Next: MC127 Vectors and ODEs
Up: Year 1
Previous: MC123 Introduction to Newtonian
MC126 Multivariate Calculus
Credits: 10 |
Convenor: Mr B. English |
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 |
Classes: |
none |
Tutorials: |
5 |
Private Study: |
52 |
Labs: |
none |
Seminars: |
none |
Project: |
none |
Other: |
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
This course aims (i) to show the student 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 hone the student's calculus skills, and
(iv) to give 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 about line integrals and double integrals
and simple tricks for computing them.
- 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 variable and graphical representation. Partial derivatives.
Chain rule. Directional derivatives. Tangent plane. Line integrals.
Properties of line integrals. Double integrals. Simple change of variable.
Transferable Skills
Calculus and algebraic manipulation skills.
The ability to tackle problems using both geometric 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
S. J. Ambler
11/20/1999