Partial Differential Equations and Applications: A Bridge for Students and Researchers in Applied Sciences

Partial Differential Equations and Applications: A Bridge for Students and Researchers in Applied Sciences offers a unique approach to this key subject by connecting mathematical principles to the latest research advances in select topics. Beginning with very elementary PDEs, such as classical heat equations, wave equations and Laplace equations, the book focuses on concrete examples. It gives students basic skills and techniques to find explicit solutions for partial differential equations. As it progresses, the book covers more advanced topics such as the maximum principle and applications, Green's representation, Schauder theory, finite time blowup and sock waves.

By exploring these topics, students gain necessary tools to deal with research topics in their own fields, whether proceeding in math or engineering areas.

《偏微分方程與應用：應用科學中學生和研究人員的橋樑》通過將數學原理與選定主題的最新研究進展相結合，提供了一種獨特的方法來探討這一關鍵主題。從非常基礎的偏微分方程開始，例如經典的熱方程、波動方程和拉普拉斯方程，本書著重於具體的例子。它為學生提供了解決偏微分方程的具體解的基本技能和技巧。隨著內容的進展，本書還涵蓋了更高級的主題，如最大值原理和應用、格林表示、Schauder理論、有限時間爆炸和激波等。

通過探索這些主題，學生們將獲得處理自己領域研究主題所需的必要工具，無論是在數學還是工程領域。