This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.
The summation in (43.37) is now the same as the right side of L. (c) of (43.2). B. Integral Property of Laguerre Polynomials. Theorem 43.4. Let Losa), L1(c), L2(a), . . . , be Laguerre polynomial solutions of (43.1).
The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions.
Beginning with a comprehensive treatment of linear differential equations with variable coefficients, the text gives a detailed discussion on some well-known special functions which provide solutions of secondorder linear ordinary ...
Problems at the end of each chapter and two Appendixes on special topics enrich the text.
The Second Edition of Ordinary Differential Equations: An Introduction to the Fundamentals builds on the successful First Edition.
McLachlan, N. W., Ordinary Non-Linwr Difierential Equations in Engineering and Physical Sciences, 2nd edition, Oxford University Press, New York, 1956. Meyer zur Capellen, Walther, Integraltafeln. Sammlung unbestimmter Integrate ...
The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations.
Editor-in-Chief Robert E. O'Malley, Jr., University of Washington Editorial Board John Boyd, University of Michigan Leah Edelstein-Keshet, University of British Columbia William G. Faris, University of Arizona Nicholas J. Higham, ...
First-rate introduction for undergraduates examines first order equations, complex-valued solutions, linear differential operators, the Laplace transform, Picard's existence theorem, and much more. Includes problems and solutions.
Providing a useful resource both in and out of the classroom, the text: Employs a unique expository style that explains the how and why of each topic covered Allows for a flexible presentation based on instructor preference and student ...