MA 205 Complex Analysis

Course Instructor :Prof. U K Anandavardhanan

Course Name:Complex Analysis MA 205

Course Type:Core(Theory)

Credits:4

Pre-requisites: MA 105 (Calculus) being an informal pre-requisite.

Course Content: Complex numbers and why are they interesting, limits, continuity and differentiability, Cauchy-Riemann equations, harmonic functions, power series, exponential function, logarithmic function, integration, Cauchy's theorem, Cauchy Integral Formula, holomorphic and analytic functions, Cauchy's estimate, Liouville's theorem, entire functions, Fundamental Theorem of Algebra, Morera's theorem, isolated roots theorem, Identity theorem, singularities, Laurent series, Cauchy Residue Theorem, Riemann Removal Singularities Theorem, real integrals and contour integration, Maximum Modulus Theorem.

Conformal mappings were a part of the prescribed syllabus, but could NOT be covered due to time constraints.

Books: Didn't refer to any book in particular, wasn't required to be honest. However, the following books were recommended:

R. V. Churchill and J. W. Brown, Complex variables and applications (7th Edition),
McGraw-Hill (2003),
E. Kreyszig, Advanced engineering mathematics (8th Edition), John Wiley (1999)

Lectures:Most of the time slides were used for teaching, however board was used sometimes to explain things not mentioned in the slides or to explain doubts. The Prof. was encouraging, answered questions effectively and was stimulating. It was fun to sit in the class. The content was also well presented and explanations were clear and effective. 80% attendance was compulsory.

Useful Online Resources:Previous years' lectures available on CDEEP were of use to some students.

Follow-Up Courses:MA 412, a full fledged course in complex analysis (exposure to real analysis might be required before taking up this course). If you have done courses in basic algebra, you might be interested in taking basic number theory courses as well.Complex analysis is widely used in both physics (especially theoretical high energy physics) and electrical engineering (even though it may not seem obvious) and one might find direct applications of it in PH 202 (Waves, Oscillations and Optics), an EP core course in 4th sem. This course should be done sincerely and seriously. One should attend classes and pay strict attention to what the Prof. is explaining, since the pace of this course might be a bit fast, owing to its half-sem duration. There are a lot of theorems and proofs and the lectures are connected with each other, so regular studies are required, otherwise one could find lectures difficult to comprehend. One might want to take summary notes of theorems, proofs and formulae during self study. Making notes in class wasn't required, since slides were well organized. Leaving studies till the last day is NOT recommended. The type of questions to be asked in the quizzes were discussed in the lectures (in some detail actually), so the one who is facing trouble with the overall lecture content, might focus on those questions in particular while preparing for the quizzes.

Assignments:Tutorial sheets were easy to moderate in difficulty, with a lot of questions for general practice of theorems and formulae and some questions involving proofs. 80% attendance was compulsory in the tutorial classes. Grading was on the lenient side and the exams were also easy to moderate in difficulty.  

Exams and Grading:2 Quizzes, of 20% weightage each and a final exam (midsem) of 60% weightage were held.

Pro-tips:One might find tutorials to be long and containing many questions of the same kind. In such a situation, one can plan to attempt some questions before the tutorial classes, some during the tutorial and leave some to attempt before the exams for revision and practice.

Respondent: Himansh Rathore