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Elementary differential equations and boundary value problems / William E. Boyce, Richard C.DiPrima

Boyce, William E.
Contributor(s): DiPrima, Richard C [].
Material type: materialTypeLabelBook; Format: print Publisher: Hoboken, NJ : Wiley, cop. 2005Edition: 8th ed.Description: XVIII, 790 p. : il. col. ; 27 cm. + 1 Disco compacto.ISBN: 0-471-43338-1.Subject(s): Matemáticas | Ecuaciones diferenciales | Problemas de contorno
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Enhanced descriptions from Syndetics:

This revision of the market-leading book maintains its classic strengths: contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. Like its predecessors, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences. Sound and Accurate Exposition of Theory--special attention is made to methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace development of the discipline and identify outstanding individual contributions.

Table of contents provided by Syndetics

  • Preface (p. vii)
  • Chapter 1 Introduction (p. 1)
  • 1.1 Some Basic Mathematical Models; Direction Fields (p. 1)
  • 1.2 Solutions of Some Differential Equations (p. 9)
  • 1.3 Classification of Differential Equations (p. 17)
  • 1.4 Historical Remarks (p. 23)
  • Chapter 2 First Order Differential Equations (p. 29)
  • 2.1 Linear Equations with Variable Coefficients (p. 29)
  • 2.2 Separable Equations (p. 40)
  • 2.3 Modeling with First Order Equations (p. 47)
  • 2.4 Differences Between Linear and Nonlinear Equations (p. 64)
  • 2.5 Autonomous Equations and Population Dynamics (p. 74)
  • 2.6 Exact Equations and Integrating Factors (p. 89)
  • 2.7 Numerical Approximations: Euler's Method (p. 96)
  • 2.8 The Existence and Uniqueness Theorem (p. 105)
  • 2.9 First Order Difference Equations (p. 115)
  • Chapter 3 Second Order Linear Equations (p. 129)
  • 3.1 Homogeneous Equations with Constant Coefficients (p. 129)
  • 3.2 Fundamental Solutions of Linear Homogeneous Equations (p. 137)
  • 3.3 Linear Independence and the Wronskian (p. 147)
  • 3.4 Complex Roots of the Characteristic Equation (p. 153)
  • 3.5 Repeated Roots; Reduction of Order (p. 160)
  • 3.6 Nonhomogeneous Equations; Method of Undetermined Coefficients (p. 169)
  • 3.7 Variation of Parameters (p. 179)
  • 3.8 Mechanical and Electrical Vibrations (p. 186)
  • 3.9 Forced Vibrations (p. 200)
  • Chapter 4 Higher Order Linear Equations (p. 209)
  • 4.1 General Theory of nth Order Linear Equations (p. 209)
  • 4.2 Homogeneous Equations with Constant Coeffients (p. 214)
  • 4.3 The Method of Undetermined Coefficients (p. 222)
  • 4.4 The Method of Variation of Parameters (p. 226)
  • Chapter 5 Series Solutions of Second Order Linear Equations (p. 231)
  • 5.1 Review of Power Series (p. 231)
  • 5.2 Series Solutions near an Ordinary Point, Part I (p. 238)
  • 5.3 Series Solutions near an Ordinary Point, Part II (p. 249)
  • 5.4 Regular Singular Points (p. 255)
  • 5.5 Euler Equations (p. 260)
  • 5.6 Series Solutions near a Regular Singular Point, Part I (p. 267)
  • 5.7 Series Solutions near a Regular Singular Point, Part II (p. 272)
  • 5.8 Bessel's Equation (p. 280)
  • Chapter 6 The Laplace Transform (p. 293)
  • 6.1 Definition of the Laplace Transform (p. 293)
  • 6.2 Solution of Initial Value Problems (p. 299)
  • 6.3 Step Functions (p. 310)
  • 6.4 Differential Equations with Discontinuous Forcing Functions (p. 317)
  • 6.5 Impulse Functions (p. 324)
  • 6.6 The Convolution Integral (p. 330)
  • Chapter 7 Systems of First Order Linear Equations (p. 339)
  • 7.1 Introduction (p. 339)
  • 7.2 Review of Matrices (p. 348)
  • 7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors (p. 357)
  • 7.4 Basic Theory of Systems of First Order Linear Equations (p. 368)
  • 7.5 Homogeneous Linear Systems with Constant Coefficients (p. 373)
  • 7.6 Complex Eigenvalues (p. 384)
  • 7.7 Fundamental Matrices (p. 393)
  • 7.8 Repeated Eigenvalues (p. 401)
  • 7.9 Nonhomogeneous Linear Systems (p. 411)
  • Chapter 8 Numerical Methods (p. 419)
  • 8.1 The Euler or Tangent Line Method (p. 419)
  • 8.2 Improvements on the Euler Method (p. 430)
  • 8.3 The Runge-Kutta Method (p. 435)
  • 8.4 Multistep Methods (p. 439)
  • 8.5 More on Errors; Stability (p. 445)
  • 8.6 Systems of First Order Equations (p. 455)
  • Chapter 9 Nonlinear Differential Equations and Stability (p. 459)
  • 9.1 The Phase Plane; Linear Systems (p. 459)
  • 9.2 Autonomous Systems and Stability (p. 471)
  • 9.3 Almost Linear Systems (p. 479)
  • 9.4 Competing Species (p. 491)
  • 9.5 Predator-Prey Equations (p. 503)
  • 9.6 Liapunov's Second Method (p. 511)
  • 9.7 Periodic Solutions and Limit Cycles (p. 521)
  • 9.8 Chaos and Strange Attractors; the Lorenz Equations (p. 532)
  • Chapter 10 Partial Differential Equations and Fourier Series (p. 541)
  • 10.1 Two-Point Boundary Valve Problems (p. 541)
  • 10.2 Fourier Series (p. 547)
  • 10.3 The Fourier Convergence Theorem (p. 558)
  • 10.4 Even and Odd Functions (p. 564)
  • 10.5 Separation of Variables; Heat Conduction in a Rod (p. 573)
  • 10.6 Other Heat Conduction Problems (p. 581)
  • 10.7 The Wave Equation; Vibrations of an Elastic String (p. 591)
  • 10.8 Laplace's Equation (p. 604)
  • Appendix A. Derivation of the Heat Conduction Equation (p. 614)
  • Appendix B. Derivation of the Wave Equation (p. 617)
  • Chapter 11 Boundary Value Problems and Sturm-Liouville Theory (p. 621)
  • 11.1 The Occurrence of Two Point Boundary Value Problems (p. 621)
  • 11.2 Sturm-Liouville Boundary Value Problems (p. 629)
  • 11.3 Nonhomogeneous Boundary Value Problems (p. 641)
  • 11.4 Singular Sturm-Liouville Problems (p. 656)
  • 11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion (p. 663)
  • 11.6 Series of Orthogonal Functions: Mean Convergence (p. 669)
  • Answers to Problems (p. 679)
  • Index (p. 737)

Author notes provided by Syndetics

William E. Boyce is currently the Edward P. Hamilton Distinguished Professor Emeritus of Science Education (Department of Mathematical Sciences) at Rensselaer
Richard C. DiPrima (deceased) received his B.S., M.S., and Ph.D. degrees in Mathematics from Carnegie-Mellon University. He joined the faculty of Rensselaer Polytechnic Institute after holding research positions at MIT, Harvard, and Hughes Aircraft. He held the Eliza Ricketts Foundation Professorship of Mathematics at Rensselaer

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Ecuaciones diferenciales y problemas con valores en la frontera / by Boyce, William E.

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