APP MTH 7045 - Applied Mathematics Topic B

North Terrace Campus - Semester 1 - 2018

Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at http://www.maths.adelaide.edu.au

  • General Course Information
    Course Details
    Course Code APP MTH 7045
    Course Applied Mathematics Topic B
    Coordinating Unit School of Mathematical Sciences
    Term Semester 1
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Available for Study Abroad and Exchange Y
    Course Description Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at http://www.maths.adelaide.edu.au
    Course Staff

    Course Coordinator: Dr Barry Cox

    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes

    Course learning outcomes

    The course title is Classical Mechanics and the Calculus of Variations.

    The motion of material bodies is one of the oldest subjects in science. Indeed one of the earliest works of modern recognisable science, Newton's Principles of Natural Philosophy, dealt with this subject in some detail. From the pioneers like Newton, Euler, various Bernoullis, Hamilton and others we have a vast body of theory to draw on. Studying mechanics from a variational perspective leads to a number of advantages. These include that often physically relevant quantities like the angular momentum, the energy and other quantities are identified by the analysis. Another perhaps surprising advantage is that the techniques developed lend themselves to wide applicability, so that problems outside of classical mechanics can be efficiently analysed using these methods.

    In this course we will briefly summarise the elementary principles of mechanics and the calculus of variations. Thereafter we we tackle the two-body central force problem including virial theorem, Bertrand's theorem and the Laplace-Runge-Lenz vector. Thereafter we will look at rigid body mechanics including Euler angles and rotations and Coriolis force. After this and time permitting we will look at oscillators, Hamilton's formulation of mechanics and application of these principles to continuous media.

    Assumed knowledge: Differential Equations II, Multivariate and Complex Calculus II, Optimal Functions and Nanomechanics III

    Learning outcomes

    On successful completion of this course students will be able to:

    1. Be able to define critical mechanical quantities such as the work, kinetic and potential energy
    2. Formulate a variational model for physical problems
    3. Derive conservation laws for physical systems
    4. Solve problems of central force
    5. Describe the Hamiltonian formulation and derive the equations of motion.
    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
    all
    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
    all
  • Learning Resources
    Required Resources
    None.
    Recommended Resources
    Goldstein, Poole, Safko, 2002, Classical Mechanics, 3rd edition, Addison-Wesley.
    Online Learning
    MyUni will be used to provide electronic resources, such as lecture notes, assignment papers, sample solutions, discussion boards, etc. It is recommended that the students make appropriate use of these resources.

    See https://myuni.adelaide.edu.au/webapps/login/
  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on lectures and exercises as the primary learning mechanism for the material. A sequence of written and/or online 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 30 90
    Tutorials 6 18
    Assignments 5 48
    Total 156
    Learning Activities Summary
    1. Burgers equation and the split-step method
    2. Korteweg de Vries equation and the inverse scattering transform
    3. Schrödinger and sine-Gordon equations
    4. Stoke's waves and perturbation methods
  • 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
    Component Weighting Objective Assessed
    Assignments 30% all
    Exam 70% all
    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    Assessment Item Distributed Due Date Weighting
    Assignment 1 Week 2 Week 4 6%
    Assignment 2 Week 4 Week 6 6%
    Assignment 3 Week 6 Week 8 6%
    Assignment 4 Week 8 Week 10 6%
    Assignment 5 Week 10 Week 12 6%
    Submission
    Assignments and projects must be left in the course hand-in box or given to the lecturer in person by the specified deadline. Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty.
    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
  • 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’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.