# Singapore University of Social Sciences

## Analysis II : Power Series and Calculus (MTH206)

### Synopsis

MTH206 introduces the analysis of pure mathematics, Topics include operations such as differentiation and integration, arising from infinite limiting processes. Students should have a sound knowledge of mathematics, as developed in Analysis I.

Level: 2
Credit Units: 5
Presentation Pattern: Every January

### Topics

• Limits
• Limits of functions
• Continuity
• Uniform continuity
• Definition of differentiation
• Properties of differentiable functions
• Define Riemann integral
• Integration
• Fundamental Theorem of Calculus
• Taylor’s Theorem
• Convergence of power series
• Manipulation of power series
• The general binomial theorem

### Learning Outcome

• Show how to prove a mathematical statement in analysis/calculus.
• Calculate the limit/derivative of real-valued functions.
• Determine the radius/interval of convergence of given power series.
• Apply the epsilon delta definition of limits to analysis problems.
• Compute the first few terms of the Taylor series of analytic functions.
• Use the Taylor polynomial of a given real-valued function to approximate the value of the function around a point up to the desired degree of accuracy.