| Credits: 10 | Convenor: Dr. M. Ainsworth | Semester: 1 (weeks 7 to 12) |
| Prerequisites: | essential: None | desirable: MC120 |
| Assessment: | Continual assessment: 20% | One and a half hour exam in May/June: 80% |
| Lectures: | 18 | Classes: | 6 |
| Tutorials: | 6 | Private Study: | 51 |
| Labs: | none | Seminars: | none |
| Project: | none | Other: | none |
| Total: | 75 |
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 is concerned with seeing 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. Naturally, this will involve dealing with functions of many variables.
Although vectors will be revised in the course, students who have not covered vectors at A-level are strongly advised to consider taking the course MC120 Vectors and Geometry.
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.
John Gilbert, Guide to Mathematical Methods, Macmillan Mathematical Guides.