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| M.S. Advanced Calculus Syllabus |
- Functions of One Variable
- Axioms for real numbers, sequences, infinite series, compact sets
- Continuity, continuity and compactness, intermediate value theorem, differentiability, Rolle's theorem, mean value theorem, Taylor's theorem
- Reimann integral, improper integrals
- Uniform convergence of sequences and series of functions, interchange of limiting operations
- Elementary functions
- Functions of bounded variation
- Functions of Several Variables
- Directional derivatives
- Differentiability
- Chain rule
- Inverse and implicit function theorems
- Taylor's theorem
- Change of variables in multiple integrals
- Vector Analysis
- Gradient, divergence and curl
- Vector identities
- Line, surface and volume integrals
- Conservative fields
- Gauss, Green and Stokes theorem
- Orthogonal curvilinear coordinates
| References |
Ross: Elementary Analysis: The Theory of Calculus
Rudin: Principles of Mathematical Analysis
Buck: Advanced Calculus
Apostol: Mathematical Analysis
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