# TEW - Linear Algebra and Calculus (2024)

## Speakers and Syllabus

 Name of the Speaker with affiliation No. of Lectures Detailed Syllabus Prof. Pralay Chatterjee,The Institute of Mathematical Sciences, Chennai. 8+2 Vector spaces, Linear maps, Matrix representation of linear maps, Row reduction, Row reduced echelon matrix, Row rank, Column rank, Solving system of linear homogeneous and non-homogeneous equations, Cramer's rule, Eigen values, Eigen vectors, Diagonalizability, Bilnear forms, Orthogonal and symmetric matrices, Canonical forms, Spectral Theorem for normal operators. Dr. Chandan Maity,IISER Behrampur. 8+2 Well ordering property of N, Principle of mathematical Induction (strong and weak) and its applications, Countable and uncountable sets, Completeness Axiom, Archimedean property, Sequence, Series and their convergence and divergence, Bolzano-Weierstrass theorem, Continuity, Intermediate value theorem, Uniform continuity, Differentiability, Mean value theorem, Maxima and minima, Taylor theorem and series, Existence of continuous but nowhere differentiable functions Dr. Sreenivasa Rao Y,NIT Warangal. 8+2 Vector functions of a single variable, Parametric representations, Position, velocity and acceleration vectors, Functions of several variables, Limits and continuity, Directional derivatives, Partial derivatives, Derivative, Tangent and normal vectors, Arc length, Curvature and torsion, Vector fields, Gradient, divergence and curl, Line integrals, Surface and volume integrals, Green's theorem (for planar vector fields), Gauss’s divergence theorem, Stokes' theorem.

References:

1. Algebra, M. Artin, Pearson Publications.

2. Linear Algebra, Hoffman and Kunze, Pearson publications.

3. Introduction to real analysis, Robert G. Bartle and Donald R. Sherbert.

4. Introduction to real analysis, William F. Trench

5. Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach, John H. Hubbard

## Time Table

 Day Date Lecture 1 (9.30-10.30) Tea (10.35-10.55) Lecturer 2 (11.00-12.00) Lecture 3 (12.00-1.00) Lunch (1.00to2.20) Lecture 4 (2.30-3.30) Tea (3.35-3.55) Discussion (4.00-500) Snacks (5.05to5.30) (Speaker’s name) (Speaker’s name) (Speaker’s name) (Speaker’s name) (Tutor’s name) Mon 29.07.24 CM PC CM PC CM, MS, AM Tue 30.07.24 CM PC CM CM PC, MS, KD Wed 31.07.24 CM PC CM SY CM, MS, AM Thu 01.08.24 CM PC SY SY SY, KD, AM Fri 02.08.24 SY PC SY SY PC, MS, KD Sat 03.08.24 SY PC SY PC SY, MS, KD

Full forms for the abbreviations of speakers and tutors:

PC : Prof. Pralay Chatterjee

CM: Dr. Chandam Maity

SY : Dr. Sreenivasa Rao Y

AM: Dr. Anirban Majumdar

MS: Dr. Mani Shankar Pandey

KD: Dr. Kushal Dhar Dwivedi

Name of the tutors:

 S. No. Name Affiliation 1 Dr. Anirban Majumdar Assistant Professor, IIITDM Kurnool 2 Dr. Mani Shankar Pandey Assistant Professor, IIITDM Kurnool 3 Dr. Kushal Dhar Dwivedi Assistant Professor, IIITDM Kurnool
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