The laws of physics are written in mathematical form, and it is clear that we will need to understand a certain amount of mathematics if we are to solve any physical problems. To see what is required, let us consider Newton¿s second law of mechanics: force equals mass times acceleration. Force and acceleration are vector quantities, having magnitude and direction, whereas mass is a scalar quantity, having only magnitude. It follows that we will have to recognise and manipulate both scalar and vector quantities. Acceleration is the rate of change, or time derivative, of velocity; it follows that we will need to understand differentiation, and its inverse process of integration. If we next consider electromagnetism, we see that electric and magnetic fields exist at every point of three dimensional space, and every instant of time; we must therefore understand functions of more than one variable, and in fact extend the ideas of differentiation and integration to such functions. Finally we may notice that all the major laws of physics involve derivatives, and thus are differential equations; we will need to understand such equations, and how to solve them in various circumstances. This two semester course develops these mathematical techniques needed by physics modules in the first and subsequent years. The sequence of topics is carefully chosen to support the physics modules in the first and second semesters. Where possible, mathematical ideas are linked to physics topics, and there is a strong emphasis on problem solving. The topics covered are:
Semester 1: Scalars and vectors; differentiation; complex numbers
Semester 2: Functions of several variables; partial differentiation; differential equations; single and multiple integrals.