This course aims to complement knowledge, skills and their application studied in MATH2469 A Calculus Toolbox for Scientists or equivalent. It provides a broad introduction to a further selection of the fundamental mathematical procedures (multi-variable differentiation and integration) and mathematical objects (vectors, vector-valued functions, matrices, series) needed by mathematicians and most applied scientists. The course builds on the foundations laid in secondary school mathematics and in turn extends those foundations to accommodate more advanced studies in mathematics undertaken in the following semester and beyond. Topic areas include vectors, matrices, infinite series, power series, vector-valued functions and functions of several variables.