Handbook

Many mathematical equations, especially those arising in real-world applications, cannot be solved exactly. This topic introduces methods for approximating the solution to a variety of equations that are commonly encountered. This includes solving both linear and non-linear algebraic equations, along with systems of equations, integration, differentiation, optimisation, and solving ordinary differential equations. Motivated by these problems, techniques are also introduced for interpolating functions and finding lines of best fit through data. Through all of the problems considered, there is a focus on estimating the error in the approximations developed, including an understanding of sources of error, such as rounding, and convergence. The topic also introduces the foundations of computer programming, focusing on how the numerical methods developed can be implemented.