Thus the boxes labelled wave motion and heat conduction cannot be opened before the box containing Fourier series has been examined in some detail.
Next we turn to tensor analysis, which enables us to express Maxwell's electromagnetic equations in a relativistically invariant form, and to develop the special theory and general theory of relativity.
There are many applied mathematics boxes which we have not explored in this book.
Several contain more than one box immediately within, some of which we have not opened, such as for the subjects of elasticity and statistical mechanics, for example. To summarize, my aim has been to attempt to bridge the gap between a course of lectures in which concepts are developed and the basic applied mathematics analysed, and the problems which are provided for students to test their understanding of the subject being studied.
One fun topic that came to mind when I read this question is traffic flow.
I spent a third of a semester in one class focusing solely on setting up, interpreting, and solving a model for freeway traffic flow. Whatever it is, you likely have the tools to solve the complicated optimization problem that emerged either exactly, or with some numerical method you learned.
A case is presented for the importance of focusing on (1) average ability students, (2) substantive mathematical content, (3) real problems, and (4) realistic settings and solution procedures for research in problem solving.
It is suggested that effective instructional techniques for teaching applied mathematical problem solving resembles “mathematical laboratory” activities, done in small group problem solving settings.
All the problems can be solved in closed analytical forms in terms of elementary functions or simple integrals.
The book starts with an introductory chapter in which there is a survey of the range of subjects which are covered in the subsequent chapters by means of a small representative selection of problems, together with some general principles for solving problems in applied mathematics.