This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
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).
This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more.
Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; further developments in the ...
Differential Equations
This highly useful text shows the reader how to formulate a partial differential equation from the physical problem and how to solve the equation.
The author developed and used this book to teach Math 286 and Math 285 at the University of Illinois at Urbana-Champaign. The author also taught Math 20D at the University of California, San Diego with this book.
This book is designed as a textbook for undergraduate students of mathematics, physics, physical chemistry, engineering, etc.
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.
Whether you need a course supplement, help preparing for an exam, or a concise reference for the subject, CliffsQuickReview Differential Equations can help. This guide covers first-order and second-order equations, power series, and more.
Teaches the Key Topics in Differential Equations The text includes all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations.