The University of Southampton
Courses

PHYS1203 Linear Algebra for Physics

Module Overview

Linear maps on vector spaces are the basis for a large area of mathematics, in particular linear equations and linear differential equations, which form the basic language of the physical sciences. This module restricts itself to multi-dimensional vector space (denoted R^n) to build an intuitive understanding of the concepts of linear algebra and tools for calculations. We begin with the geometry of lines and planes in multi-dimensional vector space looking at the intuitive concept of vectors on the one hand, and with systems of linear equations on the other. This leads us to matrix algebra, and in particular the inversion of matrices.

Aims and Objectives

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• Apply Linear Algebra methods to geometric problems in R^3 and R^n.
• Solve systems of linear equations and apply this to other questions from Linear Algebra
• Calculate the determinants, invert and perform basic operations with matrices
• Work with linear transformations of R^n and their matrices
• Find eigenvalues/eigenvectors of square matrices; diagonalize symmetric matrices

Syllabus

- Complex arithmetic - Vectors in multi-dimensions: examples from 3D space, equations of lines and planes in 2D. - Systems of linear equations, Gaussian elimination. - Matrix algebra: nxm matrices, sums, products, transpose, inverse of an nxn matrix, matrix equations. - Determinants, cofactor definition of the inverse, proof that detA≠O if and only if A invertible. - Properties of R^n, subspaces of R^n, span, null space and column space of a matrix. - Linear independence of vectors in R^n. - Scalar product and geometrical applications. - Vector product and applications in R³. - Linear transformations in R^n, examples in R² and R³. - Eigenvalues and eigenvectors. Throughout the module some theorems will be proved.

Learning and Teaching

Teaching and learning methods

Lectures, problem classes and workshops

TypeHours
Teaching54
Independent Study96
Total study time150

Hirst & Singerman (2000). Basic Algebra and Geometry.

Lang Serge. Introduction to Linear Algebra.

Leon Steven J. Linear Algebra with Application.

Larson, Edwards, Falvo. Elementary Linear Algebra.

Martin Anthony and Michele Harvey (2012). Linear Algebra: Concepts and Methods.

Lay David C. Linear Algebra and its applications.

Edwards CH & Penney DE. Elementary Linear Algebra.

Assessment

Assessment Strategy

Referral Method: By examination, the final mark will be calculated both with and without the coursework assessment mark carried forward, and the higher result taken.

Summative

MethodPercentage contribution
Class Test 10%
Coursework 20%
Final Assessment  70%

Referral

MethodPercentage contribution
Coursework marks carried forward 30%
Final Assessment  70%

Repeat Information

Repeat type: Internal & External

Pre-requisites

To study this module, you will need to have studied the following module(s):

CodeModule
MATH1006Mathematical Methods for Physical Scientists 1a

Costs

Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

Books and Stationery equipment

Students will be provided with full lecture notes. Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.