Singapore University of Social Sciences

Analysis II : Power Series and Calculus (MTH206)

Applications Open: 01 October 2019

Applications Close: 15 December 2019

Next Available Intake: January 2020

Course Types: Modular Undergraduate Course

Language: English

Duration: 6 months

Fees: To be confirmed

Area of Interest: Science & Technology

Schemes: Lifelong Learning Credit (L2C)

Funding: To be confirmed


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
E-Learning: BLENDED - Learning is done MAINLY online using interactive study materials in Canvas. Students receive guidance and support from online instructors via discussion forums and emails. This is supplemented with SOME face-to-face sessions. If the course has an exam component, this will be administered on-campus.

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

  • Describe various limits and relate these to properties of functions.
  • Compute the derivative of functions from first principles.
  • Implement the integral of functions from first principles.
  • Analyze convergence and representation properties of infinite power series.
  • Identify the power series and associated error representation of functions.
  • Employ properties of power series, including convergence, radius of convergence and their representation of functions.
  • Apply a range of mathematical techniques to solve a variety of quantitative problems.
  • Analyze and solve problems individually and/or as part of a group.
  • Solve a number of problem sets within strict deadlines.
  • Solve abstract mathematical problems using logical and systematic.
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