Course Archives Theoretical Statistics and Mathematics Unit | ||||||||||||||
Course: Analysis of Several Variables Instructor: Aniruddha C Naolekar Room: G25 Time: Currently offered Level: Postgraduate |
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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:
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Midterm
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