Fundamental Practices of Applied PDE & Beyond

The primary motivation of this book is to provide working knowledges in the introductory level of applied partial differential equations required for general mathematical modeling used in science and engineering. In addition to standard practices in elementary-level applied differential equations, topics on analytical and numerical approximation methods, and stochastic calculus and its practical application are presented at certain introductory levels. The basic requirements to digest the materials in this book are thorough understanding on calculus, basic operations in linear algebra, and some understanding on complex numbers. Rather than following a certain pedagogical structure, minimal explanations on fundamental concepts are given with minimal pure mathematical abstraction. The main focus is that solution procedures for each question are fully presented, which are critical parts in this book. Solutions are written as much in detail as possible to the extent that readers should be able to learn optimal knowledges on underlying materials that fit for given problem descriptions. It is more right to say that this book is a selected-problem-oriented guideline for assignments, quizzes, and exams in one-semester course. Accordingly, this book will work best if it is used as a hand-on reference to other standard textbooks in applied partial differential equations.