MATH203-12S2 (C) Semester Two 2012

# Linear Algebra

 15 points, 0.1250 EFTS09 Jul 2012 - 11 Nov 2012

## Description

Linear algebra is a key part of the mathematical toolkit needed in the modern study of many areas in science, commerce and engineering. This course develops the fundamental concepts of linear algebra, including orthogonality, projections and eigenvalues, with an emphasis on practical applications and use of the computer package MATLAB.

Linear algebra is a key part of the mathematical toolkit needed in the modern study of many areas in science, commerce and engineering. This course develops the fundamental concepts of linear algebra, including orthogonality, projections and eigenvalues, with an emphasis on practical applications and use of the computer package MATLAB.

Topics covered:
Linear systems. Review of Gaussian elimination, partial pivoting. Partitioned matrices. LU factorizations, tridiagonal and band systems. Vector and matrix norms. Condition number. Error analysis. Iterative methods for solving systems of linear equations. Orthogonality, Gram-Schmidt process. QR factorization. Projections, projections as transformations. Least squares approximation. Orthogonal expansions, Fourier series. Eigenvalues and eigenvectors. Characteristic equation, diagonalization. Power method and variants. Hermitian and positive definite matrices, unitary matrices, normal matrices.

Applications:
Linear difference and differential equations, stability analysis; classification of quadratic varieties; recurrence relations; population models; Markov chains.

## Learning Outcomes

At the end of the course, students will:

• be proficient in the standard techniques of matrix algebra and vector spaces: matrix factorizations (LU and QR); projections; diagonalization; iterative methods (Gauss-Seidel, power method) and convergence
• understand why these techniques work
• be able to use these techniques in a variety of applications, including using MATLAB to solve standard problems
• have developed problem solving skills both as part of a team and as an individual
• have developed written and oral communication skills, emphasizing the ability to explain what the mathematics means

This course will provide students with an opportunity to develop the Graduate Attributes specified below:

 Critically competent in a core academic discipline of their award Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

## Restrictions

MATH252, MATH254, EMTH203, EMTH204, EMTH211

 Lectures Streams Day Time Where Notes Stream 01 Monday 12:00pm-1:00pm E8 Lecture Theatre 17 Sep - 14 Oct Wednesday 12:00pm-1:00pm E6 Lecture Theatre 17 Sep - 14 Oct Thursday 3:00pm-4:00pm E5 Lecture Theatre 17 Sep - 14 Oct

 Tutorials Streams Day Time Where Notes Stream 01 Wednesday 8:00am-9:00am Erskine 033 Lab 1 9 Jul - 19 Aug,3 Sep - 14 Oct Stream 02 Tuesday 8:00am-9:00am Erskine 035 Lab 2 9 Jul - 19 Aug,3 Sep - 14 Oct Stream 03 Wednesday 1:00pm-2:00pm Erskine 035 Lab 2 9 Jul - 19 Aug,3 Sep - 14 Oct Stream 04 Friday 4:00pm-5:00pm Erskine 035 Lab 2 9 Jul - 19 Aug,3 Sep - 14 Oct

## Assessment

Assessment Due Date Percentage
Internal Assessment - TBA 50%
Final Examination 50%

## Examination and Formal Tests

 Exam Thursday 08 Nov 2012 9:30am-12:30pm

## Textbooks

Poole, Linear Algebra: A Modern Introduction, Brookes/Cole.

## Indicative Fees

Domestic fee \$622.00

International fee \$3,200.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

## All MATH203 Occurrences

• MATH203-12S2 (C) Semester Two 2012