA 205 also had a Quiz(accounted for 30% weight) and a Final Exam(60%) the rest 10% was based on tutorial sessions. The exams were on the easier side, questions were from concepts taught in the lectures and tutorials with the slightest of tweaks thus is important to solve tutorials on time. While this may seem nice to many this also made this course a high scoring one so the grading was much more like absolute grading.

### Study Material and Resources

- Lecture PDF’s
- R. V. Churchill and J. W. Brown, Complex variables and applications, McGraw-Hill
- E. Kreyszig, Advanced engineering mathematics, John Wiley
- J. M. Howie, Complex analysis, Springer-Verlag
- M. J. Ablowitz and A. S. Fokas, Complex Variables { Introduction and Applications, Cambridge University Press
- J. P. D’Angelo, An Introduction to Complex Analysis and Geometry, American Mathematical Society
- S. Kumaresan, A pathway to Complex Analysis, Techno World
- Lars Ahlfors, Complex Analysis
- John Conway, Functions of a Complex Variable
- E. M. Stein and R. Shakarchi, Complex Analysis, Princeton University Press
- M. Taylor, Introduction to Complex Analysis, , American Mathematical Society Lecture PDF’s were sufficient for this course however E. Kreyszig was highly recommended by the prof for additional readings.

### Follow-up Courses

For those pursuing a minor in Math, a lot of the content will be repeated in MA412M

### Final Takeaway

Knowledge learnt from this course will go a long way in other EE courses like EE 229(Signal Processing) and EE 302(Control Systems) also this course lays a good foundation of complex numbers which you will encouter very often as an Electrical Engineer. The topics in this course are also interesting thus it wouldn’t be hard to enjoy this course whille learning a lot.