Krishna's - Advance Calculus

SYLLABUS- ADVANCE CALCULUS, Unit-I: Continuity, Sequential Continuity, properties of continuous functions,
Uniform continuity, chain rule of differentiability, Mean value theorems and their
geometrical interpretations, Darboux's intermediate value theorem for derivatives,
Taylor's theorem with various forms of remainders.
Unit-II: Limit and Continuity of functions of two variables, Taylor's theorem for
functions of two variables, Envelops, Evolutes, Maxima and minima for function of
two variables, Lagrange multiplier method, Jacobians.
Unit-III: Beta and Gamma functions, Double and triple integrals, Dirichlet
integral, change of order of integration in double integrals.
Unit-IV: Improper integrals, convergence of Comparison test,
Convergence of Abel's test, Dirichlet's test, Convergence of
examples, Convergence of beta and gamma functions.