Calculus Ii

AY2016/2017 Semester 2

Definite integrals, Fundamental Theorems of Calculus, area of plane regions, volumes of solids, length of arcs. Mean Value Theorem for integrals, other applications of the definite integral. Techniques of integration, numerical integration, improper integrals. Sequences, monotonic and bounded sequences, Newton's method. Infinite series, tests for convergence and divergence, alternating series, absolute and conditional convergence. Power series, differentiation and integration of power series, Taylor series, Taylor's formula, binomial series, Fourier series.