## MATHS 2101 - Multivariable & Complex Calculus II

### North Terrace Campus - Semester 1 - 2016

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.

• General Course Information
##### Course Details
Course Code MATHS 2101 Multivariable & Complex Calculus II Mathematical Sciences Semester 1 Undergraduate North Terrace Campus 3 Up to 3.5 hours per week Y MATHS 1012 PURE MTH 2005, MATHS 2202 ongoing assessment 30%, exam 70%
##### Course Staff

Course Coordinator: Associate Professor Thomas Leistner

##### Course Timetable

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

• Learning Outcomes
##### Course Learning Outcomes
1. Demonstrate understanding of the basic concepts of calculus involving more than one real variable.
2. Demonstrate understanding of the basic concepts of calculus for one complex variable.
3. Be able to state and apply the major results in the course.
4. Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty.
5. Demonstrate skills in communicating mathematics orally and in writing.

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
3,5
• 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, defuse conflict and engage positively in purposeful debate
5
• Learning Resources
None.
##### Recommended Resources
1. Vector Calculus by J. E. Marsden and A. J. Tromba (Barr Smith Library 517 M364v.5)
2. Basic Complex Analysis by J. E. Marsden and M. J. Hoffman (Barr Smith Library 517.54 M364b)
##### Online 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. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/
• Learning & Teaching Activities
##### Learning & Teaching Modes
This 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 Summary
Lecture Outline
1. Geometry and topology of Rn (4 lectures)
2. Functions of many variables (3 lectures)
3. Differentiation of scalar and vector functions (5 lectures)
4. Higher order derivatives and extrema (4 lectures)
5. Integration in Rn (5 lectures)
6. Integration over curves, surfaces and volumes (3 lectures)
7. Green's, Stokes' and Gauss's theorems (3 lectures)
8. Complex differentiation (4 lectures)
9. Complex integration and Cauchy's theorems (3 lectures)
Tutorials in weeks 3, 5, 7, 9, 11 will be based on the material covered since the previous tutorial. Tutorial exercises will be distributed in the week before each tutorial.
• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

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

##### Assessment Summary
 Assessment task Task type Due Weighting Learning outcomes Examination Summative Examination period 70% All Test Summative and formative Week 8 15% All Assignments Summative and formative Weeks 3, 5, 7, 9, 11 3% each All
##### Assessment Related Requirements
An aggregate score of 50% is required to pass the course.
##### Assessment Detail
 Assessment Item Distributed Due Weighting Assignment 1 Week 2 Week 3 3% Assignment 2 Week 4 Week 5 3% Assignment 3 Week 6 Week 7 3% Assignment 4 Week 8 Week 9 3% Assignment 5 Week 10 Week 11 3% Test Week 8 Week 8 15%
##### Submission
Homework 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)
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.

• 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.

• Student Support
• Policies & Guidelines
• 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 studentâ€™s disciplinary procedures.

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

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