Class: MoWe, 1:00-2:00PM & TuFr, 12:00-1:00PM. LH1/2
Instructor: Kapil Chaudhary
Email: kapilchaudhary@gujaratuniversity.ac.in
Office: RR3 or RR4
Textbook: Brown, J. W., & Churchill, R. V. (2009). Complex variables and applications (8th ed.). McGraw-Hill.
Supplementary readings:
Pre-requisites: None.
Topics to be covered: Unit IV from the syllabus below.
Unit I: Basic Definitions and notations, Algebraic properties, Polar coordinates and Euler’s formula, Products and Quotients in exponential form. Roots of complex Numbers. Continuous complex functions. Limits Involving Point at Infinity.
Unit II: Differentiable complex functions, Cauchy Riemann equations. Harmonic functions of two variables, Reflection principle.
Unit III: Elementary functions, Contours, Contour integrals, Anti-derivatives.
Unit IV: Cauchy-Goursat theorem, Simply connected domain, Multiply connected domains. Cauchy’s integral formula and its Extension. Liouville’s theorem, Fundamental theorem of Algebra, Maximum moduli principle of functions.
The assigned instructors, Jalpa, Naisargi, and Jyoti, have covered the topics of Unit I through Unit III.
# | Date | Topic | Homework | Lecture |
---|---|---|---|---|
1 | - | Cauchy-Goursat theorem | H1 (due next week) | pdf , html |
2 | - | Proof & extension of Cauchy’s theorem | pdf , html | |
3 | - | Simply & Multiply connected domains | pdf , html | |
4 | - | Path independence & principle of deformation | pdf , html | |
5 | - | Winding number of curve & Cauchy-Integral formula | H2 (due next week) | pdf , html |
6 | - | Generalised Cauchy’s formula | pdf , html | |
7 | - | Consequences of Cauchy’s formula | pdf , html | |
8 | - | Exercises | pdf , html | |
9 | - | Liouville’s theorem | pdf , html | |
10 | - | Fundamental theorem of Algebra | H3 (due next week) | pdf , html |
11 | - | Maximum Modulus principle | Test Practice Problems | pdf , html |
12 | - | Exercises | pdf , html | |
Fr 12/08 | Test - Unit IV | |||
13 | - | Last lecture.. summary, doubts, & exercises - Unit IV | pdf , html |
Last modified: 23rd Jul, 2024, 2:10PM IST