Partial Differential Equations: Analytical Methods and Applications

Partial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners' course for graduate students. It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor.

This text introduces and promotes practice of necessary problem-solving skills. The presentation is concise and friendly to the reader. The "teaching-by-examples" approach provides numerous carefully chosen examples that guide step-by-step learning of concepts and techniques. Fourier series, Sturm-Liouville problem, Fourier transform, and Laplace transform are included. The book's level of presentation and structure is well suited for use in engineering, physics and applied mathematics courses.

Highlights:

• Offers a complete first course on PDEs
• The text's flexible structure promotes varied syllabi for courses
• Written with a teach-by-example approach which offers numerous examples and applications
• Includes additional topics such as the Sturm-Liouville problem, Fourier and Laplace transforms, and special functions
• The text's graphical material makes excellent use of modern software packages
• Features numerous examples and applications which are suitable for readers studying the subject remotely or independently

《偏微分方程：分析方法與應用》涵蓋了大學部學生的偏微分方程（PDE）課程的所有基本主題，也適用於研究生的初階課程。本書在保持數學結果的預期嚴謹性的同時，提供了定性的物理解釋。

本書介紹並促進了必要的問題解決技巧的實踐。演示簡潔友好，採用了「以例子教學」的方法，提供了許多精心選擇的例子，引導讀者逐步學習概念和技巧。書中包括傅立葉級數、斯特姆-李維爾問題、傅立葉變換和拉普拉斯變換等內容。本書的呈現水平和結構非常適合工程、物理和應用數學課程使用。

亮點：
- 提供了完整的偏微分方程初階課程
- 本書的靈活結構適合不同的課程大綱
- 以「以例子教學」的方式撰寫，提供了許多例子和應用
- 包括斯特姆-李維爾問題、傅立葉和拉普拉斯變換以及特殊函數等額外主題
- 本書的圖形材料充分利用了現代軟體包
- 提供了許多適合遠程或獨立學習的讀者的例子和應用

Victor Henner is a professor at the Department of Physics and Astronomy at the University of Louisville. He has Ph.Ds from the Novosibirsk Institute of Mathematics in Russia and Moscow State University. He co-wrote with Tatyana Belozerova Ordinary and Partial Differential Equations.

Tatyana Belozerova is a professor at Perm State University in Russia. Along with Ordinary and Partial Differential Equations, she co-wrote with Victor Henner Mathematical Methods in Physics: Partial Differential Equations, Fourier Series, and Special Functions.

Alexander Nepomnyashchy is a mathematics professor at Northwestern University and hails from the Faculty of Mathematics at Technion-Israel Institute of Technology. His research interests include non-linear stability theory and pattern formation.

Victor Henner 是路易斯維爾大學物理和天文學系的教授。他在俄羅斯的諾沃西比爾斯克數學研究所和莫斯科國立大學獲得博士學位。他與 Tatyana Belozerova 合著了《常微分方程和偏微分方程》。

Tatyana Belozerova 是俄羅斯的彼爾姆州立大學的教授。除了《常微分方程和偏微分方程》外，她還與 Victor Henner 合著了《物理學中的數學方法：偏微分方程、傅立葉級數和特殊函數》。

Alexander Nepomnyashchy 是西北大學的數學教授，來自以色列理工學院的數學學院。他的研究興趣包括非線性穩定性理論和模式形成。