This new book from one of the most published authors in all of mathematics is an attempt to offer a new, more modern take on the Differential Equations course. The world is changing. Because of the theory of wavelets, Fourier analysis is ever more important and central. And applications are a driving force behind much of mathematics.This text text presents a more balanced picture. The text covers differential equations (both ordinary and partial), Fourier analysis and applications in equal measure and with equal weight. The Riemann integral is used throughout. We do not assume that the student knows any functional analysis. We likewise do not assume that the student has had a course in undergraduate real analysis. To make the book timely and exciting, a substantial chapter on basic properties of wavelets, with applications to signal processing and image processing is included. This should give students and instructors alike a taste of what is happening in the subject today.
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).
A thorough and systematic first course in elementary differential equations for undergraduates in mathematics and science, with many exercises and problems (with answers).
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 ...
This highly useful text shows the reader how to formulate a partial differential equation from the physical problem and how to solve the equation.
Differential Equations
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.
Historical footnotes trace the development of the discipline and identify outstanding individual contributions. This book builds the foundation for anyone who needs to learn differential equations and then progress to more advanced studies.
Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful.