MATHS 7104 - Numerical Methods
North Terrace Campus - Semester 2 - 2024
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General Course Information
Course Details
Course Code MATHS 7104 Course Numerical Methods Coordinating Unit 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 Assumed Knowledge 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, MECH ENG 1102, MECH ENG 1103, MECH ENG 1104, MECH ENG 1105 or C&ENVENG 1012) Assessment Ongoing assessment, examination Course Staff
Course Coordinator: Dr Trent Mattner
Course Timetable
The full timetable of all activities for this course can be accessed from Course Planner.
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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) Attribute 1: Deep discipline knowledge and intellectual breadth
Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.
1-6 Attribute 2: Creative and critical thinking, and problem solving
Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.
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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
Instructional videos, computer-based exercises, 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.
Course material is delivered via a weekly seminar, instructional videos and online quizzes.
There will be six workshops. In these classes, you will complete work on problems that aim to enhance your understanding of the course material and ability to solve theoretical problems. You are encouraged to attempt the problems before the workshop and to complete all the remaining problems afterwards.
There will be six practical classes. Practical work will involve using Matlab to implement numerical algorithms developed in course videos. 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 Lectures/Online learning 24 (equivalent) 72 Tutorials 6 20 Assignments 5 40 Practicals 6 24 TOTALS 156 Learning Activities Summary
XSchedule 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 -
Assessment
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.
Assessment Summary
Component Weighting Objective Assessed Exam 50% All Assignments (5) 30% All Practical work 5% All Online quizzes 5% All Test 10% All Assessment Related Requirements
In order to pass the course, you must obtain:- an aggregate mark of at least 50%, AND
- at least 40% on the exam.
Assessment Detail
Assessment Item Distributed Due Date Weighting Assignment 1 Week 2 Week4 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
Submission of work will be via MyUni. Instructions for the submission of each item required will be posted in advance of the deadline.
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.
We aim to have a two week turn-around time for providing feedback on assignment work 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.
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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.
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Student Support
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Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
- Academic Credit Arrangements Policy
- Academic Integrity Policy
- Academic Progress by Coursework Students Policy
- Assessment for Coursework Programs Policy
- Copyright Compliance Policy
- Coursework Academic Programs Policy
- Elder Conservatorium of Music Noise Management Plan
- Intellectual Property Policy
- IT Acceptable Use and Security Policy
- Modified Arrangements for Coursework Assessment Policy
- Reasonable Adjustments to Learning, Teaching & Assessment for Students with a Disability Policy
- Student Experience of Learning and Teaching Policy
- Student Grievance Resolution Process
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