MATHS 2104 - Numerical Methods II

North Terrace Campus - Semester 2 - 2019

To explore complex systems, physicists, engineers, financiers and mathematicians require computational methods since mathematical models are only rarely solvable algebraically. Numerical methods, based upon sound computational mathematics, are the basic algorithms underpinning computer predictions in modern systems science. Such methods include techniques for simple optimisation, interpolation from the known to the unknown, linear algebra underlying systems of equations, ordinary differential equations to simulate systems, and stochastic simulation under random influences. Topics covered are: the mathematical and computational foundations of the numerical approximation and solution of scientific problems; simple optimisation; vectorisation; clustering; polynomial and spline interpolation; pattern recognition; integration and differentiation; solution of large scale systems of linear and nonlinear equations; modelling and solution with sparse equations; explicit schemes to solve ordinary differential equations; random numbers; stochastic system simulation.

  • General Course Information
    Course Details
    Course Code MATHS 2104
    Course Numerical Methods II
    Coordinating Unit School of Mathematical Sciences
    Term Semester 2
    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 and (COMP SCI 1012 or 1101 or 1102 or 1201, or MECH ENG 1100 or 1102 or 1103 or 1104 or 1105, or C&ENVENG 1012).
    Assumed Knowledge MATHS 2102 or MATHS 2201
    Course Description To explore complex systems, physicists, engineers, financiers and mathematicians require computational methods since mathematical models are only rarely solvable algebraically. Numerical methods, based upon sound computational mathematics, are the basic algorithms underpinning computer predictions in modern systems science. Such methods include techniques for simple optimisation, interpolation from the known to the unknown, linear algebra underlying systems of equations, ordinary differential equations to simulate systems, and stochastic simulation under random influences.

    Topics covered are: the mathematical and computational foundations of the numerical approximation and solution of scientific problems; simple optimisation; vectorisation; clustering; polynomial and spline interpolation; pattern recognition; integration and differentiation; solution of large scale systems of linear and nonlinear equations; modelling and solution with sparse equations; explicit schemes to solve ordinary differential equations; random numbers; stochastic system simulation.
    Course Staff

    No information currently available.

    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 common numerical methods and how they are used to obtain approximate solutions to otherwise intractable mathematical problems.
    2 Apply numerical methods to obtain approximate solutions to mathematical problems.
    3 Derive numerical methods for various mathematical operations and tasks, such as interpolation, differentiation, integration, the solution of linear and nonlinear equations, and the solution of differential equations.
    4 Analyse and evaluate the accuracy of common numerical methods.
    5 Implement numerical methods in Matlab.
    6 Write efficient, well-documented Matlab code and present numerical results in an informative way.
    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)
    1-6
    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
    1-6
  • Learning Resources
    Required Resources
    None.
    Recommended Resources
    E. Kreyszig, Advanced engineering mathematics, 9th edition, Wiley, 2006.
    A. Greenbaum & T. P. Chartier, Numerical methods, Princeton University Press, 2012.
    W. Cheney & D. Kincaid, Numerical mathematics and computing, Thomson, 2004.
    D. P. O'Leary, Scientific computing with case studies, SIAM, 2008.
    D. M. Etter, Engineering problem solving with Matlab, Prentice-Hall, 1993.
    W. H. Press et al, Numerical recipes in [C, Fortran, ...], Cambridge University Press, c1996-1999.
    Online Learning
    Lecture recordings and screencasts, MapleTA exercises, partial lecture notes, assignments, tutorial exercises,  and course announcements will be posted on MyUni.

  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course uses a variety of methods for delivery of the course material.

    Some lecture material is delivered using online screencasts together with interactive Maple TA exercises and quizzes. Other lecture material is delivered in traditional face-to-face lecture format.

    Tutorials are held fortnightly. In these classes, you will complete short quizzes and work on tutorial problems that aim to enhance your understanding of the lecture material and ability to solve theoretical problems. You are encouraged to attempt the problems before the tutorial and to complete all the remaining problems afterwards.

    Practicals are held fortnightly, alternating with tutorials. In these classes, you will use Matlab to implement numerical algorithms developed in lectures. Practical work must be submitted to show that you have completed the session.

    Assignments are set fortnightly. In the assignments, you are usually asked to write a Matlab program to solve a mathematical problem and present your results in a written report. Questions about theoretical aspects of the problem may also be asked.

    Workload

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    Activity Quantity Workload hours
    Lecture 24 72
    Tutorials 5 20
    Assignments 5 40
    Practicals 6 24
    TOTALS 156
    Learning Activities Summary
    Schedule
    Week 1 Matlab revision, vectorisation.
    Week 2 Polynomial interpolation. Practical 1: Matlab and vectorisation.
    Week 3 Numerical differentiation and integration. Tutorial 1: Polynomial interpolation.
    Week 4 Linear and cubic splines in one dimension. Practical 2: Numerical integration and differentiation.
    Week 5 Radial basis function splines in multiple dimensions. Tutorial 2: Numerical integration and differentation.
    Week 6 LU and QR factorisation and applications. Practical 3: Splines.
    Week 7 Norms and condition numbers. Jacobi method. Tutorial 3: LU and QR factorisation.
    Week 8 Fixed point iteration, Newton's method. Practical 4: Numerical linear algebra.
    Week 9 Euler's method, Improved Euler method, Initial-value problems. Tutorial 4: Jacobi method, fixed point iteration and Newton's method.
    Week 10 Runge Kutta methods, time-step limitations, Matlab ODE solvers. Practical 5: Newton's method and ordinary differential equations.
    Week 11 Boundary-value problems. Partial differential equations. Monte Carlo methods. Tutorial 5: Ordinary differential equations.
    Week 12 Monte Carlo methods. Review Practical 6: Test
  • 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
    Exam 50% All
    Practical test 15% All
    Assignments 25% All
    Quizzes/MapleTA 10% All
    Assessment Related Requirements
    In order to pass the course, you must obtain:
    1. an aggregate mark of at least 50%, AND
    2. at least 45% on the exam.
    Assessment Detail
    Assessment Item Distributed Due Date Weighting
    Assignment 1 Week 2 Week 4 5%
    Assignment 2 Week 4 Week 6 5%
    Assignment 3 Week 6 Week 8 5%
    Assignment 4 Week 8 Week 10 5%
    Assignment 5 Week 10 Week 12 5%

    Tutorial quizzes and MapleTA exercises will be set throughout the course. They are of equal weight.
    Submission

    You will need to submit both electronic and hardcopy components for each assignment. The electronic component must be submitted according to the assignment instructions. It will be marked electronically and the result added to your hardcopy mark. The hardcopy component must be submitted to the designated hand-in boxes within the School of Mathematical Sciences with a signed cover sheet attached.

    Late assignments will not be accepted. 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.

    Assignments will have a two week turn-around time for feedback to students.

    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

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    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.

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  • Policies & Guidelines
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