This text for first-year students of applied mathematics may also be used as a bridge between school and university study. The theoretical content is firmly based but the focus is on techniques and applications. Throughout, there are many exercises of varying difficulty, with worked solutions provided. Basic differentiation and integration techniques taught at school level are presented as a refresher. Matrix algebra, vector algebra and complex numbers are then described at sufficient depth for the student to feel comfortable with them when they reappear later in the book. Subsequent chapters move onto real variable calculus, including partial differentiation and multiple integrals. The concluding chapter in differential equations considers applications taken from both physical and economic contexts.