A Workbook for Differential Equations (Paperback)

An accessible and hands-on approach to modeling and predicting real-world phenomena using differential equations

A Workbook for Differential Equations presents an interactive introduction to fundamental solution methods for ordinary differential equations. The author emphasizes the importance of manually working through computations and models, rather than simply reading or memorizing formulas.

Utilizing real-world applications from spring-mass systems and circuits to vibrating strings and an overview of the hydrogen atom, the book connects modern research with the presented topics, including first order equations, constant coefficient equations, Laplace transforms, partial differential equations, series solutions, systems, and numerical methods. The result is a unique guide to understanding the significance of differential equations in mathematics, science, and engineering.

The workbook contains modules that involve readers in as many ways as possible, and each module begins with "Prerequisites" and "Learning Objectives" sections that outline both the skills needed to understand the presented material and what new skills will be obtained by the conclusion of the module. Detailed applications are intertwined in the discussion, motivating the investigation of new classes of differential equations and their accompanying techniques. Introductory modeling sections discuss applications and why certain known solution techniques may not be enough to successfully analyze certain situations. Almost every module concludes with a section that contains various projects, ranging from programming tasks to theoretical investigations.

The book is specifically designed to promote the development of effective mathematical reading habits such as double-checking results and filling in omitted steps in a computation. Rather than provide lengthy explanations of what readers should do, good habits are demonstrated in short sections, and a wide range of exercises provide the opportunity to test reader comprehension of the concepts and techniques. Rich illustrations, highlighted notes, and boxed comments offer illuminating explanations of the computations. The material is not specific to any one particular software package, and as a result, necessary algorithms can be implemented in various programs, including Mathematica®, Maple, and Mathcad®. The book's related Web site features supplemental slides as well as videos that discuss additional topics such as homogeneous first order equations, the general solution of separable differential equations, and the derivation of the differential equations for a multi-loop circuit. In addition, twenty activities are included at the back of the book, allowing for further practice of discussed topics whether in the classroom or for self-study.

With its numerous pedagogical features that consistently engage readers, A Workbook for Differential Equations is an excellent book for introductory courses in differential equations and applied mathematics at the undergraduate level. It is also a suitable reference for professionals in all areas of science, physics, and engineering.

一本關於微分方程建模和預測現實世界現象的易於理解和實踐的教材

《微分方程工作手冊》是一本互動式的普通微分方程基本解法方法介紹。作者強調手動計算和建模的重要性，而不僅僅是閱讀或記憶公式。

本書運用了從彈簧質量系統和電路到振動弦和氫原子的現實應用，將現代研究與所介紹的主題相結合，包括一階方程、常係數方程、拉普拉斯變換、偏微分方程、級數解、系統和數值方法。結果是一本獨特的指南，幫助讀者理解微分方程在數學、科學和工程中的重要性。

本工作手冊包含多個模塊，以盡可能多的方式讓讀者參與其中。每個模塊都以“先備知識”和“學習目標”部分開始，概述了理解所介紹材料所需的技能以及通過模塊結束時將獲得的新技能。詳細的應用交織在討論中，激發對新類微分方程及其相應技巧的研究。入門建模部分討論應用以及為什麼某些已知解法技巧可能不足以成功分析某些情況。幾乎每個模塊都以包含各種項目的部分結束，從編程任務到理論研究不等。

本書的設計旨在培養有效的數學閱讀習慣，例如檢查結果和填補計算中遺漏的步驟。與其提供冗長的解釋，本書以短節展示良好的習慣，並提供各種練習機會來測試讀者對概念和技巧的理解。豐富的插圖、突出的註釋和方框註解提供了對計算的解釋。本書的內容不特定於任何特定的軟件包，因此必要的算法可以在各種程序中實施，包括Mathematica®、Maple和Mathcad®。本書的相關網站提供補充幻燈片和視頻，討論額外的主題，如齊次一階方程、可分離微分方程的一般解和多回路電路的微分方程推導。此外，書末還包含二十個活動，無論是在課堂上還是自學，都可以進一步練習所討論的主題。

《微分方程工作手冊》具有多種教學特點，始終吸引讀者，是大學微分方程和應用數學入門課程的優秀教材。它也是科學、物理和工程各個領域的專業人士的適用參考書。