PURE MTH 3019 - Complex Analysis III

North Terrace Campus - Semester 1 - 2022

When the real numbers are replaced by the complex numbers in the definition of the derivative of a function, the resulting (complex) differentiable functions turn out to have many remarkable properties not enjoyed by their real analogues. These functions, usually known as holomorphic functions, have numerous applications in areas such as engineering, physics, differential equations and number theory, to name just a few. The focus of this course is on the study of holomorphic functions and their most important basic properties. Topics covered are: Complex numbers and functions; complex limits and differentiability; elementary examples; analytic functions; complex line integrals; Cauchy's theorem and the Cauchy integral formula; Taylor's theorem; zeros of holomorphic functions; Rouche's Theorem; the Open Mapping theorem and Inverse Function theorem; Schwarz' Lemma; automorphisms of the ball, the plane and the Riemann sphere; isolated singularities and their classification; Laurent series; the Residue Theorem; calculation of definite integrals and evaluation of infinite series using residues; Montel's Theorem and the Riemann Mapping Theorem.

Open All

Course Details

Course Code	PURE MTH 3019
Course	Complex Analysis III
Coordinating Unit	Mathematical Sciences
Term	Semester 1
Level	Undergraduate
Location/s	North Terrace Campus
Units	3
Contact	Up to 3 hours per week
Available for Study Abroad and Exchange	Y
Prerequisites	MATHS 2100 or MATHS 2101 or MATHS 2202 or ELEC ENG 2106
Assumed Knowledge	MATHS 2101
Assessment	Ongoing assessment, exam

Course Staff

Course Coordinator: Dr David Baraglia

Course Timetable

The full timetable of all activities for this course can be accessed from .

Course Learning Outcomes

1. Demonstrate understanding of the basic concepts underlying complex analyis.

2. Demonstrate familiarity with a range of examples of these concepts.

3. Prove basic results in complex analysis.

4. Apply the methods of complex analysis to evaluate definite integrals and infinite series.

5. Demonstrate understanding and appreciation of deeper aspects of complex analysis such as the Riemann Mapping theorem.

6. Demonstrate skills in communicating mathematics orally and in writing.

最新糖心Vlog Graduate Attribute	Course Learning Outcome(s)
Attribute 1: Deep discipline knowledge and intellectual breadth Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.	1,2,3,4,5
Attribute 2: Creative and critical thinking, and problem solving Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.	1,2,3,4
Attribute 3: Teamwork and communication skills Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.	6
Attribute 4: Professionalism and leadership readiness Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.	5

Learning & Teaching Modes

Each week there will be a one-hour workshop, a tutorial and a quiz. Weekly reading material will be assigned. It is expected that students have read this material before the workshop. The workshops will be a mix of lecturing, students working on problems, together and with guidance from the lecturer, and consulting. In weekly tutorials students will form small groups and work through tutorial problems and discuss them with the lecturer and their peers. Fortnightly homework assignments and weekly quizzes will help students strengthen their understanding of the theory and their skills in applying it, allowing them to gauge their progress.

Workload

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

Activity	Quantity	Workload Hours
Workshops	12	12
Assignments	5	50
Tutorials	12	24
Quizzes	10	10
Self-study		60
Total		156

Learning Activities Summary

	Lecture Schedule
Week 1	Complex numbers, functions and differentiation.
Week 2	Cauchy-Riemann equations. Elementary functions.
Week 3	Further examples, harmonic functions, complex series.
Week 4	Analytic functions. Complex antiderivatives.
Week 5	Integration of complex functions.
Week 6	Cauchy-Goursat theorem. The Cauchy integral formula.
Week 7	Consequences of the Cauchy integral formula.
Week 8	Taylor's theorem. Zeros of holomorphic functions.
Week 9	The open mapping and inverse function theorems. Isolated singularities of holomorphic functions.
Week 10	Meromorphic functions, Laurent series; residues.
Week 11	Applications of residues. Simply connected domains.
Week 12	The Riemann Mapping theorem.

The 最新糖心Vlog's policy on Assessment for Coursework Programs is based on the following four principles:

Assessment must encourage and reinforce learning.
Assessment must enable robust and fair judgements about student performance.
Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
Assessment must maintain academic standards.

Assessment Summary

Assessment Task	Task Type	Due	Weighting	Learning Outcomes
Exam	Summative	Examination Period	50%	All
Mid-semester test	Summative	Week 6	15%	1,2,3,6
Quizzes	Formative and summative	Weekly	10%	All
Assignments	Formative and summative	Even weeks	25%	All

Assessment Related Requirements

An aggregate score of 50% is required to pass the course.

Assessment Detail

Assessment	Set	Due	Weighting
Assignment 1	Week 1	Week 2	5%
Quiz 1	Week 2	Week 2	1%
Quiz 2	Week 3	Week 3	1%
Assignment 2	Week 3	Week 4	5%
Quiz 3	Week 4	Week 4	1%
Quiz 4	Week 5	Week 5	1%
Mid-semester test	Week 6	Week 6	15%
Quiz 5	Week 7	Week 7	1%
Assignment 3	Week 7	Week 8	5%
Quiz 6	Week 8	Week 8	1%
Quiz 7	Week 9	Week 9	1%
Assignment 4	Week 9	Week 10	5%
Quiz 8	Week 10	Week 10	1%
Quiz 9	Week 11	Week 11	1%
Assignment 5	Week 11	Week 12	5%
Quiz 10	Week 12	Week 12	1%

Submission

Assignments will have a maximum two-week turn-around time for feedback to students.

Course Grading

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
Grade	Mark	Description
FNS		Fail No Submission
F	1-49	Fail
P	50-64	Pass
C	65-74	Credit
D	75-84	Distinction
HD	85-100	High Distinction
CN		Continuing
NFE		No Formal Examination
RP		Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through .

Student Feedback

The 最新糖心Vlog places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the 最新糖心Vlog to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
Student Support
Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
Fraud Awareness

Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student鈥檚 disciplinary procedures.

The 最新糖心Vlog of Adelaide is committed to regular reviews of the courses and programs it offers to students. The 最新糖心Vlog of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.

Authorised by:	Deputy Vice-Chancellor and Vice-President (Academic)
Maintained by:	Course Outlines Administrator

最新糖心Vlog