TEW - Real Analysis, Multivariable Calculus and Linear Algebra (2022)
Speakers and Syllabus
Syllabus to be covered in terms of modules of 6 lectures each :
| Name of the Speaker | No. of Lectures | Detailed Syllabus |
| Prof. Koushik Ramachandran Department of Mathematics TIFR-CAM, Bangalore |
4 | Real analysis(RA): Real numbers. Sequences and series of real numbers (Cauchy sequences, Heine-Borel, Bolzano-Weierstrass). Continuity and uniform continuity. Integration. Differentiation. |
| Prof. Divakaran D Department of Mathematics Azim Premji University , Bangalore |
4 | |
| Prof. R. Venkatesh, Department of Mathematics IISC Bangalore |
4 | Linear algebra(LA):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. Multivariable calculus(MC): The derivative in higher dimensions. Gradient, divergence, curl, etc. Greens' theorem and Stoke's theorem (without the use of forms, more intuitive approach). Inverse function theorem. |
| Prof. Manjunath Krishnapur Professor, Department of Mathematics IISC Bangalore |
4 | |
| Prof. A. K. Nandakumaran Department of Mathematics IISC Bangalore |
4 | Multivariable calculus(MC): The derivative in higher dimensions. Gradient, divergence, curl, etc. Greens' theorem and Stoke's theorem (without the use of forms, more intuitive approach). Inverse function theorem. |
| Prof. Purvi Gupta Department of Mathematics IISC Bangalore |
4 |
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:
- Tao, Analysis-II (TRIM series)
- Charles Chapman Pugh, Real Mathematical Analysis
- Sudhir R Ghorpade, Balmohan V Limaye, A course in Multivariable , Calculus and Analysis
- Peter D Lax and Maria Shea Terrell, Multivariable Calculus with Applications
- Apostol, T. M., Mathematical Analysis
- Spivak, M., Calculus on Manifolds
Names of the tutor(s) / course associate with their affiliation and status:
- Linear Algebra: Dr. Kousik Dhara, Post-Doctoral Fellow, Weizmann Institute of Science, Bangalore and
Dr. Arundhati Krishnan, Post Doctoral Fellow, University of Waterloo - Real Analysis: Dr. Raisa D’souza, Assistant Professor, St. Joseph’s College, (Autonomous), Bangalore and
Dr. Tulsi Srinivasan, Assistant Professor, Azim Premji University, Bangalore - Multivariable Calculus: Aakanksha Jain, Research Scholar, Indian Institute of Science, Pritam Ganguly,
Research Scholar, Indian Institute of Science
Time Table
Tentativetime-table:
| WEEK1 | WEEK 2 | WEEK 3 | |||||||
| Day | Date | 6:00–7:00 PM | 7:10–8:10 PM | Date | 6:00–7:00 PM | 7:10–8:10 PM | Date | 6:00–7:00 PM | 7:10–8:10 PM |
| Mon | 17/01 | LA1(MK) | RA1(KR) | 24/01 | LA5(VN) | RA5(DD) | 31/01 | LA7(VN) | MC3(ND) |
| Tues | 18/01 | LA2(MK) | RA2(KR) | 25/01 | LA6(VN) | RA6(DD) | 01/02 | LA8(VN) | MC4(ND) |
| Wed | 19/01 | Tutorial LA I (KD+AR) |
Tutorial RA I (RD+TL) |
26/01 | Tutorial RA III (RD+TL) |
Tutorial LA III (KD+AR) |
02/02 | Tutorial LA IV (KD+AR) |
Tutorial MC II (AJ+PG) |
| Thu | 20/01 | LA3(MK) | RA3(KR) | 27/01 | RA7(DD) | MC1(ND) | 03/02 | MC5(PV) | MC6(PV) |
| Fri | 21/01 | LA4(MK) | RA4(KR) | 28/01 | RA8(DD) | MC2(ND) | 04/02 | MC7(PV) | MC8(PV) |
| Sat | 22/01 | Tutorial LA II (KD+AR4) |
Tutorial RA II (RD+TL) |
29/01 | Tutorial RA IV (RD+TL) |
Tutorial MC I (AJ+PG) |
05/02 | Tutorial MC III (AJ+PG) |
Tutorial MC IV (AJ+PG) |
Lecturers
ND: A. K. Nandakumaran
VN: R Venkatesh
MK: Manjunath Krishnapur
KR: Koushik Ramachandran
DD: Divakaran D
TBA: To be announced
Tutors
AR: Arundhati Krishnan,
KD: Koushik Dhara,
TL: Tulsi Srinivasan,
RD: Raisa D’souza,
AJ: Aakanksha Jain
PG: Pritam Ganguly