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Department of Mathematics & Computer Science



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MC126 Multivariate Calculus

MC126 Multivariate Calculus

Credits: 10 Convenor: Dr. P. Houston Semester: 1 (weeks 7 to 12)

Prerequisites: essential: None desirable: MC127
Assessment: Continual assessment: 20% One and a half hour exam in January: 80%

Lectures: 18 Problem Classes: none
Tutorials: 5 Private Study: 52
Labs: none Seminars: none
Project: none Other: none
Surgeries: none Total: 75

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 y=f(x). 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 (x(t),y(t),z(t)). Similarly, surfaces are represented by functions of two (or more) variables in the form z=f(x,y).

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

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. Taylor's series. 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:

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

Details of Assessment

The final assessment of this module will consist of 20% coursework and 80% from a one and a half hour examination during the January exam period. The 20% coursework contribution will be determined by students' solutions to coursework problems. The examination paper will contain 4 questions with full marks on the paper obtainable from 4 complete answers.

Next: MC127 Vectors and ODEs Up: Year 1 Previous: MC123 Introduction to Newtonian dynamics

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Last updated: 10/4/2000
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