COMPLEX ANALYSIS

MAT3CZ

2015

Credit points: 15

Subject outline

The subject extends calculus to the complex domain, where many beautiful new features appear. This gives a new perspective to many topics studied in first and second year. The new tools covered are also very useful in applications to a wide variety of areas within mathematics, as well as in other mathematically oriented sciences. The practice classes within the subject play a key role in helping the students to learn the subject content and develop graduate capabilities.

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorPeter Van Der Kamp

Available to Study Abroad StudentsYes

Subject year levelYear Level 3 - UG

Exchange StudentsYes

Subject particulars

Subject rules

Prerequisites MAT2ANA or MAT2VCA

Co-requisitesN/A

Incompatible subjectsN/A

Equivalent subjectsN/A

Special conditionsN/A

Readings

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsSubject printed text Complex Analysis available from BookshopPreliminaryN/AN/A

Graduate capabilities & intended learning outcomes

01. Differentiate and integrate functions of a complex variable, evaluating contour integrals using the Residue Theorem and some real integrals using contour integration.

Activities:
Modelled in lectures, with reinforcement in practice classes and marked feedback in assignments.
Related graduate capabilities and elements:
Critical Thinking (Critical Thinking)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Creative Problem-solving (Creative Problem-solving)
Discipline-specific GCs (Discipline-specific GCs)
Inquiry/ Research (Inquiry/ Research)

02. Solve problems by exploring the distinctive features of complex functions, such as the possible existence of branches.

Activities:
Modelled in lectures, with reinforcement in practice classes and marked feedback in assignments.
Related graduate capabilities and elements:
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Critical Thinking (Critical Thinking)
Inquiry/ Research (Inquiry/ Research)
Discipline-specific GCs (Discipline-specific GCs)
Creative Problem-solving (Creative Problem-solving)
Writing (Writing)

03. Construct complex extensions of the familiar rational, logarithm, exponential and trigonometric functions.

Activities:
Demonstrated in lectures, with reinforcement in practice classes and marked feedback in assignments.
Related graduate capabilities and elements:
Creative Problem-solving (Creative Problem-solving)
Inquiry/ Research (Inquiry/ Research)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Discipline-specific GCs (Discipline-specific GCs)
Critical Thinking (Critical Thinking)

04. Calculate Taylor and Laurent series for complex analytic functions and classify singularities.

Activities:
Modelled in lectures, with reinforcement in practice classes and marked feedback in assignments.
Related graduate capabilities and elements:
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Critical Thinking (Critical Thinking)
Writing (Writing)
Inquiry/ Research (Inquiry/ Research)
Creative Problem-solving (Creative Problem-solving)
Discipline-specific GCs (Discipline-specific GCs)

05. Apply a range of techniques for the calculation and inversion of Fourier transforms and can apply the theory of Fourier transforms in the solving of differential equations

Activities:
Demonstrated in lectures, with reinforcement in practice classes and marked feedback in assignments.
Related graduate capabilities and elements:
Writing (Writing)
Inquiry/ Research (Inquiry/ Research)
Quantitative Literacy/ Numeracy (Quantitative Literacy/ Numeracy)
Discipline-specific GCs (Discipline-specific GCs)
Critical Thinking (Critical Thinking)
Creative Problem-solving (Creative Problem-solving)

Subject options

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Start date between: and    Key dates

Melbourne, 2015, Semester 1, Day

Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorPeter Van Der Kamp

Class requirements

Lecture Week: 10 - 22
Two 1.0 hours lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

Practical Week: 10 - 22
One 1.0 hours practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

Assessments

Assessment elementComments% ILO*
Four mathematical assignments30 01, 02, 03, 04, 05
One 3 hour written exam70 01, 02, 03, 04, 05