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 

8 
Real analysis: Real numbers. Sequences and series of real numbers (Cauchy sequences, HeineBorel, BolzanoWeierstrass). Continuity and uniform continuity. Integration. Differentiation.


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.


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 selfadjoint linear operators. If possible, some `realworld' 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, AnalysisI (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:

Linear Algebra: Dr. Koushik Dhara, PostDoctoral Fellow, Indian Statistical Institute, Bangalore

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

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 2.303.30 
Discussion/ Tutorial 4.005.00 
Tea & Snacks 5.055.30 


(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