寻求分离变量法求解偏微分方程的优质参考资料

Hey there! I totally get your frustration—having solid exercises and detailed examples is key to really locking down separation of variables for PDEs. You’re right that Shearer & Levy’s Chapter 6 and Evans’ Chapter 4 cover the theory well but are light on practice material. Here are some go-to resources I’ve relied on to fill those gaps:

• 《Partial Differential Equations: An Introduction》by Walter Strauss
  This book is practically a staple for mastering separation of variables. It walks you through the method step-by-step for heat equations, wave equations, and Laplace equations, with tons of exercises ranging from basic skill-building to more challenging problems. The examples are super detailed, breaking down every part of the separation process so you can follow along easily.

• 《Elementary Differential Equations and Boundary Value Problems》by Boyce & DiPrima
  Don’t let the "Elementary" in the title fool you—this textbook has an incredibly thorough section on separation of variables for common linear PDEs and boundary value problems. It’s packed with classic practice problems, and many undergraduate PDE courses use it specifically for building up problem-solving skills. Perfect for boosting your exercise volume.

• 《PDEs: A Primer》by James Kirkwood
  If you prefer a more "hand-holding" approach, this book is great. It explains every derivation clearly, and the separation of variables chapter includes plenty of fully worked examples alongside theory. It’s ideal for reinforcing the basics and making sure you understand how to apply the method in different scenarios.

• 《Applied Partial Differential Equations》by Richard Haberman
  For a more applied angle, this resource ties separation of variables to real-world physics and engineering problems. The exercises here are focused on practical applications, which helps you connect the mathematical method to actual use cases and expand your problem-solving perspective.

These resources complement the theoretical foundation you get from Shearer & Levy and Evans by giving you the practice and detailed examples you need to really master separation of variables.

备注：内容来源于stack exchange，提问作者Math_Day