Course Archives Theoretical Statistics and Mathematics Unit
Course: Analysis of Several Variables
Instructor: T S S R K Rao
Room: G25
Time: Currently offered
Level: Postgraduate
Syllabus
Past Exams


Syllabus:Differentiability of maps from Rm to Rn and the derivative as a linear map. Higher derivatives, Chain Rule, Taylor expansions in several variables, Local maxima and minima, Lagrange multiplier. Multiple integrals, Existence of the Riemann integral for sufficiently well-behaved functions on rectangles, i.e., product of intervals. Multiple integrals expressed as iterated simple integrals. Brief treatment of multiple integrals on more general domains. Change of variables and the Jacobian formula, illustrated with plenty of examples. Inverse and implicit functions theorems. Picards Theorem. Curves in R^2 and R^3. Line integrals, Surfaces in R^3, Surface integrals, Integration of forms, Divergence, Gradient and Curl operations, Greens, Strokes and Gauss (Divergence) theorems.

Suggested Texts:
1. M. Spivak, Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus, Benjamin/Cummings (1965).
2. W. Rudin, Principles of Mathematical Analysis, Mc Graw-Hill Ed Asia (1953).
3. T. Apostol, Mathematical Analysis, Narosa Pub House (2002).
4. R. Courant and F. John, Introduction to Calculus and Analysis Vol II, Springer (1989).
5. T. Apostol, Calculus (Vol 2), Wiley Eastern (1980).

Evaluation:
Midterm Exam 40 marks
Assignment -- marks
Final Exam 60 marks
Total 100 marks


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Past Exams
Midterm
10.pdf 12.pdf 14.pdf 16.pdf 18.pdf
Semestral
10.pdf 12.pdf 14.pdf 16.pdf
Supplementary and Back Paper
10.pdf 16.pdf

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