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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.
We then return to the solution of problems in classical dynamics through the use of Lagrange's equations and Hamilton's equations, as well as Hamilton-Jacobi theory which is fundamental to quantum theory discussed towards the end of the book.
Although the subjects of Fourier series, Fourier and Laplace transforms, and integral equations, are not strictly applied mathematics, they are essential for the study of wave motions, including vibrating strings, sound waves and water waves, and for the study of heat conduction.
Here we collect 10 essential applied mathematics problems to get you thinking before you embark on your degree, although many of the problems from the physics and engineering areas will also be relevant.
They will be very useful to anyone intending to study mathematics, physics or engineering: they will give you a good mathematical grounding in some of the topics likely to arise in your degree course and refine your problem solving skills.
We now come to vector field theory which is concerned with vector functions of position in regions of space and the important theorems first proved by Gauss, Green and Stokes.
This subject enables us to solve problems in Newtonian gravitation, electricity and magnetism, and fluid dynamics.
This book attempts to show students of applied mathematics how problems can be solved.
The subject of applied mathematics is extremely wide ranging, as can be seen from the contents list of this book which is far from being comprehensive in scope since otherwise the book would be enormously long.
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.