If you've struggled to understand the finite element method, then you must read this book. I don't cover a lot of theory in this text. It's mostly a compilation of examples. The one theoretical aspect of numerical methods for solving differential equations that I will present is the finite element method. This powerful technique is more often than not buried under a mountain of esoteric details that make it inaccessible to most students of applied mathematics. I aim to reveal, not obfuscate. I trust you will find this book helpful in that respect.Understanding applied mathematics results in a richer appreciation of the world and how it works. Those who see only disconnected objects and forces miss the elegance with which such things can be described in the versatile language we call calculus. Differential equations describe the way objects and forces interact. While there are many analytical techniques for solving such problems, this book deals with numerical methods. You must understand some of the former in order to appreciate the latter. Rather than covering the minutia of every obscure method, this book will focus on what works consistently and efficiently. This is a compilation of examples, not a textbook on theory. I trust you will find it interesting and useful.