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

By: Contributor(s): Material type: TextTextPublication details: Hoboken, NJ : Wiley, c2004.Edition: 8th edDescription: xviii, 790 p. : col. ill. ; 27 cm. + 1 CD-ROM (4 3/4 in.)ISBN:
  • 0471433381 (acidfree paper)
Subject(s): DDC classification:
  • 515/.35 22
LOC classification:
  • QA371 BOY 2004
Online resources:
Contents:
Chapter 1. Introduction -- 1.1. Some Basic Mathematical Models; Direction Fields -- 1.2. Solutions of Some Differential Equations -- 1.3. Classification of Differential Equations -- 1.4. Historical Remarks -- Chapter 2. First Order Differential Equations -- 2.1. Linear Equations with Variable Coefficients -- 2.2. Separable Equations -- 2.3. Modeling with First Order Equations -- 2.4. Differences Between Linear and Nonlinear Equations -- 2.5. Autonomous Equations and Population Dynamics -- 2.6. Exact Equations and Integrating Factors -- 2.7. Numerical Approximations: Euler's Method -- 2.8. The Existence and Uniqueness Theorem -- 2.9. First Order Difference Equations -- Chapter 3. Second Order Linear Equations -- 3.1. Homogeneous Equations with Constant Coefficients -- 3.2. Fundamental Solutions of Linear Homogeneous Equations -- 3.3. Linear Independence and the Wronskian -- 3.4. Complex Roots of the Characteristic Equation -- 3.5. Repeated Roots; Reduction of Order -- 3.6. Nonhomogeneous Equations; Method of Undetermined Coefficients -- 3.7. Variation of Parameters -- 3.8. Mechanical and Electrical Vibrations -- 3.9. Forced Vibrations -- Chapter 4. Higher Order Linear Equations -- 4.1. General Theory of nth Order Linear Equations -- 4.2. Homogeneous Equations with Constant Coeffients -- 4.3. The Method of Undetermined Coefficients -- 4.4. The Method of Variation of Parameters -- Chapter 5. Series Solutions of Second Order Linear Equations -- 5.1. Review of Power Series -- 5.2. Series Solutions near an Ordinary Point, Part I -- 5.3. Series Solutions near an Ordinary Point, Part II -- 5.4. Regular Singular Points -- 5.5. Euler Equations -- 5.6. Series Solutions near a Regular Singular Point, Part I -- 5.7. Series Solutions near a Regular Singular Point, Part II -- 5.8. Bessel's Equation -- Chapter 6. The Laplace Transform -- 6.1. Definition of the Laplace Transform -- 6.2. Solution of Initial Value Problems -- 6.3. Step Functions -- 6.4. Differential Equations with Discontinuous Forcing Functions -- 6.5. Impulse Functions -- 6.6. The Convolution Integral -- Chapter 7. Systems of First Order Linear Equations -- 7.1. Introduction -- 7.2. Review of Matrices -- 7.3. Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors -- 7.4. Basic Theory of Systems of First Order Linear Equations -- 7.5. Homogeneous Linear Systems with Constant Coefficients -- 7.6. Complex Eigenvalues -- 7.7. Fundamental Matrices -- 7.8. Repeated Eigenvalues -- 7.9. Nonhomogeneous Linear Systems -- Chapter 8. Numerical Methods -- 8.1. The Euler or Tangent Line Method -- 8.2. Improvements on the Euler Method -- 8.3. The Runge-Kutta Method -- 8.4. Multistep Methods -- 8.5. More on Errors; Stability -- 8.6. Systems of First Order Equations -- Chapter 9. Nonlinear Differential Equations and Stability -- 9.1. The Phase Plane; Linear Systems -- 9.2. Autonomous Systems and Stability -- 9.3. Almost Linear Systems -- 9.4. Competing Species -- 9.5. Predator-Prey Equations -- 9.6. Liapunov's Second Method -- 9.7. Periodic Solutions and Limit Cycles -- 9.8. Chaos and Strange Attractors; the Lorenz Equations -- Chapter 10. Partial Differential Equations and Fourier Series -- 10.1. Two-Point Boundary Valve Problems -- 10.2. Fourier Series -- 10.3. The Fourier Convergence Theorem -- 10.4. Even and Odd Functions -- 10.5. Separation of Variables; Heat Conduction in a Rod -- 10.6. Other Heat Conduction Problems -- 10.7. The Wave Equation; Vibrations of an Elastic String -- 10.8. Laplace's Equation -- Appendix A.. Derivation of the Heat Conduction Equation -- Appendix B.. Derivation of the Wave Equation -- Chapter 11. Boundary Value Problems and Sturm-Liouville Theory -- 11.1. The Occurrence of Two Point Boundary Value Problems -- 11.2. Sturm-Liouville Boundary Value Problems -- 11.3. Nonhomogeneous Boundary Value Problems -- 11.4. Singular Sturm-Liouville Problems -- 11.5. Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion -- 11.6. Series of Orthogonal Functions: Mean Convergence.
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Holdings
Item type Current library Collection Call number Copy number Status Date due Barcode
Books in General collection Books in General collection Mzuzu University Library and Learning Resources Centre Non-fiction QA 371 BOY 2004 (Browse shelf(Opens below)) 6925 Available MzULM-006925

Includes bibliographical references and index.

Chapter 1. Introduction -- 1.1. Some Basic Mathematical Models; Direction Fields -- 1.2. Solutions of Some Differential Equations -- 1.3. Classification of Differential Equations -- 1.4. Historical Remarks -- Chapter 2. First Order Differential Equations -- 2.1. Linear Equations with Variable Coefficients -- 2.2. Separable Equations -- 2.3. Modeling with First Order Equations -- 2.4. Differences Between Linear and Nonlinear Equations -- 2.5. Autonomous Equations and Population Dynamics -- 2.6. Exact Equations and Integrating Factors -- 2.7. Numerical Approximations: Euler's Method -- 2.8. The Existence and Uniqueness Theorem -- 2.9. First Order Difference Equations -- Chapter 3. Second Order Linear Equations -- 3.1. Homogeneous Equations with Constant Coefficients -- 3.2. Fundamental Solutions of Linear Homogeneous Equations -- 3.3. Linear Independence and the Wronskian -- 3.4. Complex Roots of the Characteristic Equation -- 3.5. Repeated Roots; Reduction of Order -- 3.6. Nonhomogeneous Equations; Method of Undetermined Coefficients -- 3.7. Variation of Parameters -- 3.8. Mechanical and Electrical Vibrations -- 3.9. Forced Vibrations -- Chapter 4. Higher Order Linear Equations -- 4.1. General Theory of nth Order Linear Equations -- 4.2. Homogeneous Equations with Constant Coeffients -- 4.3. The Method of Undetermined Coefficients -- 4.4. The Method of Variation of Parameters -- Chapter 5. Series Solutions of Second Order Linear Equations -- 5.1. Review of Power Series -- 5.2. Series Solutions near an Ordinary Point, Part I -- 5.3. Series Solutions near an Ordinary Point, Part II -- 5.4. Regular Singular Points -- 5.5. Euler Equations -- 5.6. Series Solutions near a Regular Singular Point, Part I -- 5.7. Series Solutions near a Regular Singular Point, Part II -- 5.8. Bessel's Equation -- Chapter 6. The Laplace Transform -- 6.1. Definition of the Laplace Transform -- 6.2. Solution of Initial Value Problems -- 6.3. Step Functions -- 6.4. Differential Equations with Discontinuous Forcing Functions -- 6.5. Impulse Functions -- 6.6. The Convolution Integral -- Chapter 7. Systems of First Order Linear Equations -- 7.1. Introduction -- 7.2. Review of Matrices -- 7.3. Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors -- 7.4. Basic Theory of Systems of First Order Linear Equations -- 7.5. Homogeneous Linear Systems with Constant Coefficients -- 7.6. Complex Eigenvalues -- 7.7. Fundamental Matrices -- 7.8. Repeated Eigenvalues -- 7.9. Nonhomogeneous Linear Systems -- Chapter 8. Numerical Methods -- 8.1. The Euler or Tangent Line Method -- 8.2. Improvements on the Euler Method -- 8.3. The Runge-Kutta Method -- 8.4. Multistep Methods -- 8.5. More on Errors; Stability -- 8.6. Systems of First Order Equations -- Chapter 9. Nonlinear Differential Equations and Stability -- 9.1. The Phase Plane; Linear Systems -- 9.2. Autonomous Systems and Stability -- 9.3. Almost Linear Systems -- 9.4. Competing Species -- 9.5. Predator-Prey Equations -- 9.6. Liapunov's Second Method -- 9.7. Periodic Solutions and Limit Cycles -- 9.8. Chaos and Strange Attractors; the Lorenz Equations -- Chapter 10. Partial Differential Equations and Fourier Series -- 10.1. Two-Point Boundary Valve Problems -- 10.2. Fourier Series -- 10.3. The Fourier Convergence Theorem -- 10.4. Even and Odd Functions -- 10.5. Separation of Variables; Heat Conduction in a Rod -- 10.6. Other Heat Conduction Problems -- 10.7. The Wave Equation; Vibrations of an Elastic String -- 10.8. Laplace's Equation -- Appendix A.. Derivation of the Heat Conduction Equation -- Appendix B.. Derivation of the Wave Equation -- Chapter 11. Boundary Value Problems and Sturm-Liouville Theory -- 11.1. The Occurrence of Two Point Boundary Value Problems -- 11.2. Sturm-Liouville Boundary Value Problems -- 11.3. Nonhomogeneous Boundary Value Problems -- 11.4. Singular Sturm-Liouville Problems -- 11.5. Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion -- 11.6. Series of Orthogonal Functions: Mean Convergence.

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