Chapter 1
Introduction

The purpose of an engineering education is predict outputs given inputs within the physical world. By doing this, experiments do not need to be conducted to predict a certain behavior; instead, an equation can be used. This saves time and money. The models/equations used to predict behavior within the physical world can be boiled down to two classifications. These are empirical models and analytical models. Empirical models are based off of the observation of patterns. Essentially, we are fitting an equation to a dataset. Analytical models are mathematical manipulations based off of physical axioms. The process of combining mathematical manipulations to physical axioms in the goal of obtaining a analytical equation is called deriving.

The objective of this book is to provide a coherent overview of how the physical world is modeled, specifically geared at engineering applications. In order to accomplish this, fundamental physical concepts are introduced. Derivations for the most important analytical equations in engineering are presented.

Many books already exist which include the information summarized herein. However, two factors differentiate this book from the prevailing literature. The first is, as already mentioned, this book is comprehensive. Physics and engineering are intimately connected, and many derivations used within engineering derive from physics derivations/axioms. In addition, many engineering topics themselves are closely connected. Current textbooks and courses themselves are segmented. For example, dynamics (chapter ??) and solid mechanics (chapter ??) are grouped and taught separately from each other and from fluid mechanics (chapter ??). However, fluids are modeled by using the same physical axioms as dynamics (chapter ??) combined with differential approaches (differential equations are overviewed in chapter 2) used in solid mechanics (chapter ??). By combining engineering, math, and physics topics into a single book, connections can be made which would be otherwise be left out. The second differentiate of this book is the target tone. As you may have experience with, engineering textbooks are often extremely boring. In fact, I have personally used textbooks to help myself fall asleep before when having insomnia. In this book, a more conversational tone is adopted in the hope of a more pleasurable reading experience. In addition, information is provided concisely; the minimum information is provided so that the reader can fully understand the concept/derivation. Some books that have served as an inspiration for me when writing this book are Transmission Electron Microscopy by Williams and Carter, Welding Metallurgy by Kou and Phase Transformations in Metals and Alloys by Porter, Easterling, and Sherif.

While this book is written to be comprehensive, the material presented herein assumes the reader posses a high school level physics and math understanding. The mathematics in this book begins at a calculus level. Although basic physics and chemistry concepts are reviewed, the reader is expected to be familiar with basic physical phenomena such as waves.