If you will pardon the pun, an electrical and computer engineering (ECE) student must be solidly grounded in mathematical analysis to succeed in calculus, differential equations, Laplace transforms, and other areas of high-level mathematics. Fortunately, one of the classic, proven texts in the field, Principles of Mathematical Analysis, is available for free in several electronic file formats at https://archive.org/details/1979RudinW.
Written by the late, great Walter Rudin of the University of Wisconsin, Principles of Mathematical Analysis has been a well-respected textbook for well over 40 years, and it is admired for its clear and concise prose style. The book is nearly devoid of graphics, and it would certainly not win any awards for production values. However, it is a clear and thorough introduction to the field of mathematical analysis, with the following eleven chapters:
- The Real and Complex Number Systems
- Basic Topology
- Numerical Sequences and Series
- The Riemann-Stieltjes Integral
- Sequences and Series of Functions.
- Some Special Functions
- Functions of Several Variables
- Integration of Differential Forms
- The Lebesgue Theory
Not all of these topics are required for an undergraduate ECE student, but most are useful background, and it is good to have a quick way to learn should an unexpected topic appear in a class.
A separate answer key, written by Roger Cook of the University of Vermont, is available at https://minds.wisconsin.edu/handle/1793/67009.