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Linear Ordinary Differential Equations

Linear Ordinary Differential Equations

  • Date Published: December 1997
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • format: Paperback
  • isbn: 9780898713886


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About the Authors
  • Linear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions.

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    Product details

    • Date Published: December 1997
    • format: Paperback
    • isbn: 9780898713886
    • length: 348 pages
    • dimensions: 253 x 178 x 15 mm
    • weight: 0.636kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • Table of Contents

    Preface. 1. Simple Applications. Introduction
    Compartment systems
    Springs and masses
    Electric circuits
    2. Properties of Linear Systems. Introduction
    Basic linear algebra
    First-order systems
    Higher-order equations
    3. Constant Coefficients. Introduction
    Properties of the exponential of a matrix
    Nonhomogeneous systems
    Structure of the solution space
    The Jordan canonical form of a matrix
    The behavior of solutions for large t
    Higher-order equations
    4. Periodic Coefficients. Introduction
    Floquet's theorem
    The logarithm of an invertible matrix
    The behavior of solutions for large t
    First-order nonhomogeneous systems
    Second-order homogeneous equations
    Second-order nonhomogeneous equations
    5. Analytic Coefficients. Introduction
    Analytic functions
    First-order linear analytic systems
    Equations of order n
    The Legendre equation and its solutions
    6. Singular Points. Introduction
    Systems of equations with singular points
    Single equations with singular points
    Infinity as a singular point
    7. Existence and Uniqueness. Introduction
    Convergence of successive approximations
    Continuity of solutions
    More general linear equations
    Estimates for second-order equations
    8. Eigenvalue Problems. Introduction
    Inner products
    Boundary conditions and operators
    Nonhomogeneous boundary value problems
    9. Eigenfunction Expansions. Introduction
    Selfadjoint integral operators
    Eigenvalues for Green's operator
    Convergence of eigenfunction expansions
    Extensions of the expansion results
    10. Control of Linear Systems. Introduction
    Convex sets
    Control of general linear systems
    Constant coefficient equations
    Time-optimal control

  • Authors

    Earl A. Coddington

    Robert Carlson

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