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Recommendations for Mathematics for Physics and Engineering

On this page you can find some resources that provide the most important mathematical topics for physicists and engineers in one place. Some typical examples of such topics are complex numbers, vectors, matrices, vector analysis, fourier series, ODEs and PDEs (ordinary differential equations and partial differential equations) series solutions of differential equations, functions of a complex variable and probability. A good knowledge of calculus is a prerequisite for understanding most of these topics. If you have difficulties with this subject, you may want to look at some recommendations for Introductions to Calculus first.

Generally speaking, math texts for physicists tend to be more advanced than those for engineers, mainly because for understanding subjects like quantum mechanics, physicists cannot rely on intuition but have to use some very sophisticated mathematical methods. However, there are some texts (like Boas) that provide a very gentle introduction to mathematics, so even if you are an engineering student they might be the best texts for you (if you skip those topics that you do not need for your studies).

Much easier than the other texts on this page is Engineering Mathematics 1 by Craw, Dagger and Pulham. It covers the minimum of mathematics that you need in electronics.

Very popular, especially with physics students, is Mathematical Methods in the Physical Sciences by Mary L. Boas. But also engineering students should have a look at it. For EE students I have added a few comments to the table of content to show you for which area in EE each math topic that is covered Boas might be useful.

Very comprehensive is the free Introduction to Methods of Applied Mathematics by Sean Mauch. Some parts are missing (especially in the advanced chapters about partial differential equations, calculus of variations and nonlinear differential equations), but on 2321 pages it provides a lot of information.

More advanced than Boas is the free Mathematical Tools for Physics by James Nearing. You will probably most profit from it if you have already a basic knowledge of the topics that are covered. Then Nearing will teach you how to apply them most effectively.

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