# Course Title: Computational Mathematics

## Part A: Course Overview

Course Title: Computational Mathematics

Credit Points: 12.00

## Terms

### Teaching Period(s)

MATH2136

City Campus

145H Mathematical & Geospatial Sciences

Face-to-Face

Sem 2 2006,
Sem 2 2007,
Sem 2 2008,
Sem 2 2009,
Sem 2 2010,
Sem 2 2011,
Sem 2 2012,
Sem 2 2013,
Sem 2 2014,
Sem 2 2015,
Sem 2 2016

MATH2136

City Campus

171H School of Science

Face-to-Face

Sem 2 2017

Course Coordinator: Dr John Gear

Course Coordinator Phone: +61 3 9925 2589

Course Coordinator Email: john.gear@rmit.edu.au

Course Coordinator Location: Building 8, level 9, room 21

Pre-requisite Courses and Assumed Knowledge and Capabilities

MATH1142 Calculus 1
MATH1144 Calculus 2

Or equivalent first year university mathematics courses.
MATH2109 or any equivalent course that gives basic knowledge in programming with Maple, Mathematica or MatLab.

Assumed Knowledge

• Ability to formulate and solve differential equations.
• Ability to recognize the properties of matrices; solve linear systems; calculate determinants of matrices; find eigenvalues and eigenvectors.
• Ability to create a Taylor series approximation to a function of one variable.
• Knowledge of one of the following symbolic manipulation packages: Maple or Mathematica or knowledge of MatLab.
• Skill in writing a simple program in either: Maple, Mathematica or MatLab.

Course Description

Computational Mathematics introduces and studies fundamental operations and methods that are the tools of mathematicians and applied scientists. The course introduces the numerical methods necessary for the determination of the errors in computation, solution of nonlinear equations, systems of linear equations, systems of ordinary differential equations, the evaluation of definite integrals by numerical quadrature and the approximation of functions and data. The foundation is laid for the more specialist mathematics courses that are undertaken in subsequent years. This course provides the basic computational skills required for all courses in mathematics, computer science, applied sciences and engineering.

Objectives/Learning Outcomes/Capability Development

This course contributes to the following Program Learning Outcomes for BP083 Bachelor of  Science (Mathematics)

Knowledge and technical competence

• use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.

Problem-solving

• synthesize and flexibly apply knowledge to characterize, analyse and solve a wide range of problems
• balance the complexity / accuracy of the mathematical / statistical models used and the timeliness of the delivery of the solution.

Communication

• communicate both technical and non-technical material in a range of forms (written, electronic, graphic, oral) and tailor the style and means of communication to different audiences. Of particular interest is the ability to explain technical material, without unnecessary jargon, to lay persons such as the general public or line managers.

On successful completion of this course, you should be able to:

1. Solve nonlinear equations using various numerical methods such as bisection method, Newton’s method, secant method and fixed point iteration method and implement using a computer.
2. Solve large systems of linear equations using Gaussian elimination, factorisation methods, implement using a computer and identify where numerical error may occur.
3. Approximate functions and data using polynomial and rational interpolation or polynomial and rational least squares approximation and explain the concept of error estimation.
4. Solve a system of ordinary differential equations using various numerical methods (taking into account criteria such as convergence, rate of convergence, accuracy and, where appropriate, consistency and stability) and implement using a computer.
5. Evaluate definite integrals using numerical quadrature (such as Gaussian quadrature, Newton-Cotes methods) and implement using a computer.
6. Numerically determine eigenvalues and eigenvectors for very large matrices using a variety of methods.

Overview of Learning Activities

This course is presented using a mixture of classroom instruction; problem-based tutorial classes; exercises; online quizzes and tests and programming assignments.

An online course site will be used to disseminate course materials, and to provide you access to self-assessment quizzes and tests.

The course is divided into six topics.

1. Numerical solution of linear systems.
2. Numerical solution of non-linear equations.
3. Approximation of functions and data.
5. Numerical solution of ordinary differential equations.
6. Numerical determination of matrix eigenvalues.

Online Assessment:
Online quizzes are designed to provide instant feedback and can be attempted repeatedly until proficiency in the learning objectives is achieved. You should aim to master each Online quiz before attempting the corresponding Online test. Each test has an associated quiz that opens at least one week before the test and remains open during the test period. You are given two attempts at each test.

Some online questions require answers to be entered using a specific syntax. Examples of this syntax are given in the Teaching and Assessment Schedule, available from the course site. It is your responsibility to master the syntax with the quizzes before attempting the corresponding online test. Answers marked as incorrect, due to syntax errors, will not be remarked.

Programming Assignments:
The programming assignments are designed to make you aware of efficient ways to structure your computations and appreciate criteria such as convergence, rate of convergence and accuracy. The programming assignments will be supported by Mathematica notebooks, Maple worksheets and Matlab example sheets.

Final Examination:
Typical exam style questions are provided to assist in your preparation for the final examination. The sample exam questions are a guide only. All material presented in the course is examinable.

Overview of Learning Resources

The Blackboard site links to the Google site where you will find:

1. Teaching and Assessment schedule and guide to online tests.
2. Programming Assignments
3. Course notes for each topic.
4. Recommended references
5. Topic exercises and answers (if available).
6. Sample exam questions
7. Maple demonstration documents, worksheets and introductory worksheet.
8. Matlab demonstration documents and videos
9. Mathematica demonstration documents and introductory notebook
10. Excell demonstration documents and videos

A library guide is available at http://rmit.libguides.com/mathstats

Overview of Assessment

Weighting 36%

This assessment task supports CLOs 1, 2, 3, 4 & 5.
There are nine online tests, each worth 4% The online tests commence in week 3. Each test is open for two teaching weeks. Some tests will remain open for three over the mid-semester break.  Each test has an associated quiz that opens at least one week before the test and remains open during the test period. You should aim to master each online quiz before attempting the corresponding online test. You are given two attempts at each test.

Weighting 24%

This assessment task supports CLOs 1, 2, 3 4 & 5.
The programming assignments will be completed using the either the symbolic manipulation packages Mathematica or Maple, or using Matlab, or equivalent. They should be submitted online by the notified due date and time. Common (copied) or late assignments will not be marked. Where necessary they should include an interpretation and discussion of the results and methods used. It is your responsibility to ensure that your work is submitted by the due date and time.

The assessment of your performance in assignments will be based on:

• Accuracy of technical computations and results
• Discussion of relevant issues such as appropriateness of the mathematical model, sources of error in the numerical solution and computational efficiency.
• Clarity and thoroughness of the work presented.

Weighting 40%

Three hour, open book examination.
This assessment supports CLOs 1, 2, 3, 4, 5 & 6.
Handheld calculators are required.
The assessment of your performance in the examination will be based on the accuracy of technical computations, clarity and thoroughness.
All material presented in this course is examinable.