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Elementary Differential Equations, 11th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between.

The authors have sought to combine a sound and accurate but not abstract exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications.

While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study.

The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two? Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. It deals mainly with the three fundamental equations of mathematical physics, namely the heat equation, the wave equation, and Laplace's equation.

The goal of the book is to obtain a formal solution to a given problem either by the method of separation of variables or by the method of general solutions and to verify that the formal solution possesses all the required properties.

To provide the mathematical justification for this approach, the theory of Sturm-Liouville problems, the Fourier series, and the Fourier transform are fully developed. The book assumes a knowledge of advanced calculus and elementary differential equations. It has been designed for undergraduates and first year graduate students majoring in mathematics, physics, engineering, or science. The text provides an introduction to the basic equations of mathematical physics and the properties of their solutions, based on classical calculus and ordinary differential equations.

Advanced concepts such as weak solutions and discontinuous solutions of nonlinear conservation laws are also considered. Author : Martha L. This valuable resource is appropriate for a first semester course in introductory ordinary differential equations including Laplace transforms , but is also ideal for a second course in Fourier series and boundary value problems, and for students with no background on the subject. The book provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies.

Gives students a complete foundation on the subject, providing a strong basis for learning how to read technical material in more advanced texts Includes new, comprehensive exercise sets throughout, ranging from straightforward to challenging Offers applications and extended projects relevant to the real-world through the use of examples in a broad range of contexts.

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