Department of Mathematics & Computer Science

MC126 Multivariate Calculus

Explanation of Pre-requisites

The basic calculus skills which will be reinforced by MC127 are very important for this module.

Course Description

Most people are familiar with the idea of a curve being represented by an equation of the form . Calculus is very useful in calculating properties of curves, such as their gradients at a point and the area underneath the curve.

More interesting are curves and surfaces that exist in two or more dimensions. Such curves are represented by vector-valued functions of the form . Similarly, surfaces are represented by functions of two (or more) variables in the form .

This course will show how calculus can be used to calculate properties of curves and surfaces, such as the length of a curve, the area of a surface and the volume of a solid, and will also show how to deal with functions of many variables.

Aims

The aims of this course are: (i) to illustrate how calculus can be used to calculate important properties of curves, surfaces and volumes; (ii) to enable the student to deal with functions of many variables; (iii) to improve the student's calculus skills, and (iv) to provide practice in algebraic manipulation.

Objectives

• Students should know how to deal with vector valued functions.
• Students should know about the vectorial representation of curves, and how to compute their tangent vectors.
• Students should know about functions of two variables and know how to compute partial and directional derivatives and tangent planes to the graphs of such functions.
• Students should know how to compute double integrals.
• Students should be able to compute volumes and areas of simple geometrical objects by using appropriate integrals.

Syllabus

Vector valued functions. Graphical representation. Tangent vectors. Functions of two variables and graphical representation. Partial derivatives. Chain rule. Tangent plane. Directional derivatives. Extreme values. Double integrals. Simple change of variable.

Transferable Skills

Calculus and algebraic manipulation skills.

The ability to tackle problems using both geometrical and analytical methods.

Reading list

Essential:

Background:

John Gilbert, Guide to Mathematical Methods, Macmillan Mathematical Guides.

Details of Assessment

Author: S. J. Ambler, tel: +44 (0)116 252 3884
Last updated: 2001-09-20
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This document has been approved by the Head of Department.
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