Differential Equations: Theory, Technique, and Practice

Differential equations is a fundamental subject in modern mathematics, dating back to Newton and Leibniz. It is used in engineering, physics, life sciences, and mathematical modeling. This book covers classical ideas and provides an entry to newer ones, with advanced topics such as the Laplace transform, Sturm–Liouville theory, and boundary value problems. It also emphasizes modeling, computer calculations, and graphics to provide real-life answers. The third edition is re-organized to make it more useful and accessible, with the most frequently taught topics up front and major applications isolated in their own chapters.

Format: Hardback
Length: 471 pages
Publication date: 30 May 2022
Publisher: Taylor & Francis Ltd

Differential equations, a venerable branch of modern mathematics, boasts a rich history that traces its origins back to the pioneering work of Newton and Leibniz. Shortly after the invention of calculus, the minds of Bernoulli, Euler, and others turned to the study of mathematical physics, encompassing the heat equation and the wave equation. Notably, Newton himself applied his mathematical prowess to solve differential equations, delving into both the realm of planetary motion and the intricate study of optics.

Today, differential equations assume a central role in diverse fields such as engineering, physics, life sciences, and mathematical modeling. This comprehensive text serves as a comprehensive introduction to classical concepts while also providing a gateway to more contemporary developments. The author meticulously addresses advanced topics such as the Laplace transform, Sturm–Liouville theory, and boundary value problems, drawing upon both traditional and modern perspectives.

This book originated as a modernization of George Simmons' renowned work, Differential Equations with Applications and Historical Notes. Prof. Simmons graciously invited the author to revise and update his book, resulting in the third edition, which has now become the author's own distinctive creation. This text seamlessly blends the timeless wisdom of classical differential equations with the cutting-edge advancements of modern theory, modeling, and computing.

Modeling brings differential equations to life, making abstract concepts tangible and relatable. By employing computer calculations and graphics, students can obtain real-life answers to complex problems, fostering a deep understanding and practical application of the subject matter. The symbiotic relationship between synthetic analysis and computational techniques creates a rich learning experience that equips students with the skills necessary for further exploration in more applied domains.

In addition to its core content, this text features several valuable features. "Anatomy of an Application" sections provide practical insights into how differential equations are applied in real-world scenarios. Historical notes, a hallmark of this text, offer a glimpse into the historical development of differential equations and their significance in advancing scientific knowledge. "Math Nuggets" provide concise perspectives on key mathematical concepts, enhancing students' understanding and retention.

In conclusion, differential equations stand as a testament to the enduring power of mathematics in unraveling the mysteries of the natural world. This comprehensive text, enriched with historical insights, advanced topics, and practical applications, serves as an invaluable resource for students, scholars, and practitioners alike. By embracing the fusion of classical and modern perspectives, it prepares individuals to tackle complex problems and contribute to the ongoing advancements in engineering, physics, life sciences, and mathematical modeling.

Weight: 1060g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032102702
Edition number: 3 ed