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Advanced Calculus

Topology of Euclidean spaces. Bolzano-Weierstrass and Heine-Borel Theorems. Continuity and uniform continuity. Differentiability, Mean value theorems, Taylor's theorem. Sequences and series of real numbers and power series. Pointwise and uniform convergence of sequences and series of functions. Riemann-Stieltjes Integral.

Differentiability of functions of several variables. Inverse function theorem. Implicit function theorem. Multiple integrals. Line and surface integrals. Green's Theorem, Stokes' Theorem, Divergence Theorem.


References:

1.
Walter Rudin, Principles of Mathematical Analysis
2.
Tom M. Apostol, Mathematical Analysis.
3.
R. Creighton Buck, Advanced Calculus.



Peter Monk
2002-08-27