Linear Ordinary Differential Equations by Coddington and Carlson

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Linear Ordinary Differential Equations by Coddington and Carlson

PDF Free Download | Linear Ordinary Differential Equations by Earl A. Coddington and Robert Carlson

  • Simple Applications
  • Introduction
  • Compartment systems
  • Springs and masses
  • Electric circuits
  • Notes
  • Exercises
  • Properties of Linear Systems
  • Introduction
  • Basic linear algebra
  • Vector spaces
  • Matrices
  • Vector spaces of functions
  • First-order systems
  • Introduction
  • First-order homogeneous systems
  • The Wronskian
  • First-order nonhomogeneous systems
  • Higher-order equations
  • Linear equations of order n
  • Nonhomogeneous linear equations of order n
  • Notes
  • Exercises
  • Constant Coefficients
  • Introduction
  • Properties of the exponential of a matrix
  • Nonhomogeneous systems
  • Structure of the solution space
  • A special case
  • The general case
  • Some examples
  • Real solutions
  • The Jordan canonical form of a matrix
  • The behavior of solutions for large t
  • Higher-order equations
  • Exercises
  • Periodic Coefficients
  • Introduction
  • Floquet’s theorem
  • The logarithm of an invertible matrix
  • Multipliers
  • The behavior of solutions for large t
  • First-order nonhomogeneous systems
  • Second-order homogeneous equations
  • Second-order nonhomogeneous equations
  • Notes
  • Exercises
  • Analytic Coefficients
  • Introduction
  • Convergence
  • Normed vector spaces
  • Normed vector spaces of functions
  • Analytic functions
  • First-order linear analytic systems
  • Equations of order n
  • The Legendre equation and its solutions
  • The Legendre equation
  • The Legendre polynomials
  • Legendre functions of the second kind
  • Notes
  • Exercises
  • Singular Points
  • Introduction
  • Systems of equations with singular points
  • Singular points of the first kind: A special case
  • Two results about matrices
  • The special case, continued
  • Singular points of the first kind: The general case
  • Singular points of the second kind
  • Single equations with singular points
  • Equations of order n
  • The Euler equation
  • The second-order equation
  • The Bessel equation
  • The Bessel equation, continued
  • Infinity as a singular point
  • Notes
  • Exercises
  • Existence and Uniqueness
  • Introduction
  • Convergence of successive approximations
  • Continuity of solutions
  • More general linear equations
  • Estimates for second-order equations
  • Notes
  • Exercises
  • Eigenvalue Problems
  • Introduction
  • Inner products
  • Boundary conditions and operators
  • Eigenvalues
  • Selfadjoint eigenvalue problems
  • Eigenvalue asymptotics
  • Nonhomogeneous boundary value problems
  • Nonhomogeneous problems
  • Green’s functions
  • Notes
  • Exercises
  • Eigenfunction Expansions
  • Introduction
  • Eigenvalues for Green’s operator
  • Convergence of eigenfunction expansions
  • Extensions of the expansion results
  • Notes
  • Exercises
  • Control of Linear Systems
  • Introduction
  • Convex sets
  • Control of general linear systems
  • Constant coefficient equations
  • Time-optimal control
  • Notes
  • Exercises

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