Browse Hierarchy SPA4121: Mathematical Techniques I

This module develops the mathematical techniques that will be used and built upon throughout the rest of Physics and Astronomy. Topics include vectors and their operations (addition, subtraction, scalar multiplication, dot / cross products); functions of a single variable; single variable calculus (including integration and differentiation); functions of many variables and partial differentiation; Taylor series (including the binomial expansion, and for functions of two variables); Fourier series; proof by induction; properties of complex numbers; hyperbolic functions; integration techniques (e.g. substitution, by parts, partial fractions); applications of integration (e.g. averages of functions, volumes of revolution); multiple integration with applications; Fourier transforms.