Both mathematics and basic electrical engineering go hand in hand when theory and analysis of topics in basic electrical engineering subjects are discussed. This text book introduces the application of a wide range of applied mathematics ranges from a very simple mathematical operations like algebraic equations or complex numbers to a much more sophisticated mathematical theories like Gauss's, theorem, Stokes's theorem, and Maxwell's equations. It is impossible to compile in one book all the mathematical operations involved in the development of electrical engineering theories. However, we have attempted to cover a wide variety of applied mathematics and the associated basic classical electrical engineering topic. This book is not a text book for mathematics and is not a text book for basic electrical engineering. It is a text book offering the mathematical tools and theories needed to discuss several classical electrical engineering subjects. Undergraduate and graduate students can utilize this book to help them comprehend the basics in classical electrical engineering topics. The book contains several examples on each theory discussed. Furthermore, the appendix is offering additional examples covering most of the theories discussed. The reader should have a background in calculus, differential equations, complex numbers, geometry, integration, differentiation, and matrices, etc.