000			05076cam a2200325 i 4500
999			_c1624 _d1624
001			13105955
005			20210905103803.0
008			030227s2004 maua b 001 0 eng
020			_a0321188888
040			_aDLC _cDLC _dDLC _erda
082	0	0	_a515.35 _221 _bN.R.F
100	1		_aNagle, R. Kent. _96722 _eauthor
245	1	0	_aFundamentals of differential equations.
250			_asixth edition / _bR. Kent Nagle, Edward B. Saff, Arthur David Snider.
264		4	_aBoston : _bPearson Addison Wesley, _cc2004.
264		1	_cc2004.
300			_axx, 835 pages : _billustrations (some color) ; _c24 cm. + _e3 computer discs (4 3/4 in.)
336			_2rdacontent _atext
337			_2rdamedia _aunmediated
338			_2rdacarrier _avolume
504			_aIncludes bibliographical references and index.
505	0		_a(Most chapters end with a Chapter Summary, Review Problems and Group Projects.)1. Introduction. Background.Solutions and Initial Value Problems.Direction Fields.The Approximation Method of Euler.2. First Order Differential Equations. Introduction: Motion of a Falling Body.Separable Equations.Linear Equations.Exact Equations.Special Integrating Factors.Substitutions and Transformations.3. Mathematical Models and Numerical Methods Involving First Order Equations. Mathematical Modeling.Compartmental Analysis.Heating and Cooling of Buildings.Newtonian Mechanics.Electrical Circuits.Improved Euler's Method.Higher-Order Numerical Methods: Taylor and Runge-Kutta.4. Linear Second Order Equations. Introduction: The Mass-Spring Oscillator.Homogeneous Linear Equations; the General Solution.Auxiliary Equations with Complex Roots.Nonhomogeneous Equations: the Method of Undetermined Coefficients.The Superposition Principle and Undetermined Coefficients Revisited.Variation of Parameters.Qualitative Considerations for Variable-Coefficient and Nonlinear Equations.A Closer Look at Free Mechanical Vibrations.A Closer Look at Forced Mechanical Vibrations.5. Introduction to Systems and Phase Plane Analysis. Interconnected Fluid Tanks.Elimination Method for Systems with Constant Coefficients.Solving Systems and Higher-Order Equations Numerically.Introduction to the Phase Plane.Coupled Mass-Spring Systems.Electrical Systems.Dynamical Systems, Poincare Maps, and Chaos.6. Theory of Higher-Order Linear Differential Equations. Basic Theory of Linear Differential Equations.Homogeneous Linear Equations with Constant Coefficients.Undetermined Coefficients and the Annihilator Method.Method of Variation of Parameters.7. Laplace Transforms. Introduction: A Mixing Problem.Definition of the Laplace Transform.Properties of the Laplace Transform.Inverse Laplace Transform.Solving Initial Value Problems.Transforms of Discontinuous and Periodic Functions.Convolution.Impulses and the Dirac Delta Function.Solving Linear Systems with Laplace Transforms.8. Series Solutions of Differential Equations. Introduction: The Taylor Polynomial Approximation.Power Series and Analytic Functions.Power Series Solutions to Linear Differential Equations.Equations with Analytic Coefficients.Cauchy-Euler (Equidimensional) Equations.Method of Frobenius.Finding a Second Linearly Independent Solution.Special Functions.9. Matrix Methods for Linear Systems. Introduction.Review 1: Linear Algebraic Equations.Review 2: Matrices and Vectors.Linear Systems in Normal Form.Homogeneous Linear Systems with Constant Coefficients.Complex Eigenvalues.Nonhomogeneous Linear Systems.The Matrix Exponential Function.10. Partial Differential Equations. Introduction: A Model for Heat Flow.Method of Separation of Variables.Fourier Series.Fourier Cosine and Sine Series.The Heat Equation.The Wave Equation.Laplace's Equation.11. Eigenvalue Problems and Sturm-Liouville Equations. Introduction: Heat Flow in a Nonuniform Wire.Eigenvalues and Eigenfunctions.Regular Sturm-Liouville Boundary Value Problems.Nonhomogeneous Boundary Value Problems and the Fredholm Alternative.Solution by Eigenfunction Expansion.Green's Functions.Singular Sturm-Liouville Boundary Value Problems.Oscillation and Comparison Theory.12. Stability of Autonomous Systems. Introduction: Competing Species.Linear Systems in the Plane.Almost Linear Systems.Energy Methods.Lyapunov's Direct Method.Limit Cycles and Periodic Solutions.Stability of Higher-Dimensional Systems.13. Existence and Uniqueness Theory. Introduction: Successive Approximations.Picard's Existence and Uniqueness Theorem.Existence of Solutions of Linear Equations.Continuous Dependence of Solutions.Appendices. Newton's Method.Simpson's Rule.Cramer's Rule.Method of Least Squares.Runge-Kutta Precedure for n Equations.Answers to Odd-Numbered Problems. Index.
650		0	_aDifferential equations.
700	1		_aSaff, E. B., _d1944- _96724 _eauthor
700	1		_aSnider, Arthur David, _d1940- _96725 _eauthor
906			_a7 _bcbc _corignew _d1 _eocip _f20 _gy-gencatlg
942			_2ddc _cBK