Book for Mathematics applied to engineering

Question

I need a reference (book or lecture notes) for engineering which covers the following subjects:

1. Preliminaries of integration, series of functions, simple and uniform convergences.
2. Laplace Transform and Applications
3. Fourier transform and applications
4. Z-Transform and Applications
5. Distributions
6. Special functions, gamma, beta, Bessel functions

Answer 1

A classic textbook is Advanced Engineering Mathematics by Erwin Kreyszig. The textbook itself is 1280 pages long and covers everything in the your list outside of Z-Transforms. I used the textbook for an upper level undergraduate engineering mathematics course and found the explanations to be suitable to an engineer. The textbook also includes a large amount of practice problems. If you are interested in functional analysis, Kreysig also wrote Introductory Functional Analysis with Applications.

If you are interested in learning more about applied mathematics at the research level, I would recommend the Princeton Companion to Applied Mathematics.

Answer 2

Try any one of the following ...

Higher Engineering Mathematics by B.S. Grewal.

Advanced Engineering Mathematics by Erwin Kreyszig

Advanced Engineering Mathematics by R. K. Jain and S.R.K. Iyengar

Advanced Engineering Mathematics by Dennis G Zill and Warren S Wright