PURE MTH 3019 - Complex Analysis III
North Terrace Campus - Semester 1 - 2023
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General Course Information
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 Planner.
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Learning Outcomes
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.University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University 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.
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Learning Resources
Required Resources
None.Recommended Resources
In increasing order of difficulty, the following books are available in the BSL. The closest to the level of this course is 2.
1. Churchhill & Brown: Complex Variables and Applications; 517.53 C563
2. Marsden & Hoffman: Basic Complex Analysis; 517.54 M363b
3. Conway: Functions of One Complex Variable; 517.53 C767f
4. Ahlfors: An Introduction to the Theory of Analytic Functions of One Complex Variable; 517.53 A28Online Learning
This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, sample solutions, discussion boards, etc. It is recommended that students make appropriate use of these resources. -
Learning & Teaching Activities
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. -
Assessment
The University'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 20% 1,2,3,6 Quizzes Formative and summative Weekly 5% 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 0.5% Quiz 2 Week 3 Week 3 0.5% Assignment 2 Week 3 Week 4 5% Quiz 3 Week 4 Week 4 0.5% Quiz 4 Week 5 Week 5 0.5% Mid-semester test Week 6 Week 6 20% Quiz 5 Week 7 Week 7 0.5% Assignment 3 Week 7 Week 8 5% Quiz 6 Week 8 Week 8 0.5% Quiz 7 Week 9 Week 9 0.5% Assignment 4 Week 9 Week 10 5% Quiz 8 Week 10 Week 10 0.5% Quiz 9 Week 11 Week 11 0.5% Assignment 5 Week 11 Week 12 5% Quiz 10 Week 12 Week 12 0.5% 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 Access Adelaide.
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Student Feedback
The University 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 University 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.
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Student Support
- Academic Integrity for Students
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- Academic Support with writing and study skills
- Careers Services
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- Student Life Counselling Support - Personal counselling for issues affecting study
- Students with a Disability - Alternative academic arrangements
- YouX Student Care - Advocacy, confidential counselling, welfare support and advice
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Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
- Academic Credit Arrangements Policy
- Academic Integrity Policy
- Academic Progress by Coursework Students Policy
- Assessment for Coursework Programs Policy
- Copyright Compliance Policy
- Coursework Academic Programs Policy
- Elder Conservatorium of Music Noise Management Plan
- Intellectual Property Policy
- IT Acceptable Use and Security Policy
- Modified Arrangements for Coursework Assessment Policy
- Reasonable Adjustments to Learning, Teaching & Assessment for Students with a Disability Policy
- Student Experience of Learning and Teaching Policy
- Student Grievance Resolution Process
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