Course Title: Residues and Integral Transforms

Part A: Course Overview

Course Title: Residues and Integral Transforms

Credit Points: 12.00

Course Code	Campus	Career	School	Learning Mode	Teaching Period(s)
MATH2159	City Campus	Undergraduate	145H Mathematical & Geospatial Sciences	Face-to-Face	Sem 1 2006

Course Coordinator: Gary Fitz-Gerald

Course Coordinator Phone: +61 3 9925 2278

Course Coordinator Email: garyfitz@rmit.edu.au

Pre-requisite Courses and Assumed Knowledge and Capabilities

A passing grade in MATH1129 or its equivalent.

Course Description

Residues and Integral Transforms introduces the role of integral transforms within the context of mathematical physics to the solution of partial differential equations and the representation of waves. It further develops the facility for determining transforms and their inverses using contour integration methods and for understanding their properties, advantages over other standard methods and their practical limitations.

Objectives/Learning Outcomes/Capability Development

On successful completion of this course, you will be able to:
• Evaluate Laplace, Fourier, Mellin, Hilbert and Hankel transforms using contour integration methods where appropriate
• Determine Laurent series expansions
• Identify singularities of complex-valued functions
• Solve a range of mathematical models of physical problems using the most appropriate transform in each case

These attributes directly support the graduate capabilities prescribed in your program guide under the headings GC1, 2, 3 & 5.

Overview of Learning Activities

The key concepts and their application to practical problem solving will be explained and illustrated in lectures.

Assignments and/or WebLearn quizzes and tests will provide feedback on your mastery of the major concepts developed in this course.

Overview of Learning Resources

The learning resources needed for each module will be made available at the required stages during the course. Some of this material will also be available on RMIT’s DLS.

Overview of Assessment

There will be two 2-hour exams at the end of the semester which will gauge your understanding of the modules studied within the semester. One 2-hour exam will cover the mathematical development of the theory. The other 2-hour exam will cover applications to physical problems.
WebLearn tests and/or written assignments will also contribute to the assessment in some of the modules.