Mathematical Tools for Science - ZPEM2302

The emphasis of this course is on developing mathematical tools for a variety of different modelling contexts from the Sciences. The course is taught in two strands, Data Analysis and Multivariable Calculus. The Data Analysis strand uses data from simple experimental and observational studies, and introduces graphical methods for data presentation and exploration. It discusses the important concepts of populations, samples and randomness, and explains how to relate sample values to population values and test claims about population parameters. Association between different measurements is quantified, and methods of modelling the relationship between two variables are studied. The Multivariable Calculus strand describes surfaces in three dimensions using contour plots, partial derivatives and the gradient vector. Of great importance is the location of maxima or minima of the function, leading to a discussion of the methods of optimisation for functions of several variables, especially when auxiliary constraints must also be satisfied. Case studies in both strands will illustrate how the mathematical tools operate in a wide range of disciplines including Geography, Chemistry, Physics and Oceanography. The computer package MATLAB will be used throughout the course, particularly for its powerful graphics capabilities.