Free book Derivations of Applied Mathematics is a book of applied mathematical proofs. If you have seen a mathematical result, if you want to know why the result is so, you can look for the proof here.

**Description**

The book’s purpose is to convey the essential ideas underlying the derivations of a large number of mathematical results useful in the modeling of physical systems. To this end, the book emphasizes main threads of mathematical argument and the motivation underlying the main threads, deëmphasizing formal mathematical rigor. It derives mathematical results from the purely applied perspective of the scientist and the engineer.

**Contents**

- Introduction
- Classical algebra and geometry
- Trigonometry
- The derivative
- The complex exponential
- Primes, roots and averages
- The integral
- The Taylor series
- Integration techniques
- Cubics and quartics
- The matrix
- Rank and the Gauss-Jordan
- Inversion and orthonormalization
- The eigenvalue
- Vector analysis
- Vector calculus
- The Fourier series
- The Fourier and Laplace transforms

**Book Details**