# Course Title: Numerical Methods

## Part B: Course Detail

Teaching Period: Term2 2008

Course Code: BUSM6022L

Course Title: Numerical Methods

School: 155T Life & Physical Sciences

Campus: City Campus

Program: C6050 - Advanced Diploma of Electrical Engineering

Course Contact : Selva Venkatesan

Course Contact Phone: +61 3 9925 4964

Course Contact Email:selva.venkatesan@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

David Farmer         office 8.9.68

ph 9925 2683        david.farmer@ems.rmit.edu.au

Nominal Hours: 60

Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.

Pre-requisites and Co-requisites

Satisfactory completion of Calculus, Vectors and Mathematical Transforms

Course Description

Learners should able to understand the concept of obtaining an approximate numerical solution to mathematical problems which are not amenable to solution by analytical techniques. Also they need to see the pitfalls in relying on results obtained without proper selection of numerical techniques and careful analysis of results.

National Codes, Titles, Elements and Performance Criteria

 National Element Code & Title: UTENES008A Provide technical leadership in the workplace

Learning Outcomes

1. Implement selected algorithms, both by hand and writing a computer program
2. Compare different algorithms with regard to efficiency and accuracy.
3. Analyse the errors in a numerical solution.
4. Report work undertaken on problems in a clear and comprehensive manner
5 Application of appropriate methods for solving non-linear equations, comparing efficiency and convergence of each method.
6. Use and compare various methods for obtaining approximate solutions to systems of linear equations.
7. Compare various algorithms for obtaining numerical solutions of ordinary differential equations.
8. Apply the concept of and use interpolation methods

Details of Learning Activities

Students will be provided with classroom tutorial instruction in each of the units in order to complete the learning outcomes, tasks and assessment outcomes using the software- Maple, provided and recommended materials, references and the textbook.

Teaching Schedule

Note: Dates and activities may alter. Students will be advised in advance

 Week Starting Week Number Content 7 Jul 1 A short introduction to the Maple language 14 Jul 2 The bisection method for root finding 21 Jul 3 Newton’s method for root finding 28 Jul 4 An Introduction to polynomial interpolation 4 Aug 5 Examples of Interpolation of polynomial 11 Aug 6 The trapezoidal rule 18 Aug 7 The Simpson’s rule 25 Aug 8 Revision 1 Sep 9 Test 1 worth 50% 8 Sep 10 Newton-Cotes Integration 15 Sep 11 Taylor polynomials and Taylor series 22 Sep Student Vacation 29 Sep 12 Solving Linear Differential Equations with constant coefficients 6 Oct 13 Euler’s Method of solving DE numerically 13  Oct 14 Introduction to Matrices and Linear systems 20 Oct 15 Solving Linear system with tridiagonal coefficient matrix 27 Oct 16 Revision 3 Nov 17 Test 2 worth 50%

Learning Resources

Prescribed Texts

 RMIT Lecture Notes

References

 The Maple Book, Frank Garvan

Other Resources

Overview of Assessment

Test 1 worth 50%
Test 2 worth 50%

Mid Semester Test

Topics: Bisection Method for root finding, Newton’s method of root finding, Interpolation, Trapezoidal Rule, Simpson’s rule

Duration: 2 hours

Date: The week beginning 3rd September 2007

Worth: 50% of overall score

Final Semester Examination

Topics: Newton – cotes Integration, First and Second Order Differential Equations, Taylor’s polynomial and Series, Matrices and Linear System and Tri diagonal Matrices

Duration: 2 hours

Date: The week beginning 5th November 2007

Worth: 50% of overall score

Note: This course outline is subject to change. Students should check with their lecturer

Assessment Matrix

Course Overview: Access Course Overview