Introduction to Non-linear Differential and Integral Equations (Dover Books on Mathematics)

Book Details

• Author: Harold Thayer Davis

• Publisher: Dover

• Binding: Paperback

• Format: Import

• Number of Pages: 566

• Release Date: 01-12-1960

• ISBN: 9780486609713

• Languages: English

• Package Dimensions:

  • Length: 8.4 inches

  • Width: 5.5 inches

  • Height: 1.9 inches

About The Book
"Introduction to Nonlinear Differential and Integral Equations" by Harold Thayer Davis provides a thorough and accessible introduction to the field of nonlinear equations, a critical area of mathematical physics. As interest in nonlinear equations has grown significantly in recent years, particularly due to advances in computational methods, this book remains an invaluable resource for understanding the analytical and computational approaches to solving these equations.

The text starts with a broad survey of nonlinear equations and their applications in various domains of physics, with an emphasis on how machines have expanded our knowledge of these complex problems. Davis argues that while computational tools are essential, analytical methods still provide invaluable insights, especially when dealing with singularities that only analytical techniques, grounded in the work of pioneers like Poincaré, Liapunov, and Painlevé, can uncover.

The book covers a range of essential topics, starting with first-order differential equations, followed by a discussion of the Riccati equation, which acts as a bridge between linear and nonlinear equations. The text then introduces second-order equations through Volterra’s problem and the pursuit problem, followed by in-depth explorations of elliptic integrals, theta functions, Painlevé transcendents, and continuous analytical continuation. The book also discusses phenomena in the phase plane and introduces nonlinear mechanics through classical problems such as Van der Pol’s equation, Emden’s equation, and the Duffing problem.

Later chapters tackle nonlinear integral equations, variational calculus, and the numerical integration of nonlinear equations. Throughout, the book strikes a balance between classical analytical methods and modern machine computations, providing a well-rounded perspective on the subject.

With 566 pages of meticulously organized content, this book serves as a comprehensive introduction to nonlinear equations, suitable for mathematically sophisticated readers. Its manageable size (8.4 x 5.5 x 1.9 inches) ensures that it remains an accessible and practical resource for both students and researchers in the field of applied mathematics and physics.