Partial Differential Equations : An Introduction, 2/e (Hardcover)

Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. While focusing on the three most classical partial differential equations (PDEs)—the wave, heat, and Laplace equations—this detailed text also presents a broad practical perspective that merges mathematical concepts with real-world application in diverse areas including molecular structure, photon and electron interactions, radiation of electromagnetic waves, vibrations of a solid, and many more.

Rigorous pedagogical tools aid in student comprehension; advanced topics are introduced frequently, with minimal technical jargon, and a wealth of exercises reinforce vital skills and invite additional self-study. Topics are presented in a logical progression, with major concepts such as wave propagation, heat and diffusion, electrostatics, and quantum mechanics placed in contexts familiar to students of various fields in science and engineering. By understanding the properties and applications of PDEs, students will be equipped to better analyze and interpret central processes of the natural world.

「偏微分方程」提供了一個平衡且全面的介紹，介紹了解決包含多個變數未知函數的問題所需的概念和技巧。雖然重點放在三個最經典的偏微分方程（波動方程、熱方程和拉普拉斯方程）上，但這本詳細的教材還提供了廣泛的實際觀點，將數學概念與分子結構、光子和電子相互作用、電磁波輻射、固體振動等多個領域的實際應用相結合。

嚴謹的教學工具有助於學生理解；高級主題經常被介紹，並且只使用最少的技術術語，大量的練習強化了重要的技能並鼓勵進一步的自學。主題按照邏輯進行呈現，重要概念（如波動傳播、熱和擴散、靜電學和量子力學）被放置在科學和工程各個領域的學生熟悉的背景中。通過理解偏微分方程的性質和應用，學生將能夠更好地分析和解釋自然界的核心過程。