MATHS 7104 - Numerical Methods
North Terrace Campus - Semester 2 - 2020
General Course Information
Course Code MATHS 7104 Course Numerical Methods Coordinating Unit School of Mathematical Sciences Term Semester 2 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3.5 hours per week Available for Study Abroad and Exchange Y Prerequisites MATHS 2102 or MATHS 2201 or MATHS 2106 and (COMP SCI 1012 or COMP SCI 1101 or COMP SCI 1102 or COMP SCI 1201 or ENG 1002 or ENG 1003 or MECH ENG 1100 or MECH ENG 1102 or MECH ENG 1103 or MECH ENG 1104 or MECH ENG 1105 or C&ENVENG 1012). Assumed Knowledge MATHS 2102 or MATHS 2201 or MATHS 2106 and (COMP SCI 1012 or 1101 or 1102 or 1201, or ENG 1002 or 1003 or MECH ENG 1100, 1102, 1103, 1104, 1105 or C&ENVENG 1012) 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 Coordinator: Dr Edward Green
The full timetable of all activities for this course can be accessed from Course Planner.
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
Recommended ResourcesE. 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 LearningLecture recordings and screencasts, MapleTA exercises, partial lecture notes, assignments, tutorial exercises, and course announcements will be posted on MyUni.
Learning & Teaching Activities
Learning & Teaching ModesThis 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 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.
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: Partial differential equations and Monte Carlo integration
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Component Weighting Objective Assessed Exam (3 hours) 65% All Assignments 25% All Practicals 6% All Quizzes/MapleTA 4% All
Assessment Related RequirementsIn order to pass the course, you must obtain:
- an aggregate mark of at least 50%, AND
- at least 45% on the exam.
Assessment Item Distributed Due Date Weighting Assignment 1 Week 2 Week4 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.
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.
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.
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