Singapore University of Social Sciences

Analysis II : Power Series and Calculus

Analysis II : Power Series and Calculus (MTH206)


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


  • 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.
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