Elementary Differential Equations (10TH)

Elementary Differential Equations (10TH)

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  • 製本 Hardcover:ハードカバー版/ページ数 644 p.
  • 言語 ENG,ENG
  • 商品コード 9780470458327
  • DDC分類 515

Full Description


Boyce/DiPrima is the best-seller in its market and extremely popular. The format remains unchanged, but exercises and examples have been updated to reflect the most current scenarios and topics.

Table of Contents

    Chapter 1 Introduction                         1  (30)
1.1 Some Basic Mathematical Models; 1 (9)
Direction Fields
1.2 Solutions of Some Differential 10 (9)
Equations
1.3 Classification of Differential 19 (7)
Equations
1.4 Historical Remarks 26 (5)
Chapter 2 First Order Differential Equations 31 (106)
2.1 Linear Equations; Method of 31 (11)
Integrating Factors
2.2 Separable Equations 42 (9)
2.3 Modeling with First Order Equations 51 (17)
2.4 Differences Between Linear and 68 (10)
Nonlinear Equations
2.5 Autonomous Equations and Population 78 (17)
Dynamics
2.6 Exact Equations and Integrating 95 (7)
Factors
2.7 Numerical Approximations: Euler's 102(10)
Method
2.8 The Existence and Uniqueness Theorem 112(10)
2.9 First Order Difference Equations 122(15)
Chapter 3 Second Order Linear Equations 137(84)
3.1 Homogeneous Equations with Constant 137(8)
Coefficients
3.2 Solutions of Linear Homogeneous 145(13)
Equations; the Wronskian
3.3 Complex Roots of the Characteristic 158(9)
Equation
3.4 Repeated Roots; Reduction of Order 167(8)
3.5 Nonhomogeneous Equations; Method of 175(11)
Undetermined Coefficients
3.6 Variation of Parameters 186(6)
3.7 Mechanical and Electrical Vibrations 192(15)
3.8 Forced Vibrations 207(14)
Chapter 4 Higher Order Linear Equations 221(26)
4.1 General Theory of nth Order Linear 221(7)
Equations
4.2 Homogeneous Equations with Constant 228(8)
Coefficients
4.3 The Method of Undetermined 236(5)
Coefficients
4.4 The Method of Variation of Parameters 241(6)
Chapter 5 Series Solutions of Second Order 247(62)
Linear Equations
5.1 Review of Power Series 247(7)
5.2 Series Solutions Near an Ordinary 254(11)
Point, Part I
5.3 Series Solutions Near an Ordinary 265(7)
Point, Part II
5.4 Euler Equations; Regular Singular 272(10)
Points
5.5 Series Solutions Near a Regular 282(6)
Singular Point, Part I
5.6 Series Solutions Near a Regular 288(8)
Singular Point, Part II
5.7 Bessel's Equation 296(13)
Chapter 6 The Laplace Transform 309(50)
6.1 Definition of the Laplace Transform 309(8)
6.2 Solution of Initial Value Problems 317(10)
6.3 Step Functions 327(9)
6.4 Differential Equations with 336(7)
Discontinuous Forcing Functions
6.5 Impulse Functions 343(7)
6.6 The Convolution Integral 350(9)
Chapter 7 Systems of First Order Linear 359(92)
Equations
7.1 Introduction 359(9)
7.2 Review of Matrices 368(10)
7.3 Systems of Linear Algebraic 378(12)
Equations; Linear Independence,
Eigenvalues, Eigenvectors
7.4 Basic Theory of Systems of First 390(6)
Order Linear Equations
7.5 Homogeneous Linear Systems with 396(12)
Constant Coefficients
7.6 Complex Eigenvalues 408(13)
7.7 Fundamental Matrices 421(8)
7.8 Repeated Eigenvalues 429(11)
7.9 Nonhomogeneous Linear Systems 440(11)
Chapter 8 Numerical Methods 451(44)
8.1 The Euler or Tangent Line Method 451(11)
8.2 Improvements on the Euler Method 462(6)
8.3 The Runge-Kutta Method 468(4)
8.4 Multistep Methods 472(6)
8.5 Systems of First Order Equations 478(4)
8.6 More on Errors; Stability 482(13)
Chapter 9 Nonlinear Differential Equations 495(94)
and Stability
9.1 The Phase Plane: Linear Systems 495(13)
9.2 Autonomous Systems and Stability 508(11)
9.3 Locally Linear Systems 519(12)
9.4 Competing Species 531(13)
9.5 Predator-Prey Equations 544(10)
9.6 Liapunov's Second Method 554(11)
9.7 Periodic Solutions and Limit Cycles 565(12)
9.8 Chaos and Strange Attractors: The 577(12)
Lorenz Equations
Answers to Problems 589(48)
Index 637