Engineers are responsible for designing, modelling and analysing solutions to physical problems from the world around us. Mathematics provides the crucial framework by which we carry out this process. This is the first of a sequence of three courses designed to develop the core mathematical theory necessary in this modelling and solution process. In this course students focus on the theory of single-variable calculus, multi-variable calculus, and vector calculus. Key applications of this theory to the student's area of engineering specialisation are also introduced and students will learn how to model basic physical phenomena mathematically.