Essential Ordinary Differential Equations

This textbook provides an engaging and comprehensive account of the theory of ordinary differential equations, suitable for advanced undergraduate students of mathematics. It covers linear differential equations, separable equations, series solutions, matrix exponentials, and Sturm–Liouville theory, with project sections for further exploration. Prerequisites include analysis, multivariate calculus, linear algebra, and familiarity with metric spaces. The numerous exercises and projects offer ample opportunities for practice and independent study.

Format: Paperback / softback
Length: 283 pages
Publication date: 26 November 2022
Publisher: Springer International Publishing AG

This textbook provides an engaging and comprehensive account of the theory of ordinary differential equations, designed specifically for advanced undergraduate students of mathematics. Drawing upon the authors extensive teaching expertise, the book offers a well-structured series of topics that collectively cover a fundamental body of knowledge in this field. Each topic is treated with meticulous attention to detail, ensuring a thorough understanding.

The book begins with a thorough exploration of linear differential equations, covering key concepts such as general boundary conditions, Greens functions, and solutions. The subsequent chapters delve into separable equations, quadrature methods, series solutions of linear equations, matrix exponentials, and culminating in Sturm–Liouville theory, an indispensable tool for partial differential equations and mathematical physics.

The theoretical foundations of the material, including the existence and uniqueness of solutions, dependence on initial values, and various mathematical techniques, are extensively discussed. A notable aspect of this book is the inclusion of project sections that extend beyond the main text, introducing important additional topics and guiding the student through a combination of exercises and explanations. These project sections provide valuable opportunities for hands-on learning and further exploration.

Designed as the foundation for a course aimed at upper undergraduate students, this textbook assumes a solid background in analysis (both real and complex), multivariate calculus, and linear algebra. Some familiarity with metric spaces is also beneficial. The extensive exercise set within the text offers ample practice opportunities, while the aforementioned projects can be utilized for guided study. Additionally, some exercises include hints to facilitate independent study.

In summary, this textbook offers a valuable resource for advanced undergraduate students seeking to deepen their understanding of ordinary differential equations. With its engaging writing style, rigorous treatment of topics, and practical project sections, it provides a comprehensive and well-rounded foundation for further study in this field.

Weight: 456g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031115301
Edition number: 1st ed. 2023