This module is the second in a series of four mathematical units for students across the Faculty of Science. It continues the basic calculus of ENV-1A61 Mathematics for Scientists I into the study of ordinary differential equations that are used to mathematically model many different systems across the sciences, and the use of further integrals to calculate lengths of lines, surface areas, and volumes. Power series expansions are used to represent and simplify functions, and an introduction to complex numbers is given. There is a continuing emphasis on applied examples, and the use of numerical computing software (Matlab).