Introduction Class
Sequences and series of functions, pointwise and uniform convergence
Uniform convergence , Mn-test
Test for convergence of a series
Continue, Weierstrass M-test
Abel’s Test
Dirichlet’s tests
Cauchy criterion for uniform convergence
Uniform convergence and continuity
Uniform convergence and integration
Power series
Tauber’s theorems, uniqueness theorem for power series
Taylor's theorem, Rearrangements of terms of a series
Riemann’s theorem and examples
Introduction class of Functions of several variables, linear transformations
Linear transformations-properties and theorems
Derivatives in an open subset of Rn
Chain rule, Partial derivatives
Interchange of the order of differentiation
Taylor’s theorem
Contraction mapping, Banach contraction theorem