TEW - Linear Algebra, Multivariable Calculus and Complex Analysis (2023)
Speakers and Syllabus
Syllabus to be covered in terms of modules of 6 lectures each:
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Name of the Speaker with affiliation, who will cover each module of 6 lectures. |
No. of Lectures |
Detailed Syllabus |
|
Prof. G. Bharali Professor, Department of Mathematics IISC Bangalore |
6 |
Multivariable calculus Part 1: Review of Euclidean Spaces, Derivatives, Partial Derivatives and the Chain Rule, Taylor’s formula, Maxima and Minima |
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Prof. S. Thangavelu Professor, Department of Mathematics IISC Bangalore |
6 |
Complex Analysis: Analytic functions, Harmonic functions, Power Series, Taylor's series, Complex Integrations, Rouché’s theorem and applications of the Residue Theorem, with an emphasis on computing/estimating improper Riemann integrals via contour integration. |
|
Prof. R. Venkatesh Assistant Professor, Department of Mathematics IISC, Bangalore |
6 |
Linear Algebra: Vector spaces, Bases; Linear transformations; Eigen values and eigen vectors; Diagonalisation and Triangularisation of linear operators; Determinants of linear transformations and their elementary properties.
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Prof. Thirupathi Gudi Professor, Department of Mathematics IISC Bangalore |
6 |
Multivariable calculus Part 2: Evaluation of multiple integrals, change of order of integration, Gradient, divergence, curl, etc. Greens' theorem and Stoke's theorem, evaluation of Integrals using them, Inverse function theorem |
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
- 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
- Complex analysis:
S. Ponnusamy, Foundations of Complex Analysis
S. Ponnusamy and H. Silverman, Complex Variables with Applications
L. V. Ahlfors, Complex Analysis
James Ward Brown and Ruel V. Churchill, Complex Variables and Applications Erwin Kreyszig, Advanced Engineering Mathematics
Names of the tutor(s) / course associate with their affiliation and status:
1. Dr. Abhishek Das, Assistant Professor, VIT Vellore
2. Dr. Ankush Chanda, Assistant Professor, VIT Vellore
3. Dr. Gouranga Mallick, Assistant Professor, VIT Vellore
Time Table
Time-table(with names of speakers and tutors):
|
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 5.05-5.30 |
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(name of the speaker |
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(name of the speaker) |
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Name of the speaker |
Name of the speaker/tutor |
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Mon |
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GB |
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ST |
GB |
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ST |
VR/AD |
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Tues |
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ST |
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GB |
ST |
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GB |
TG/AC |
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Wed |
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GB |
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ST |
GB |
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ST |
VR/GM |
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Thu |
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TG |
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RV |
TG |
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RV |
VP/AD |
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Fri |
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RV |
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TG |
RV |
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TG |
ST/AC |
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Sat |
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TG |
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RV |
TG |
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RV |
VP/ GM |
GB: Prof. G. Bharali
ST: Prof. S. Thangavelu
TG: Prof. Thirupathi Gudi
RV: Prof. R. Venkatesh
AD: Dr. Abhishek Das
AC: Dr. Ankush Chanda
GM: Dr. Gouranga Mallick