1. Vectors in Three-Dimensional Space -- 2. Vector Fields -- 3. Fundamental Equations for Fluid Mechanics -- 4. Integral Theorems -- 5. Coordinate Transformations; Definitions of Vectors and Tensors -- 6. Partial Differential Equations of the First Order -- 7. Partial Differential Equations of the Second Order -- 8. The Elliptic Case: Two Complex Characteristics -- 9. Applications of Complex Variables -- 10. The Parabolic Case: Two Coinciding Characteristics -- 11. The Hyperbolic Case: Two Real Characteristics -- 12. Hyperbolic Quasi Linear Partial Differential Equations -- 13. The Navier-Stokes Equations -- Appendix A. Numerical Integration of the Cauchy Integral -- Appendix B. List of Problems with Page Numbers.

This textbook presents the application of mathematical methods and theorems to solve engineering problems, rather than focusing on mathematical proofs. Applications of Vector Analysis and Complex Variables in Engineering explains the mathematical principles in a manner suitable for engineering students, who generally think quite differently than students of mathematics. The objective is to emphasize mathematical methods and applications, rather than emphasizing general theorems and principles, for which the reader is referred to the literature.