TEW - Real Analysis, Multivariable Calculus and Linear Algebra (2020)

Speakers and Syllabus


 

Syllabus to be covered in terms of modules of 6 lectures each :

 

Name of the Speaker with affiliation, who will cover each module of 6 lectures.

 

No. of Lectures

Detailed Syllabus

  • Prof. Koushik Ramachandran Department of Mathematics,TIFR-CAM, Bangalore

8

Real analysis: Real numbers. Sequences and series of real numbers (Cauchy sequences, Heine-Borel, Bolzano-Weierstrass). Continuity and uniform continuity. Integration. Differentiation.

 

  • Prof. A. K. Nandakumaran Professor, Department of Mathematics,IISC Bangalore
  • Prof. Tulsi Srinivasan, Assistant Professor, Azim Premji University

8

Multivariable calculus: The derivative in higher dimensions. Gradient, divergence, curl, etc. Greens' theorem and Stokes's theorem (without the use of forms, more intuitive approach). Inverse function theorem.

 

  • Prof. R. Venkatesh
  • Prof. Manjunath Krishnapur
    Professor, Department of Mathematics IISC Bangalore

 

8

Linear algebra: Finite dimensional vector spaces over real or complex fields. Dual space, linear transformations. Determinant, characteristic polynomial, Eigenvalues and eigenvectors. Spectral theorem for self-adjoint linear operators. If possible, some `real-world' uses of matrices will be discussed.

 

References:
Linear algebra:

  • Gilbert Strang, Linear Algebra and Its Applications
  • Sheldon Axler, Linear algebra done right
  • David C Lay, Linear Algebra and its applications
  • Otto Bretscher, Linear Algebra with Applications

Real analysis:

  • Robert G Bartle and Donald R Sherbert, Introduction to Real Analysis
  • Sterling K Berberian, A first course in Real Analysis
  • Elementary Analysis, Kenneth A Ross
  • Sudhir R Ghorpade, Balmohan V Limaye, A course in Calculus and Real Analysis
  • Apostol, T. M., Mathematical Analysis
  • Tao, Analysis-I (TRIM series)
  • Ajit Kumar, S Kumaresan, A basic course in Real Analysis

Multivariable calculus:

  • Apostol, T. M., Mathematical Analysis
  • Spivak, M., Calculus on Manifolds
  • Sudhir R Ghorpade, Balmohan V Limaye, A course in Multivariable , Calculus and Analysis
  • Joel R Hass, Christopher E Heil, Maurice D Weir, Thomas’ Calculus
  • James Stewart, Multivariable Calculus
  • Peter D Lax and Maria Shea Terrell, Multivariable Calculus with Applications

Names of the tutor(s) / course associate with their affiliation and status:

  1. Linear Algebra: Dr. Koushik Dhara, Post-Doctoral Fellow, Indian Statistical Institute, Bangalore

  2. Real Analysis: Dr. Raisa D’souza, Assistant Porfessor, St. Joseph’s College, (Autonomous), Bangalore

  3. Multivariable Calculus: Dr.. Tulsi Srinivasan, Assistant Professor, Azim Premji University, Bangalore

 

 

 

 


Time Table

 

Day

Date

Lecture 1

9.30–10.30

Tea

10.35–10.55

Lecture 2

11.00–12.00

Lecture 3

12.05–1.05

Lunch

1.05–2.25

Lecture 4

2.30-3.30

Discussion/ Tutorial

4.00-5.00

Tea & Snacks

5.05-5.30

 

 

(name of the speaker

 

(name of the speaker)

 

 

Name of the speaker

Name of the speaker/tutor

 

Mon

13 Jul

MK

 

MK

KR

 

KR

KD

 

Tues

14 Jul

KR

 

KR

MK

 

MK

RD

 

Wed

15 Jul

VN

 

VN

TL

 

TL

TL

 

Thu

16 Jul

KR

 

KR

TL

 

TL

RD

 

Fri

17 Jul

ND

 

ND

VN

 

VN

KD

 

Sat

18 Jul

ND

 

ND

KR

 

KR

TL

 

ND: Prof. A. K. Nandakumaran
VN: Prof. R Venkatesh
MK: Prof. Manjunath Krishnapur
KR: Prof. Koushik Ramachandran
TL: Dr. Tulsi Srinivasan
KD: Dr. Koushik Dhara
RD: Dr.. Raisa D’souza

 

 

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