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Introduction to Differential Equations
 
Michael E. Taylor University of North Carolina, Chapel Hill, NC
Front Cover for Introduction to Differential Equations
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Hardcover ISBN: 978-0-8218-5271-2
Product Code: AMSTEXT/14
List Price: $82.00
MAA Member Price: $73.80
AMS Member Price: $65.60
Electronic ISBN: 978-1-4704-1127-5
Product Code: AMSTEXT/14.E
List Price: $77.00
MAA Member Price: $69.30
AMS Member Price: $61.60
Bundle Print and Electronic Formats and Save!
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Front Cover for Introduction to Differential Equations
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  • Front Cover for Introduction to Differential Equations
  • Back Cover for Introduction to Differential Equations
Introduction to Differential Equations
Michael E. Taylor University of North Carolina, Chapel Hill, NC
Available Formats:
Hardcover ISBN:  978-0-8218-5271-2
Product Code:  AMSTEXT/14
List Price: $82.00
MAA Member Price: $73.80
AMS Member Price: $65.60
Electronic ISBN:  978-1-4704-1127-5
Product Code:  AMSTEXT/14.E
List Price: $77.00
MAA Member Price: $69.30
AMS Member Price: $61.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $123.00
MAA Member Price: $110.70
AMS Member Price: $98.40
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 142011; 409 pp
    MSC: Primary 34;

    The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis.

    The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponential and trigonometric functions, which plays a central role in the subsequent development of this chapter. Chapter 2 provides a mini-course on linear algebra, giving detailed treatments of linear transformations, determinants and invertibility, eigenvalues and eigenvectors, and generalized eigenvectors. This treatment is more detailed than that in most differential equations texts, and provides a solid foundation for the next two chapters. Chapter 3 studies linear systems of differential equations. It starts with the matrix exponential, melding material from Chapters 1 and 2, and uses this exponential as a key tool in the linear theory. Chapter 4 deals with nonlinear systems of differential equations. This uses all the material developed in the first three chapters and moves it to a deeper level. The chapter includes theoretical studies, such as the fundamental existence and uniqueness theorem, but also has numerous examples, arising from Newtonian physics, mathematical biology, electrical circuits, and geometrical problems. These studies bring in variational methods, a fertile source of nonlinear systems of differential equations. The reader who works through this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations.

    Readership

    Undergraduate students interested in ordinary differential equations.

  • Table of Contents
     
     
    • Cover
    • Title page
    • Contents
    • Preface
    • Single differential equations
    • Linear algebra
    • Linear systems of differential equations
    • Nonlinear systems of differential equations
    • Bibliography
    • Index
    • Back Cover
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Volume: 142011; 409 pp
MSC: Primary 34;

The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis.

The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponential and trigonometric functions, which plays a central role in the subsequent development of this chapter. Chapter 2 provides a mini-course on linear algebra, giving detailed treatments of linear transformations, determinants and invertibility, eigenvalues and eigenvectors, and generalized eigenvectors. This treatment is more detailed than that in most differential equations texts, and provides a solid foundation for the next two chapters. Chapter 3 studies linear systems of differential equations. It starts with the matrix exponential, melding material from Chapters 1 and 2, and uses this exponential as a key tool in the linear theory. Chapter 4 deals with nonlinear systems of differential equations. This uses all the material developed in the first three chapters and moves it to a deeper level. The chapter includes theoretical studies, such as the fundamental existence and uniqueness theorem, but also has numerous examples, arising from Newtonian physics, mathematical biology, electrical circuits, and geometrical problems. These studies bring in variational methods, a fertile source of nonlinear systems of differential equations. The reader who works through this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations.

Readership

Undergraduate students interested in ordinary differential equations.

  • Cover
  • Title page
  • Contents
  • Preface
  • Single differential equations
  • Linear algebra
  • Linear systems of differential equations
  • Nonlinear systems of differential equations
  • Bibliography
  • Index
  • Back Cover
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