Edited by Brent Lewis, Nihan Onder, and Andrew Prudil, Elsevier Press, 2021, ISBN: 9780128236819 (Paperback), xix +404 pages, $100 (list)
The authors of this text have abstracted and summarized in this text their offering of a third-year two semester course in advanced mathematics in the Department of Chemistry and Chemical Engineering at the Royal Military College of Canada. Some applied mathematics matter from related engineering courses has also been added here. With these additions, the text is also purported also to be of value to most other engineers post-graduation. The text was selected for review here as it may be of value to you as a reference or as a foundation teaching text. Some knowledge of COMSOL and MAPLE is needed to fully utilize this text.
The body of the text consists of 14 chapters, 13 of which cover a subset of the mathematical material covered. Chapter 1 introduces the history of differential equations and outlines the text organization and uses. Chapters 2–14 cover subsets of the course material, specifically the following:
2. Ordinary Differential Equations
3. Laplace and Fourier Transform Methods
4. Matrices and Linear Systems of Equations
5. Analytical Methods for Solving Partial Differential Equations
6. Difference Numerical Methods for Differential Equations
7. Finite Element Technique
8. Treatment of Experimental Results
9. Numerical Analysis
10. Introduction to Complex Analysis
12. Nonlinear Differential Equations
13. Integral Equations
14. Calculus of Variations
Each chapter contains 2–6 subsets of the material covered, with a well-illustrated set of example applications. Each chapter concludes with a set of relevant problems for the reader (average 9, range 4–18); a solutions manual for these is available.
A 5-page Appendix A lists Maple software package commands, and a 4-page Appendix B touches on Geodesic formulation. (MATLAB would be a nice addition.)
Overall, this reviewer considers this text to offer a good and useful coverage of advanced mathematics for engineers. It gives useful and succinct coverage of the topics included.