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Following on from "Basic Mathematics for the Physical Sciences" by the same author team, this book is aimed at all students in the physical sciences taking a second course in mathematics. It consists of self-paced modules that can be studied as part of a traditional course or as an open or distance learning course and it also gives lecturers the flexibility to cover topics at different rates and in any order they choose.
Chapter 1: Vectors and Matrices; Introduction to Vectors and Matrices; Scalar Product of Vectors; Vector Product of Vectors; Matrices and Determinants; Chapter 2: Complex Numbers; Introducing Complex Numbers; Polar Representation of Complex Numbers; Demoivre's Theorem and Complex Algebra; Chapter 3: Further Differentiation; Series Expansions and Approximations; Taylor Expansions and Polynomial Approximations; Hyperbolic Functions and Differentiation; Chapter 4: Further Integration; Applications of Integration; Further Integration; Chapter 5: Differential Equations and Vector Calculus; Introducing Differential Equations; Solving First-Order Differential Equations; Solving Second-Order Differential Equations; Waves and Partial Differential Equations; Vector Calculus; Appendix: Mathematics Handbook.