• Offered by Mathematical Sciences Institute
  • ANU College ANU Joint Colleges of Science
  • Course subject Mathematics
  • Areas of interest Mathematics
  • Academic career Undergraduate
  • Course convener
    • AsPr Barry Croke
    • Dr Raquel Salmeron
  • Mode of delivery In Person
  • Co-taught Course MATH6405
  • Offered in First Semester 2018
    See Future Offerings

This course shows the modelling process in the context of differential equations and case studies from a number of areas such as population dynamics, economics, electric circuits, mechanical systems, fluid flow, physics and astrophysics. Analytic methods from the elementary theory of differential equations and calculus will be provided to allow for the analysis of the various models being investigated. The numerical package MATLAB will be used to study model behaviour and to obtain deeper understanding of the consequences of analytical studies.

Topics to be covered include:

First order differential equations; second order linear equations; systems of first order equations; nonlinear differential equations; power series solutions; Bessel and Legendre equations; the gamma function.

Advanced Vector Calculus - Curves and surfaces in three dimensions; parametric representations; curvilinear coordinate systems; Surface and volume integrals; use of Jacobians; gradient, divergence and curl; identities involving vector differential operators; the Laplacian; Green's and Stokes' theorems.

 

Learning Outcomes

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

1. Explain the fundamental concepts of differential equations and vector calculus and their role in modern applied mathematics and real-world contexts.
2. Demonstrate accurate and efficient use of techniques involved in solving differential equations and applying vector differential operators.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from the theory of differential equations.
4. Apply problem-solving using techniques in differential equations and vector calculus in diverse situations in physics, engineering and other mathematical contexts.

Indicative Assessment

Assessment will be based on:

    • Exams (65%; LO 1-5)
    • Tutorial participation and presentation (10%; LO 1-5)
    • Assignments (15%; LO 1-5)
    • Quizzes (10%; LO 1-5)

      The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

      Workload

      Three lectures per week and regular tutorials.

      Requisite and Incompatibility

      If you have successfully completed MATH1113 with a mark of at least 80 and are currently enrolled in MATH1014, then you may enrol in this course. Otherwise to enrol in this course you must have successfully completed either MATH1116 or MATH1014.

      Prescribed Texts

       *) Dennis G. Zill, A First Course in Differential Equation with Modelling Applications.
       *) James Stewart, Essential Calculus (the same textbook used in MATH1013 and MATH1014).

      Majors

      Specialisations

      Fees

      Tuition fees are for the academic year indicated at the top of the page.  

      If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

      Student Contribution Band:
      Band 2
      Unit value:
      6 units

      If you are an undergraduate student and have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). You can find your student contribution amount for each course at Fees.  Where there is a unit range displayed for this course, not all unit options below may be available.

      Units EFTSL
      6.00 0.12500
      Note: Please note that fee information is for current year only.

      Offerings and Dates

      The list of offerings for future years is indicative only

      First Semester

      Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery
      2668 19 Feb 2018 26 Feb 2018 31 Mar 2018 25 May 2018 In Person

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