MATHS 7101 - Multivariable & Complex Calculus
North Terrace Campus - Semester 1 - 2018
General Course Information
Course Code MATHS 7101 Course Multivariable & Complex Calculus Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3.5 hours per week Available for Study Abroad and Exchange Y Prerequisites MATHS 1012 Incompatible PURE MTH 2005, MATHS 2202 Course Description The mathematics required to describe most "real life" systems involves functions of more than one variable, so the differential and integral calculus developed in a first course in Calculus must be extended to functions of more variables. In this course, the key results of one-variable calculus are extended to higher dimensions: differentiation, integration, and the link between them provided by the Fundamental Theorem of Calculus are all generalised. The machinery developed can be applied to another generalisation of one-variable Calculus, namely to complex calculus, and the course also provides an introduction to this subject. The material covered in this course forms the basis for mathematical analysis and application across an extremely broad range of areas, essential for anyone studying the hard sciences, engineering, or mathematical economics/finance.
Topics covered are: introduction to multivariable calculus; differentiation of scalar- and vector-valued functions; higher-order derivatives, extrema, Lagrange multipliers and the implicit function theorem; integration over regions, volumes, paths and surfaces; Green's, Stokes' and Gauss's theorems; differential forms; curvilinear coordinates; an introduction to complex numbers and functions; complex differentiation; complex integration and Cauchy's theorems; and conformal mappings.
Course Coordinator: Dr Thomas Leistner
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes
- Demonstrate understanding of the basic concepts of calculus involving more than one real variable.
- Demonstrate understanding of the basic concepts of calculus for one complex variable.
- Be able to state and apply the major results in the course.
- Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty.
- 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) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
all Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
all Teamwork and communication skills
- developed from, with, and via the SGDE
- honed through assessment and practice throughout the program of studies
- encouraged and valued in all aspects of learning
3 Career and leadership readiness
- technology savvy
- professional and, where relevant, fully accredited
- forward thinking and well informed
- tested and validated by work based experiences
5 Self-awareness and emotional intelligence
- a capacity for self-reflection and a willingness to engage in self-appraisal
- open to objective and constructive feedback from supervisors and peers
- able to negotiate difficult social situations, diffuse conflict and engage positively in purposeful debate
- Vector Calculus by J. E. Marsden and A. J. Tromba (Barr Smith Library 517 M364v.5)
- Basic Complex Analysis by J. E. Marsden and M. J. Hoffman (Barr Smith Library 517.54 M364b)
Online LearningThis 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. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/
Learning & Teaching Activities
Learning & Teaching ModesThis course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Lectures 35 87.5 Tutorials 5 20.5 Assignments 6 48 Total 156
Learning Activities SummaryLecture Outline
- Geometry and topology of Rn (4 lectures)
- Functions of many variables (4 lectures)
- Differentiation of scalar and vector functions (5 lectures)
- Higher order derivatives and extrema (5 lectures)
- Integration in R2 and R3 (4 lectures)
- Integration over curves and Greens Theorem (4 lectures)
- Integration over surfaces, Stokes' and Gauss's theorems (3 lectures)
- Complex calculus (6 lectures)
Small Group Discovery ExperienceIn the tutorials.
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 task Task type Due Weighting Learning outcomes Examination Summative Examination period 70% All Test Summative and formative Week 7 15% All Assignments Summative and formative Weeks 2, 4, 6, 8, 10, 12 2.5% each All
Assessment Related RequirementsAn aggregate score of 50% is required to pass the course.
Assessment Item Distributed Due Weighting Assignment 1 Week 1 Week 2 2.5% Assignment 2 Week 3 Week 4 2.5% Assignment 3 Week 5 Week 6 2.5% Assignment 4 Week 7 Week 8 2.5% Assignment 5 Week 9 Week 10 2.5% Assignment 6 Week 11 Week 12 2.5% Test Week 7 Week 7 15%
SubmissionHomework assignments must be submitted on time with a signed assessment cover sheet. Late assignments will not be accepted. Assignments will be returned within two weeks. Students may be excused from an assignment for medical or compassionate reasons. Documentation is required and the lecturer must be notified as soon as possible.
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.
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.
- Academic Support with Maths
- Academic Support with writing and speaking skills
- Counselling Service - Personal counselling for issues affecting study
- International Student Care - Ongoing support
- Student Care - Advocacy, confidential counselling, welfare support and advice
- Students with a Disability - Alternative academic arrangements
- Reasonable Adjustments to Teaching & Assessment for Students with a Disability Policy
Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
- Academic Credit Arrangement Policy
- Academic Honesty Policy
- Academic Progress by Coursework Students Policy
- Assessment for Coursework Programs
- 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
- Student Experience of Learning and Teaching Policy
- Student Grievance Resolution Process
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