Written for undergraduate students in mathematics, the book covers the material in a comprehensive but concise manner, combining mathematical rigour with physical insight. There are many diagrams to illustrate the physical meaning of the mathematical concepts, which are essential for a full understanding of the subject. Full use is made of the elegant and concise suffix notation. Each chapter concludes with a summary of the most important points, and there are worked examples that cover all of the material. The final chapter introduces some of the most important applications of vector calculus, including mechanics and electromagnetism.