This module aims to build on the basic techniques of calculus that the learner has already encountered and familiarise the learner with more advanced techniques. First and second order differential equations and their applications are investigated. Functions of several variables are introduced. Partial derivatives and directional derivatives are described. Vector differential and integral calculus are explored. Integration in three dimensions, the reversal of the order of integration, changes of coordinates and the fundamental integral theorems are analysed.
- First order ordinary differential equations
- Second order ordinary differential equations with constant coefficients
- Surfaces and functions of more than one independent variable
- Differential calculus of more than one variable
- Integral calculus of several variables
- Polar coordinates
Solution by direct integration and separation of variables. Methods for first order linear, homogeneous and Bernoulli equations. Examples and applications of first order differential equations.
General and particular solutions. Resonance. Applications of second order differential equations.
Partial derivatives, gradient, divergence, curl, directional derivatives, maxima and minima problems. Lagrange multipliers. Statement of chain rule and Taylor series in several variables.
Line integrals and curve parameterisation, conservative forces and path independence. Double and triple integrals, reversal of the order of integration, applications to volume and surface integrals. Integral theorems. Change of variables, the Jacobian.
Plane polar, cylindrical and spherical polar coordinates.
Lectures are primarily used to impart module content to the learner. Problem-solving sessions and
tutorials support learners and are designed to encourage learners to work both individually and in groups.
|Module Content & Assessment