Worked Examples in Mathematics for Scientists & Engineers

This rich collection of fully worked problems in many areas of mathematics covers all the important subjects students are likely to encounter in their courses, from introductory to final-year undergraduate classes. Because lecture courses tend to focus on theory rather than examples, these exercises offer a valuable complement to classroom teachings, promoting the understanding of mathematical techniques and helping students prepare for exams. They will prove useful to undergraduates in mathematics; students in engineering, physics, and chemistry; and postgraduate scientists looking for a way to refresh their skills in specific topics.
The problems can supplement lecture notes and any conventional text. Starting with functions, inequalities, limits, differentiation, and integration, topics encompass integral inequalities, power series and convergence, complex variables, hyperbolic function, vector and matrix algebra, Laplace transforms, Fourier series, vector calculus, and many other subjects.

Geoffrey Stephenson (1927–2018) was Reader in the Department of Mathematics at the Imperial College of Science and Technology, London. He was the author of several mathematical texts, including Dover's An Introduction to Matrices, Sets and Groups.

Contents

Preface
1. Functions
2. Inequalities
3. Limits
4. Differentiation
5. Integration
6. Integral inequalities
7. Power series and convergence
8. Complex variables
9. Hyperbolic functions
10. Partial differentiation
11. Stationary values of functions of two variables
12. Determinants and difference equations
13.Vector algebra
14. Matrix algebra
15, Line and double integrals
16. Ordinary differential equations
17. Special functions
18. Laplace transform
19. Fourier series
20. Vector calculus
21. Partial differential equations
22. Functions of matrices
23. Contour integration
24. Fourier transforms
25. Calculus of variations
26. Suffix notation
Index