Literature:

	JE Marsden and AJ Tromba Vector Calculus, Freeman
	D.E. Bourne and P.C. Kendall, Vector Analysis and Cartesian Tensors, Chapman and Hall.

Assingments:

Status: Core for Maths.

Commitment: 45 lectures (30 in Term 1, 15 in Term 2, Weeks 16-20).

Content: An introduction to 3D vector algebra and analysis, with applications to the geometry of lines, planes and curves and to elementary mechanics. Conics, linear and affine transformations and their representations by matrices. Basic matrix algebra. Differentiation of maps between low dimensional spaces and applications to critical point theory and to gradient and conservative force fields. Line, surface and volume integrals and applications. An introduction to rigid body motion.

Aims: Real life happens in three dimensions. The aim of this module is to teach methods of studying three-dimensional vectors and functions of three-dimensional space. Methods of geometry, differentiation and integration are discussed and some applications to mechanics are described.

Objectives: On successful completion of this module students should be able to:

• Perform basic operations and calculations from 3D vector algebra and linear matrix theory and apply these to problems from geometry and mechanics;

• Be able to differentiate maps between low dimensional spaces and apply this to the geometry of curves, to mechanics and to critical points and functions;

• Understand and be able to calculate line, surface and volume integrals and apply these simple problems, including calculation of inertia tensors of rigid bodies;

• Be able to apply all these techniques to elementary problems from mechanics, including central force theory, rigid body motion and fluid dynamics.

Leads to: This module leads on directly to MA231 Vector Analysis and, together with MA113 Differential Equations A, thereby provides the foundations for most future applied mathematics modules, including MA112 Experimental Mathematics, PX253 Partial Differential Equations, MA209 Variational Principles, MA235 Introduction to Mathematical Biology and MA240 Modelling Nature's Nonlinearity. The more algebraic and geometric aspects of the module also lead on to modules such as MA106 Linear Algebra, MA125 Introduction to Geometry and MA243 Geometry.