Differential Equations with MATLAB: Exploration, Applications, and Theory
暫譯: 使用 MATLAB 的微分方程：探索、應用與理論
McKibben, Mark, Webster, Micah D.
相關主題
商品描述
A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance.
The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics.
The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors' accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB(R) GUIs allows students to discover patterns and make conjectures.
商品描述(中文翻譯)
一本獨特的本科數學建模課程教科書，《Differential Equations with MATLAB: Exploration, Applications, and Theory》，為學生提供了對涉及常微分方程（ODEs）和偏微分方程（PDEs）數學模型的實用和理論方面的理解。該書呈現了一個統一的視角，涵蓋了超過20個不同模型的研究和分析，這些模型跨越物理、工程和金融等學科。
本書的第一部分介紹了線性常微分方程系統。文本從十個不同領域發展數學模型，包括藥物動力學、化學、經典力學、神經網絡、生理學和電路。第二部分專注於線性偏微分方程，涵蓋了在十個其他領域中出現的偏微分方程，這些領域包括熱傳導、波動傳播、流體通過裂隙岩石的流動、圖案形成和金融數學。
作者通過提出各類問題來吸引學生的參與，包括驗證細節、證明實際結果的猜想、分析理論發展中的大致輪廓，以及將理論應用於特定模型。作者的易讀風格鼓勵學生積極地學習材料並回答這些問題。此外，廣泛使用 MATLAB(R) GUI 使學生能夠發現模式並提出猜想。
