Singapore University of Social Sciences

Applied Complex Analysis (MTH302)

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

Some deep theorems of complex analysis are developed and applications to areas such as fluid mechanics and complex sets are studied. MTH302 follows on from MTH301.

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

Topics

  • Residue theorem.
  • Improper integrals.
  • Modulus of a differentiable function.
  • Schwartz’s lemma.
  • The argument principle.
  • Rouche’s theorem, local mapping and the logarithmic function.
  • Evaluation of real integrals.
  • The probability integral.
  • Analytic continuation.
  • Riemann mapping theorem and Möbious transformations.
  • Theorem on harmonic functions, Julia and Mandelbrot sets.
  • Flows and streamlines.

Learning Outcome

  • Use the Residue Theorem.
  • Solve contour integrals.
  • Verify when an entire function is a polynomial and when a meromorphic function is a rational function or harmonic.
  • Apply the notion of an analytic function and the maximum modulus principle.
  • Calculate improper integrals using contour integration.
  • Demonstrate when to use various complex transformations.
  • Construct a range of mathematical techniques to solve a variety of problems related to complex valued analysis.
  • Formulate solutions to problems individually and/or as part of a group.
  • Analyze and solve a number of problem sets within strict deadlines.
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