Mathematics III - MATH F211

Semester I 2024-2025

Instructor: Dr. Yasmeen Akhtar (for the first half of the course), Dr. Minhajul (for the second half of the course)

IC: Dr. Minhajul

Audience: 2nd Year B.E. students at BITS Pilani K K Birla Goa Campus 

Schedule: Monday, Wednesday, Friday 3:00-3:50 PM at LT1

Course Handout: Available on Quanta.

Lecture: 

02/08/24 - Introduction and instructions related to the course, definitions, and general remarks on solutions of ODE, Geometric interpretation, Existence and Uniqueness of solution of first-order IVP

05/08/24 - More on Picard's Theorem, Orthogonal Trajectories, Variable Separable Equations, Homogeneous Equation

07/08/24 - More on Homogeneous Equation, Exact Equation 

09/08/24 - Integrating Factor

12/08/24 - First-order Linear Differential Equation, Bernoulli's Equation, Second-order Linear Differential Equation: Existence and Uniqueness Theorem

14/08/24 - The General Solution of Second-order Linear Differential Equation

16/08/24 - Problems based on General and Particular Solutions of Second-order Linear Differential Equation

19/08/24 - Holiday

21/08/24 -  Problems, Finding a linearly independent solution using a known solution of a second-order linear differential equation

23/08/24 - The General Solution of Homogeneous Second-order Linear Differential Equation with Constant Coefficient, Euler's equidimensional equation

26/08/24 - Holiday 

28/08/24 - Finding a particular solution: Method of Undetermined Coefficients

30/08/24 - Method of Undetermined Coefficients

02/09/24 - Method of Variation of Parameters, Higher Order Linear Equations

04/09/24 - Solving Euler's equidimensional equation without transforming to a constant coefficient equation,  Operator Method

06/09/24 - Operator Method

09/09/24 - System of first-order differential equations

11/09/24 - Solving homogeneous system of two first-order linear differential equations

13/09/24 - Solving nonhomogeneous system, Review of Power Series

16/09/24 - Holiday

18/09/24 - Power Series Method for Solving First order differential equation

20/09/24 - Power Series Method for Solving Second-order Linear Differential Equations (Ordinary points)

22/09/24 - Quiz 1 (11:00 am to 12:00 noon)

23/09/24 - Regular singular point and Frobenius Method 

25/09/24 - Frobenius Method 

End of the first half of the course (Section 30 in the textbook)

27/09/24- Instructor for Section 31 onwards- Dr. Minhajul