With its thorough coverage of analytic concepts, geometric concepts, programs and algorithms, and applications, this is an unsurpassed pedagogical tool.
Designed for use in a 1-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, 2nd-order partial differential equations, wave equation, potential equation, heat equation, and more. Includes exercises. 1961 edition.
Designed for use in a 1-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure ...
This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the applications quickly. The author has used preliminary notes in teaching such a course at Arizona State University over the past two years. This book focuses on the key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models involving delay differential equations. The book begins with a survey of mathematical models involving delay equations.
This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to ...
This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinicbifurcation and Liapunov exponents.Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007).Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.
This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith.
Introduction to Ordinary Differential Equations and some ApplicationsBy Edward Burkard
Introduction to Ordinary Differential Equations and some ApplicationsBy Edward Burkard
These materials - developed and thoroughly class tested over many years by the authors -are for use in courses at the sophomore/junior level. A prerequisite is the calculus of one variable, although calculus of several variables, and linear algebra are recommended. The text covers the standard topics in first and second order equations, power series solutions, first order systems, Laplace transforms, numerical methods and stability of non-linear systems. Liberal use is made of programs in Mathematica, both for symbolic computations and graphical displays. The programs are described in separate sections, as well as in the accompanying Mathematica notebooks. However, the book has been designed so that it can be read with or without Mathematica and no previous knowledge of Mathematica is required. The CD-ROM contains the Mathematica solution of worked examples, a selection of various Mathematica notebooks, Mathematica movies and sample labs for students. Mathematica programs and additional problem/example files will be available online through the TELOS Web site and the authors dedicated web site.
The text covers the standard topics in first and second order equations, power series solutions, first order systems, Laplace transforms, numerical methods and stability of non-linear systems.
This text's integrated applications and models, along with graphical and numerical procedures, motivate and explain mathematical techniques. Applied exercises are drawn from a variety of fields, including engineering and life sciences. Numerical methods are covered early and woven throughout the text. The author uses a spiraling approach to develop more abstract concepts so students aren't overwhelmed with definitions and theorems at first.
This text's integrated applications and models, along with graphical and numerical procedures, motivate and explain mathematical techniques.
