Introduction to differential equations / Michael E. Taylor

Author:: Taylor, Michael E., 1946-
Published:: Providence, R.I. : American Mathematical Society, [2011]
Copyright Date:: ©2011
Physical Description:: xii, 409 pages : illustrations ; 27 cm.

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Contents:

Machine generated contents note: ch. 1 Single Differential Equations -- 1.The exponential and trigonometric functions -- 2.First order linear equations -- 3.Separable equations -- 4.Second order equations - reducible cases -- 5.Newton's equations for motion in 1D -- 6.The pendulum -- 7.Motion with resistance -- 8.Linearization -- 9.Second order constant coefficient linear equations homogeneous -- 10.Nonhomogeneous equations I - undetermined coefficients -- 11.Forced pendulum resonance -- 12.Spring motion -- 13.RLC circuits -- 14.Nonhomogeneous equations II - variation of parameters -- 15.Variable coefficient second order equations -- 16.Higher order linear equations -- A.Where Bessel functions come from -- ch. 2 Linear Algebra -- 1.Vector spaces -- 2.Linear transformations and matrices -- 3.Basis and dimension -- 4.Matrix representation of a linear transformation -- 5.Determinants and invertibility -- 6.Eigenvalues and eigenvectors -- 7.Generalized eigenvectors and the minimal polynomial -- 8.Triangular matrices -- 9.Inner products and norms -- 10.Norm, trace, and adjoint of a linear transformation -- 11.Self-adjoint and skew-adjoint transformations -- 12.Unitary and orthogonal transformations -- A.The Jordan canonical form -- B.Schur's upper triangular representation -- C.The fundamental theorem of algebra -- ch. 3 Linear Systems of Differential Equations -- 1.The matrix exponential -- 2.Exponentials and trigonometric functions -- 3.First order systems derived from higher order equations -- 4.Nonhomogeneous equations and Duhamel's formula -- 5.Simple electrical circuits -- 6.Second order systems -- 7.Curves in R3 and the Frenet-Serret equations -- 8.Variable coefficient systems -- 9.Variation of parameters and Duhamel's formula -- 10.Power series expansions -- 11.Regular singular points -- A.Logarithms of matrices -- ch. 4 Nonlinear Systems of Differential Equations -- 1.Existence and uniqueness of solutions -- 2.Dependence of solutions on initial data and other parameters -- 3.Vector fields, orbits, and flows -- 4.Gradient vector fields -- 5.Newtonian equations -- 6.Central force problems and two-body planetary motion -- 7.Variational problems and the stationary action principle -- 8.The brachistochrone problem -- 9.The double pendulum -- 10.Momentum-quadratic Hamiltonian systems -- 11.Numerical study - difference schemes -- 12.Limit sets and periodic orbits -- 13.Predator-prey equations -- 14.Competing species equations -- 15.Chaos in multidimensional systems -- A.The derivative in several variables -- B.Convergence, compactness, and continuity -- C.Critical points that are saddles -- D.Periodic solutions of x" + x = εψ(x) -- E.A dram of potential theory -- F.Brouwer's fixed-point theorem.

Subject(s):

Differential equations

ISBN:

9780821852712 (acid-free paper)
082185271X (acid-free paper)

Bibliography Note:

Includes bibliographical references (pages 403-405) and index.

Source of Acquisition:

Physical and Mathematical Sciences copy: Purchased with funds from the James and Joyce Gettys Libraries Endowment in the Math Library and in the School of Information Sciences and Technology; 2010.

Endowment Note:

James and Joyce Gettys Libraries Endowment in the Math Library and in the School of Information Sciences and Technology

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