TEW - Linear Algebra & Multivariable Calculus (2022)

Speakers and Syllabus

 Speakers and Tutors
1. Dr. Dinesh Khurana, Panjab University, Chandigarh.
2. Dr. Jotsaroop Kaur, IISER Mohali.
3. Dr. Ved Prakash Gupta, JNU Delhi.
4. Dr. Vaibhav Vaish, IISER Mohali.

Syllabus

1. .Dinesh Khurana: Vector spaces and their basic properties,Linear Transformations and Matrices, Change of Basis, Triangulation and Diagonalization,Modules, Modules versus Vector Spaces, Free Modules, Matrices over PIDs, Smith Normal Form, Structure Thcorem for Finitcly Generated Modules over PlIDs and itsApplications.
2. Jotsaroop Kaur: Review of Euclidean Spaces, Derivatives, Partial Derivatives and the Chain Rule, Mean Value Theorem, Taylor's Formula, Inverse and Implicit Function Theorems, Maxima and Minima, Method of Lagrange Multipliers.
3.  Dr. Ved Prakash Gupta: Inner Product Spaces, Gram-Schmidt Procedure,Operators on Inner Product Spaces: Normal operator, Self-Adjoint Operator, Spectral Theorems, Singular Value Decomposition.
4.  Vaibhav Vaish: Surfaces, Level surfaces, A need for the Implicit Function Theorem, Curvature of a curve, Devising notion of curvature for a surface and a need for Taylor's formula.

Time Table

 Typical daily schedule
(Tea Breaks:10.35-10.55, 3.35-3.55, Lunch: 1-2.20, Snacks Break: 5-5.30)

DK-Dinesh Khurana
JK- Jotsaroop Kaur
VP-Ved Prakash Gupta
VV-Vaibhav Vaish
L-Lecture
T-Tutorial