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This book, first published in 1998, is the second in a two volume work and introduces integral and differential calculus, waves, matrices, and eigenvectors for undergraduates in physics and engineering. Together, the two volumes cover all the mathematics needed for an introductory course in the physical sciences. The approach taken is to learn through understanding real examples, showing mathematics as a tool for understanding physical systems and their behaviour. The aim is to make the student feel at home with real problems by creating a toolkit through a wide range of examples. The traditional approach of teaching theory for its own sake is not used in this course. Dr. Lyons brings a wealth of teaching experience to this refreshing textbook on the fundamentals of mathematics for physics and engineering.