The Best Introductory Books on Differential Equations

I recommend an excellent book for non-mathematics majors titled Differential Equations and Their Applications (Chinese title: 《微分方程及其应用》). This book is practically written for engineering students, particularly those in physics, as an introduction to ordinary differential equations. It strikes a perfect balance between theory and practical applications, offers numerous worked examples, and is often used as a self-study resource.

The author, Martin Braun, is a Professor of Mathematics at Queens College. He has authored several textbooks related to differential equations, but this book is the most popular one. It is widely adopted as a textbook in many universities and has been translated into multiple languages. It is regarded as a premier textbook in applied mathematics.

The book mainly covers the fundamentals of ordinary differential equations, higher-order differential equations, systems and matrices, nonlinear differential equations, partial differential equations, and Fourier analysis. With an engaging, fluid, yet highly professional style, the author leads readers on an in-depth exploration of the mysteries of differential equations, making the experience immersive and captivating. Despite the technical nature of differential equations, the explanations are smooth and natural, inspiring readers to delve deeper into related materials after completing the book. For inquisitive students, the author’s insightful discussions stem from a clear intention to facilitate comprehension of differential equations’ core concepts. Whether encountering differential equations for the first time or seeking to review and consolidate knowledge, the book’s clear, vivid, and approachable explanations will prove immensely valuable. Each concept is paired with corresponding application examples, linking theory with practice to enhance understanding. It is recommended to follow the sequence: start with first-order equations, then higher-order, followed by systems, nonlinear equations, partial differential equations, and finally Fourier analysis. For each case study, it is beneficial to first independently construct the differential equation model.

A solid background in calculus is essential for studying this book, and familiarity with linear algebra will greatly accelerate mastering its content. Additionally, since this book is primarily designed for engineering students, it does not delve deeply into the theory of differential equations. Mathematics majors may prefer more theoretical textbooks on differential equations.