MATH365-15S2 (C) Semester Two 2015

Applications of Complex Variables

15 points

Details:
Start Date: Monday, 13 July 2015
End Date: Sunday, 15 November 2015
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 24 July 2015
  • Without academic penalty (including no fee refund): Friday, 9 October 2015

Description

Applications of complex variable theory in the physical and engineering sciences. Contour integration. Conformal mappings.

Complex variables is essentially an extension of calculus to complex- valued functions of a complex variable. We will show that such an extension follows a fairly natural course. The mathematical rewards are tremendous and far-reaching, and beautiful results abound.
There is a variety of applications of complex functions in Engineering and Science, and it also leads naturally to the field of special functions which itself has many applications. This course will cover the basic theory with an emphasis on some of these applications. It is strongly recommended for students in Mathematics, Engineering and Physics.

Topics:
Complex numbers and functions of a complex variable. Analytic functions and Cauchy-Riemann equations. Cauchy's theorem. Taylor and Laurent series. Singularities. Residue theorem and evaluation of definite integrals.

Learning Outcomes

At the end of the course the student will be familiar with the following topics:
 - complex numbers and functions of a complex variable
 - analytic functions and the Cauchy-Riemann equations
 - Cauchy's theorem.  Taylor and Laurent series.  Singularities

Students will be able to evaluate definite integrals and  calculate Laplace transforms using the calculus of residues

Students will also be familiar with:
 - conformal mappings and applications to electrostatics, heat and fluid flow
 - Legendre polynomials, properties of these, and applications to sphere in a  uniform electric field, potential of a ring of charge

Alternatively students will be familiar with the properties and applications of another family of special functions.

Prerequisites

MATH264, EMTH204, (MATH261 and MATH262), EMTH202, MATH243, MATH202 or MATH240; or, a high level of achievement in EMTH210 with Head of School approval.

Restrictions

MATH342

Course Coordinator / Lecturer

Rick Beatson

Lecturer

Ngin-Tee Koh

Assessment

Assessment Due Date Percentage 
Tutorials 10%
Test 30%
Final Examination 60%

Indicative Fees

Domestic fee $699.00

International fee $3,450.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH365 Occurrences

  • MATH365-15S2 (C) Semester Two 2015
Previous year Next year