COURSE CONTENT:

• Real Analysis : 

  1.  Metric spaces: definition and examples.

  2.  Open, closed and bounded sets, interior, closure and boundary.

  3.  Convergence, completeness, continuity, uniform continuity, connectedness, compactness and separability.

  4.  Heine-Borel theorem, pointwise and uniform convergence of real-valued functions, equicontinuity and Ascoli-Arzela theorem.

• Complex Analysis :

  1.  Limits, continuity and differentiability of functions of a complex variable.

  2.  Analytic functions and the Cauchy-Riemann equations, Definition of contour integrals.

  3.  Cauchy's integral formula, derivatives of analytic functions, Morera's and Liouville's theorems.

  4.  Maximum modulus principle, Taylor and Laurent series, Isolated singular points and residues, Cauchy's residue theorem and applications.

For more details click here. 

Tutorial Sheets and Lecture Notes:

• Lecture Notes:

  1.  Lecture 1         

  2.  Lecture 2 

  3.  Lecture 3 

  4.  Lecture 4

  5.  Lecture 5

  6.  Lecture 6

  7.  Lecture 7

  8.  Lecture 8

  9.  Lecture 9 

  10.  Lectures 10, 11, 12 

  11.  Lectures 13-16 

  12. Lectures 17-21 

  13. Complex-1

Complex Analysis.2 -- Churchill and Brown, Complex Analysis. John B. Conway, Functions of one complex variable

Quiz-2 Solution

Major Solution

• Tutorial Sheets:

  1.  Assignment 1 

  2.  Assignment 2 

  3.  Assignment 3 

  4.  Assignment 4 

  5.  Assignment 5 

  6.  Assignment 6

  7. Assignment 7

  8. Assignment 8

  9. Assignment 9

Grading Policy:

• Three quizzes (best two will be considered) - 30%

• One Minor - 30%

• One Major - 40%

Lecture and Tutorial Schedule:

• Lecture timing: Tuesday, Wednesday, Friday (10:00 - 11:00 AM), LH-108

• Tutorial timing: 

  1.  Monday (1:00 - 2:00 PM), II LT 3 (Naveen Gupta), Group-1  

  2.  Tuesday (1:00 - 2:00 PM), II LT 3 (Lalit Mohan), Group-2 

  3.  Thursday (1:00 - 2:00 PM), II LT 3 (Arvish Dabra), Group-3 

  4.  Friday  (1:00 - 2:00 PM), II LT 3 (Santak Panda), Group-4 

Tentative Quiz Schedule:  1. Quiz 1- 06.02.2024

                                             2. Quiz 2- 18.3.2024

                                             3. Quiz 3-  12.04.2024