mat3cz complex analysis
COMPLEX ANALYSIS
MAT3CZ
2017
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
Learning resources
Readings
| Resource Type | Title | Resource Requirement | Author and Year | Publisher |
|---|---|---|---|---|
| Readings | Subject printed text Complex Analysis available from Bookshop | Preliminary | . | . |
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:
- Literacies and Communication Skills(Writing,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Discipline -Specific Knowledge and Skills(Discipline-Specific Knowledge and Skills)
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:
- Literacies and Communication Skills(Writing,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Discipline -Specific Knowledge and Skills(Discipline-Specific Knowledge and Skills)
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:
- Literacies and Communication Skills(Writing,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Discipline -Specific Knowledge and Skills(Discipline-Specific Knowledge and Skills)
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:
- Literacies and Communication Skills(Writing,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Discipline -Specific Knowledge and Skills(Discipline-Specific Knowledge and Skills)
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:
- Literacies and Communication Skills(Writing,Quantitative Literacy)
- Literacies and Communication Skills(Writing,Quantitative Literacy)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Inquiry and Analytical Skills(Critical Thinking,Creative Problem-solving,Inquiry/Research)
- Discipline -Specific Knowledge and Skills(Discipline-Specific Knowledge and Skills)
Subject options
Select to view your study options…
Melbourne, 2017, Semester 1, Day
Overview
Online enrolmentYes
Maximum enrolment sizeN/A
Enrolment information
Subject Instance Co-ordinatorPeter Van Der Kamp
Class requirements
PracticalWeek: 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.
LectureWeek: 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.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| Four mathematical assignments (1400 word equiv total) | 30 | 01, 02, 03, 04, 05 | |
| One 3 hour written exam | 70 | 01, 02, 03, 04, 05 |