Mathematical Methods Course


  • Basic Information

    •
    • Instructor : Siva Athreya .
    • Email : athreya@isibang.ac.in or athreya@icts.res.in

    • References and Texts

      • [AWH] Arfken, George B and Weber, Hans J and Harris, Frank E Mathematical methods for physicists: a comprehensive guide Academic press, 2011.

    • Classes:

      •  Day and Time : Tuesday and Thursday : 2:00-3:30pm

    • Homework:

      •  All Homeworks should be uploaded onto the respective Moodle platform by 10pm on the due date.


Week # Board Photos in Each Week Homework
(Due Dates)		 Topics
0 September 25-29th: Day 0
 (October 5th, 2023)
Homework 1
  • Ordinary Differential Equations
    1. Introduction, Order of a Linear ODE
    2. Separation of Variables
    [AWH] Chapter 7
1 Oct 2nd- - 6th: Day 1, Day 2
(October 12th, 2023)
Homework 2
  • Ordinary Differential Equations
    1. Existence and Uniquness of 1st order non-linear ODE, (IVP)
    2. Gronwall's Lemma and Applications
    3. Bernoulli Equations
    4. Stable and Non-Stable Equilibrium
    5. Homogenous 2nd Order Linear ODE
    6. Linearly independent Solutions and Wronksian
    [AWH] Chapter 7
2 Oct 9th -15th: Day 3, Day 4
(October 19th, 2023)
Homework 3
  • Ordinary Differential Equations
    1. Power Series Solution
    [AWH] Chapter 7
  • Complex Analysis
    1. Simply Connected, Open Sets
    2. Holomorphic Functions
    3. Cauchy Riemann Equations
    [AWH] Chapter 11
3 Oct 16th - 22nd
(October 17th, 2023)
Worksheet 1
(October 19th, 2023)
Worksheet 2
  • Ordinary Differential Equations
    1. Frobenius Method
    2. Hermite Polynomials
    3. Legendre Polynomials
    4. Bessel Functions
    [AWH] Chapter 7
4 Oct 23-27: Day 5
(November, 2nd 2023)
Homework 4
  • Complex Analysis
    1. Contour Integration
    2. Cauchy and Goursat Theorem
    3. Isolated Zeros
    4. Taylor Series
    [AWH] Chapter 11
5 Oct 30 - Nov 3: Day 6
(November 7th, 2023)
Homework 5
Test.
  • Complex Analysis
    1. Laurent Series
    2. Singularities: Isolated (poles), Essential, Removable
    3. Residues and Cauchy's Theorem
    4. Branch cuts
    5. Logarithm
    [AWH] Chapter 11
Last Modified: July 19th, 2024. ISI Courses Page ICTS Courses Page