This textbook provides a thorough introduction to the essential mathematical techniques needed in the physical sciences. Carefully structured as a series of self-paced and self-contained chapters, this text covers the basic techniques on which more advanced material is built. Starting with arithmetic and algebra, the text then moves on to cover basic elements of geometry, vector algebra, differentiation and finally integration, all within an applied environment. The reader is guided through these different techniques with the help of numerous worked examples, applications, problems, figures,...

Aimed at advanced undergraduates, this self-contained textbook covers the key ideas of special and general relativity together with their applications. The textbook introduces students to basic geometric concepts, such as metrics, connections and curvature, before examining general relativity in more detail. It shows the observational evidence supporting the theory, and the description general relativity provides of black holes and cosmological space-times. The textbook is in full colour, with numerous worked examples and exercises with solutions. Key points and equations are highlighted for...