Exploring Partial Differential Equations: A Computational Approach

Aram Manaselyan

Partial differential equations (PDEs) are among the most powerful tools in mathematics, providing the essential framework for describing change, motion and field dynamics. From the flow of heat and the propagation of electromagnetic waves to the complexities of quantum mechanics and modern financial markets, PDEs form the foundation of the technologies and theories shaping our world.

This book provides a practical, accessible introduction to PDEs, uniquely leveraging the computational power of Wolfram Language. By seamlessly integrating symbolic derivation, efficient numerical methods and high-quality visualization, this text allows readers to bridge the gap between abstract theory and real-world application.

The curriculum is designed to build intuition progressively. Students begin with fundamental concepts—such as classification and boundary conditions—before mastering the three classical equations of mathematical physics: the heat, wave and Laplace equations. The journey culminates in an exploration of the most influential equations in modern science, including the Black–Scholes, Schrödinger, Maxwell and Navier–Stokes equations.

To ensure mastery, the text includes a "nutshell" summary study guide and sample exam. Readers can also download the free, interactive ebook edition to engage with live Wolfram Language code. Additional materials, including videos and quizzes, can be found online in the companion Wolfram U course.