mat3cz complex analysis
COMPLEX ANALYSIS
MAT3CZ
2019
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 previous years. 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. Students will apply theoretical content knowledge and graduate capabilities in their practical classes. This subject addresses La Trobe's Innovation and Entrepreneurship Essential. Innovation and Entrepreneurship entails developing the ability to tackle problems creatively, generating new ideas, taking calculated risks and creating change to achieve ambitions - now and in the future.
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 text Complex Analysis available on LMS | Preliminary | . | . |
Graduate capabilities & intended learning outcomes
01. Differentiate and integrate functions defined on the complex plane.
- Activities:
- Modelled in lectures, with reinforcement in practice classes and marked feedback in assignments.
- Related graduate capabilities and elements:
- 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 and a group project.
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Speaking,Cultural Literacy)
- Literacies and Communication Skills(Speaking,Cultural 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)
- Personal and Professional Skills(Teamwork including leadership and working in groups,Autonomy and independence,Ethical behaviour,Adaptability Skills,Study and Learning Skills)
- Personal and Professional Skills(Teamwork including leadership and working in groups,Autonomy and independence,Ethical behaviour,Adaptability Skills,Study and Learning Skills)
- Personal and Professional Skills(Teamwork including leadership and working in groups,Autonomy and independence,Ethical behaviour,Adaptability Skills,Study and Learning Skills)
- Personal and Professional Skills(Teamwork including leadership and working in groups,Autonomy and independence,Ethical behaviour,Adaptability Skills,Study and Learning Skills)
- Personal and Professional Skills(Teamwork including leadership and working in groups,Autonomy and independence,Ethical behaviour,Adaptability Skills,Study and Learning Skills)
- 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 and a group project
- Related graduate capabilities and elements:
- Literacies and Communication Skills(Speaking,Cultural Literacy)
- Literacies and Communication Skills(Speaking,Cultural 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)
- Personal and Professional Skills(Teamwork including leadership and working in groups,Autonomy and independence,Ethical behaviour,Adaptability Skills,Study and Learning Skills)
- Personal and Professional Skills(Teamwork including leadership and working in groups,Autonomy and independence,Ethical behaviour,Adaptability Skills,Study and Learning Skills)
- Personal and Professional Skills(Teamwork including leadership and working in groups,Autonomy and independence,Ethical behaviour,Adaptability Skills,Study and Learning Skills)
- Personal and Professional Skills(Teamwork including leadership and working in groups,Autonomy and independence,Ethical behaviour,Adaptability Skills,Study and Learning Skills)
- Personal and Professional Skills(Teamwork including leadership and working in groups,Autonomy and independence,Ethical behaviour,Adaptability Skills,Study and Learning Skills)
- 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:
- 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:
- 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, 2019, Semester 1, Day
Overview
Online enrolmentYes
Maximum enrolment sizeN/A
Enrolment information
Subject Instance Co-ordinatorPeter Van Der Kamp
Class requirements
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.
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.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| Four mathematical assignments (1250 word equiv total) | 25 | 01, 02, 03, 04, 05 | |
| One 2 hour written exam (2000 words equivalent) | 50 | 01, 02, 03, 04, 05 | |
| One group project (3600 word equiv for group of four students, 900 words per student) | Students are to comment on the engagement of their group members. Individual marks may depend on their engagement. | 25 | 02, 03 |