COMPLEX ANALYSIS

MAT3CZ

2018

Credit points: 15

This subject addresses La Trobe's Innovation and Entrepreneurship Essential. Innovation and Entrepreneurship is about using your creativity to generate new ideas, understand and solve complex problems and thrive in a fast-changing world.

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

Readings

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsSubject printed text Complex Analysis available from BookshopPreliminary..

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,Cultural Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy,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)
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 (Writing,Quantitative Literacy,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 (Writing,Quantitative Literacy,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:
Literacies and Communication Skills (Writing,Quantitative Literacy,Cultural Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy,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)
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,Cultural Literacy)
Literacies and Communication Skills (Writing,Quantitative Literacy,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)
Discipline -Specific Knowledge and Skills (Discipline-Specific Knowledge and Skills)

Subject options

Select to view your study options…

Start date between: and    Key dates

Melbourne, 2018, 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 assignments (1250 word equiv total)25 01, 02, 03, 04, 05
One 2 hour written exam50 01, 02, 03, 04, 05
One group project (3600 word equiv for group of four students, 900 words per student)25 02, 03