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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
• 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
• 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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