TEW - Linear Algebra & Multivariable Calculus (2020)
Speakers and Syllabus
- 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, Finitely Generated Modules over PIDs and their structure, Rational and Jordan Canonical Forms.
- Amit Kulshrestha: 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.
- Varadharaj Srinivasan: Inner Product Spaces, Gram-Schmidt Procedure,Operators on Inner Product Spaces: Normal operator, Self-Adjoint Operator, Spectral Theorems, Singular Value Decomposition.
- Vaibhav Vaish: Surfaces, Level surfaces, A need for the Implicit Function Theorem, Projecting globe as a 2D-map, Curvature of a curve, Devising notion of curvature for a surface and a need for Taylor’s formula, Normal sections, Normal and Geodesic curvature, Principal curvature, Gauss’ Theorema Egregium.
Typical daily schedule
(Tea Breaks:10.35-10.55, 3.35-3.55, Lunch: 1-2.20, Snacks Break: 5-5.30)