000			05300nam a2200277 a 4500
999			_c10955 _d10955
003			AR-sfUTN
008			170717s1984 nyu||||| |||| 00| 0 eng d
020			_a0471032948
040			_cAR-sfUTN
041			_aeng
080			_a517.9 R733 _22000
100	1		_aRoss, Shepley L. _95198
245	1	0	_aDifferential equations / _cShepley L. Ross.
250			_a3rd.
260			_aNew York : _bJohn Wiley and Sons, _c1984
300			_a807 p.
336			_2rdacontent _atexto _btxt
337			_2rdamedia _asin mediación _bn
338			_2rdacarrier _avolumen _bnc
505	8	0	_aCONTENIDO PART ONE. FUNDAMENTAL METHODS AND APPLICATIONS One. Differential Equations and Their Solutions 3 1.1 Classification of Differential Equations; Their Origin and Application 3 1.2 Solutions 7 1.3 Initial- Value Problems, Boundary-Value Problems, and Existence of Solutions 15 Two. First-Order Equations for Which Exact Solutions Are Obtainable 25 2.1 Exact Differential Equations and Integrating Factors 25 2.2 Separable Equations and Equations Reducible to This Form 39 2.3 Linear Equations and Bernoulli Equations 49 2.4 Special Integrating Factors and Transformations 61 Three. Applications of First-Order Equations 70 3.1 Orthogonal and Oblique Trajectories 70 3.2 Problems in Mechanics 77 3.3 Rate Problems 89 Four. Explicit Methods of Solving Higher-Order Linear Differential Equations 102 4.1 Basic Theory of Linear Differential Equations 102 4.2 The Homogeneous Linear Equation with Constant Coefficients 125 4.3 The Method of Undetermined Coefficients 137 4.4 Variation of Parameters 155 4.5 The Cauchy-Euler Equation 164 4.6 Statements and Proofs of Theorems on the Second-Order Homogeneous Linear Equation 170 Five. Applications of Second-Order Linear Differential Equations with Constant Coefficients 179 5.1 The Differential Equation of the Vibrations of a Mass on a Spring 179 5.2 Free, Undamped Motion 182 5.3 Free, Damped Motion 189 5.4 Forced Motion 199 5.5 Resonance Phenomena 206 5.6 Electric Circuit Problems 211 Six. Series Solutions of Linear Differential Equations 221 6.1 Power Series Solutions About an Ordinary Point 221 6.2 Solutions About Singular Points; The Method of Frobenius 233 6.3 Bessel's Equation and Bessel Functions 252 Seven. Systems of Linear Differential Equations 264 7.1 Differential Operators and an Operator Method 264 7.2 Applications 278 7.3 Basic Theory of Linear Systems in Normal Form: Two Equations in Two Unknown Functions 290 7.4 Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions 301 7.5 Matrices and Vectors 312 7.6 The Matrix Method for Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions 346 7.7 The Matrix Method for Homogeneous Linear Systems with Constant Coefficients: n Equations in n Unknown Functions 355 Eight. Approximate Methods of Solving First-Order Equations 377 8.1 Graphical Methods 377 8.2 Power Series Methods 384 8.3 The Method of Successive Approximations 390 8.4 Numerical Methods 394 Nine. The Laplace Transform 411 9.1 Definition, Existence, and Basic Properties of the Laplace Transform 411 9.2 The Inverse Transform and the Convolution 431 9.3 Laplace Transform Solution of Linear Differential Equations with Constant Coefficients 441 9.4 Laplace Transform Solution of Linear Systems 453 PART TWO. FUNDAMENTAL THEORY AND FURTHER METHODS Ten. Existence and Uniqueness Theory 461 10.1 Some Concepts from Real Function Theory 461 10.2 The Fundamental Existence and Uniqueness Theorem 473 10.3 Dependence of Solutions on Initial Conditions and on the Function 488 10.4 Existence and Uniqueness Theorems for Systems and Higher-Order Equations 495 Eleven. The Theory of Linear Differential Equations 505 11.1 Introduction 505 11.2 Basic Theory of the Homogeneous Linear System 510 11.3 Further Theory of the Homogeneous Linear System 522 11.4 The Nonhomogeneous Linear System 533 11.5 Basic Theory of the nth-Order Homogeneous Linear Differential Equation 543 11.6 Further Properties of the nth-Order Homogeneous Linear Differential Equation 558 11.7 The nth-Order Nonhomogcneous Linear Equation 569 11.8 Sturm Theory 573 Twelve. Sturm-Liouville Boundary-Value Problems and Fourier Series 588 12.1 Sturm-Liouville Problems 588 12.2 Orthogonality of Characteristic Functions 597 12.3 The Expansion of a Function in a Series of Orthonorma Functions 601 12.4 Trigonometric Fourier Series 608 Thirteen. Nonlinear Differential Equations 632 13.1 Phase Plane, Paths, and Critical Points 632 13.2 Critical Points and Paths of Linear Systems 644 13.3 Critical Points and Paths of Nonlinear Systems 658 13.4 Limit Cycles and Periodic Solutions 692 13.5 The Method of Kryloff and Bogoliuboff 707 Fourteen. Partial Differential Equations 715 14.1 Some Basic Concepts and Examples 715 14.2 The Method of Separation of Variables 722 14.3 Canonical Forms of Second-Order Linear Equations with Constant Coefficients 743 14.4 An Initial Value Problem; Characteristics 757 Appendices 771 Answers 777 Suggested Reading 801 Index 803
650			_aDIFFERENTIAL EQUATIONS
650			_aECUACIONES DIFERENCIALES
942			_cBK _2udc