MATHS 2101 - Multivariable & Complex Calculus II

North Terrace Campus - Semester 1 - 2015

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
    Course Multivariable & Complex Calculus II
    Coordinating Unit School of Mathematical Sciences
    Term Semester 1
    Level Undergraduate
    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 Staff

    Course Coordinator: Professor Michael Murray

    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.
    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)
    Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. 1,2,3,4
    The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 3,4
    An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 4
    Skills of a high order in interpersonal understanding, teamwork and communication. 5
    A proficiency in the appropriate use of contemporary technologies. 4,5
    A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. 1,2,3,4,5
    An awareness of ethical, social and cultural issues within a global context and their importance in the exercise of professional skills and responsibilities. 4,5
  • Learning Resources
    Required 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.
    Workload

    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.

    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.

  • 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
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