Calculus and Analysis 2
Module code: MA1016
This module builds upon the already discussed topics in MA1015. For example, previously studied topics let us understand many new things: When does an infinite sequence of numbers converge to a limit? When does an infinite sum converge to a limit? When does a function have a Taylor series representation? And so forth. In particular, we will study sequence convergence using key theorems like the Squeeze Theorem, and the Monotone Convergence Theorem which help us rigorously analyse sequence behaviour without always needing explicit limits. The study of the convergence of series using several important tests is also the part of this course. We will discuss the Integral Test that assesses convergence by comparing a series to a corresponding improper integral, and the Comparison Test that talks about convergence using a known benchmark series. Similarly, the well-known Ratio and Root Tests for checking the absolute convergence of the series will be studied. This module will also focus on generalising the already studied topics of continuity/differentiability of functions of one variable to two or more variables. Lastly, attention will be given to study some methods for finding the solutions of differential equations, in particular, for second order differential equations.