This book is intended for students who have had a two-semester or three-semester introductory calculus course. Its purpose is to help students develop, in a short time, a basic competence in each of the many areas of mathematics needed in advanced courses in physics, chemistry, and engineering. Students are given sufficient depth to gain a solid foundation (this is not a recipe book). At the same time, they are not overwhelmed with detailed proofs that are more appropriate for students of mathematics. The emphasis is on mathematical methods rather than applications, but students are given some idea of how the methods will be used along with some simple applications.

1. Infinite Series, Power Series
 2. Complex Numbers
 3. Linear Algebra
 4. Partial Differentiation
 5. Multiple Integrals
 6. Vector Analysis
 7. Fourier Series and Transforms
 8. Ordinary Differential Equations
 9. Calculus of Variations
 10. Tensor Analysis
 11. Special Functions
 12. Legendre, Bessel, Hermite, and Laguerre functions
 13. Partial Differential Equations
 14. Functions of a Complex Variable
 15. Probability and Statistics