Singapore University of Social Sciences

Advanced Calculus

Advanced Calculus (MTH318)

Synopsis

MTH318 Advanced Calculus will introduce students to the calculus of series, sequences and series of functions. Students will be exposed to various tests of convergence of series as well as notions of pointwise and uniform convergence of sequences of functions. The emphasis of the course will be on applications of the results presented to solve problems.

Level: 3
Credit Units: 5
Presentation Pattern: Every January

Topics

  • Infinite series
  • Absolute convergence
  • Conditional convergence
  • Tests for Absolute Convergence
  • Tests for Conditional Convergence
  • Pointwise and Uniform Convergence
  • Interchange of Limits
  • Series of Functions
  • Weierstrass M-test
  • Power series
  • Interval of convergence
  • Termwise differentiation

Learning Outcome

  • Determine whether given series is absolutely convergent, conditionally convergent or divergent.
  • Show the validity of given mathematical statements in advanced calculus.
  • Discuss the convergence of sequences and functions.
  • Give counter-examples of mathematical statements in advanced calculus.
  • Calculate the uniform limit of functions and integrals.
  • Compute the interval of convergence for a given power series.
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