If you have ever sat with a student who understands the theory perfectly well but freezes the moment they face an actual problem, you will immediately see the value of this book. Stephenson’s Worked Examples in Mathematics for Scientists and Engineers is exactly what the title promises, and it delivers on that promise consistently.
This is a companion volume to Stephenson’s Mathematical Methods for Science Students, though it stands perfectly well on its own. The entire premise is straightforward: take the mathematical methods that science and engineering students need, and show them, in detail, how those methods are actually applied. No lengthy theoretical preamble. Just clear, carefully constructed examples worked through from start to finish.
The topics span the usual ground for this level, including differential equations, Laplace transforms, Fourier series, vector calculus and complex numbers. What Stephenson does well is vary the difficulty within each topic, so students can build confidence on accessible examples before tackling the more demanding ones. The solutions are thorough without being unnecessarily verbose, which I find is the right balance for this kind of text.
In my experience, books like this are often undervalued compared to the main textbooks, but they are frequently what actually gets students over the line in assessments. Understanding a method and being able to execute it fluently under pressure are two different things, and worked example books bridge that gap.
I would recommend this to any student in their first or second year of a science or engineering degree, or to teachers looking for well-structured problems to use in class.