# Course Title: Numerical Techniques

## Part A: Course Overview

Course Title: Numerical Techniques

Credit Points: 12.00

## Terms

### Teaching Period(s)

MATH2391

City Campus

Undergraduate

171H School of Science

Face-to-Face

Sem 2 2022

Course Coordinator: Dr. Geetika Verma

Course Coordinator Phone: NA

Course Coordinator Email: geetika.verma@rmit.edu.au

Course Coordinator Availability: By appointment, by email

Pre-requisite Courses and Assumed Knowledge and Capabilities

MATH1142 Calculus 1, MATH1144 Calculus 2, MATH2311 Applied Linear Algebra or equivalent first year university mathematics courses.   MATH2109 Mathematical Computing and Algorithms or any equivalent course that gives basic knowledge in manipulating algorithms and programming with Maple, Mathematica or Matab.

Course Description

Numerical Techniques introduces and studies fundamental operations and methods that are the tools of mathematicians, statisticians and applied scientists. The course introduces the numerical methods necessary for the determination of the errors in computation, the manipulation of large data, numerical linear algebra, solution of linear and nonlinear 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 Applied Mathematics and Statistics.   PLO2. Knowledge and technical competence

• use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.
PLO03. 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.
PLO05. 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.

You will be provided with the opportunity to clarify main concepts through questions that are designed to promote teamwork and critical thinking. You will be encouraged to work in small groups, but to present your own solution to each set task. This will be achieved through practice class sessions where you will receive feedback whilst attempting to formulate mathematical models and to determine their solutions. It will provide a forum for you to discuss your solution strategies with colleagues and in these discussions to develop your analytical ability and communication skills. Staff members will oversee these activities responding when necessary.

Overview of Learning Resources

You will have access to learning resources comprising the recommended references, a set of detailed course notes and other relevant materials such as extra notes, exercises and assignments. These are available online via the RMIT Learning Hub (Canvas). You will also have access to RMIT Library online and other hardcopy resources.

Library Subject Guide for Mathematics & Statistics http://rmit.libguides.com/mathstats

Overview of Assessment

Assessment tasks:

Assessment Task 1: Problem-solving exercises
Weighting 30%
This assessment supports CLOs 1, 2, 3 & 4

Assessment Task 2: Programming Assignments
Weighting 50%
This assessment supports CLOs 1, 2, 3, 4 & 5

Assessment Task 3: In-class Practical Test
Weighting 20%
This assessment supports CLOs 2, 3, 4, 5 & 6