Useful Advanced Mathematics textbooks.
This list will be updated regularly. If you know any other advanced mathematics books that are tailored for engineers, I would love to hear from you!
Linear Algebra
Linear Algebra Done Right, Sheldon Axler.
Real Analysis
1- Understanding Analysis, Stephen Abbott.
2- Principles of Mathematical Analysis, Walter Rudin.
3- Dr Francis Su Course. (Online videos available). Highly recommended!
Functional Analysis
1- Measure, Integration and Real Analysis, Sheldon Axler. A rigorous systematic approach. Prerequisites: basics of Real Analysis. Professor Axler provides supplementary materials on Real Analysis.
2- Linear Operator Theory in Engineering and Science, Arch W. Naylor , George R. Sell. Comprehensive Textbook that provides an engineering tone to many of the abstract functional analysis concepts.
3- Introductory Functional Analysis with Applications, Dr Kreyszig is the author of one of the most used engineering mathematics textbooks. His book on functional analysis is very well organized. The main concepts of each subject are summarized early before the formal treatment. In my opinion, this is very helpful for engineers who want to use the book for self studying.