Advanced Engineering Mathematics
The tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. It goes into the following topics at great depth differential equations, partial differential equations, Fourier analysis, vector analysis, complex analysis, and linear algebra/differential equations.
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I absolutely do NOT recommend this text for those learning new material. It does have a lot of engineering applications and could possibly be used as a resource for those applications, but the math behind it all is poorly explained and several key pieces of information have been left out. I have routinely had to take the name of the topic from the book and research other online sources in order to learn the material. I have an undergrad in math and 78 grad credits between math & education and this is by far the most difficult textbook I've had to struggle through.