Singapore University of Social Sciences

Fundamentals of Complex Analysis

Applications Open: 01 October 2019

Applications Close: 30 November 2019

Next Available Intake: January 2020

Schemes: Lifelong Learning Credit (L2C)

Language: English

Duration: 6 months

Fees: To be confirmed

Area of Interest: Science & Technology


Synopsis

Complex numbers, complex functions and the analysis of functions of one complex varaible are introduced. The understanding of the basic theory and the techniques of complex analysis is the ket to succesful applications. The course aims to introduce the basic fundamental concepts and show how they are woven together to provide a powerful tool for application.

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

Topics

  • Complex number field.
  • Complex functions.
  • Sequences.
  • Subsets of the complex plane.
  • Continuous functions.
  • Limits.
  • Complex differentiation.
  • Paths, rectifiable path, smooth path, length of a path.
  • Contour and contour integration.
  • Cauchy’s integral theorem.
  • Cauchy’s integral formula.
  • Taylor and Laurent series, and residues.

Learning Outcome

  • Interpret properties of complex numbers and complex valued functions.
  • Solve convergence problems of complex valued sequences and series.
  • Employ limits, continuity of complex valued functions.
  • Test the derivative of a complex valued function.
  • Compute the integral of a complex valued function, and relate to various open and closed paths.
  • Indicate the nature of singularities of complex functions.
  • Construct a range of mathematical techniques to solve a variety of complex valued analysis problems.
  • Formulate solutions to problems individually and/or as part of a group.
  • Analyze and solve a number of problem sets within strict deadlines.
Back to top
Back to top