Boundary value problems and partial differential equations [[electronic resource] ] : student solutions manual / / David L. Powers

• Record Nr.: UNINA9910457174103321
• Autore: Powers David L
• Pubbl/distr/stampa: Amsterdam ; ; Boston, : Elsevier Academic Press, c2006
• ISBN: 1-283-73487-7; 0-08-091673-2
• Edizione: [5th ed.]
• Descrizione fisica: 1 online resource (164 p.)
• Disciplina: 515.35; 515/.35
• Soggetti: Boundary value problems; Differential equations, Partial; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di contenuto: Front Cover; Boundary Value Problems and Partial Differential Equations: Student Solutions Manual; Copyright Page; TABLE OF CONTENTS; Chapter 0. Ordinary Differential Equations; 0.1 Homogeneous Linear Equations; 0.2 Nonhomogeneous Linear Equations; 0.3 Boundary Value Problems; 0.4 Singular Boundary Value Problems; 0.5 Green's Functions; Miscellaneous; Chapter 1. Fourier Series and Integrals; 1.1 Periodic Functions and Fourier Series; 1.2 Arbitrary Period and Half-Range Expansions; 1.3 Convergence of Fourier Series; 1.4 Uniform Convergence; 1.5 Operations on Fourier Series; 1.6 Mean Error and Convergence in Mean1.7 Proof of Convergence; 1.8 Numerical Fourier Coefficients; 1.9 Fourier Integral; 1.10 Complex Methods; 1.11 Applications of Fourier Series and Integrals; Miscellaneous Exercises; Chapter 2. The Heat Equation; 2.1 Derivation and Boundary Conditions; 2.2 Steady-State Ternperatures; 2.3 Example: Fixed End Temperatures; 2.4 Example: Insulated Bar; 2.5 Example: Different Boundary Conditions; 2.6 Example: Convection; 2.7 Sturm-Liouville Problems; 2.8 Expansion in Series of Eigenfunctions; 2.9 Generalities on the Heat Conduction Problem; 2.10 Serni-Infinite Rod2.11 Infinite Rod; 2.12 The Error Function; Miscellaneous; Chapter 3. The Wave Equation; 3.1 The Vibrating String; 3.2 Solution of the Vibrating String Problem; 3.3 D'Alemberts Solution; 3.4 One-Dimensional Wave Equations: Generalities; 3.5 Estimation of Eigenvalues; 3.6 Wave Equation in Unbounded Regions; Miscellaneous; Chapter 4. The Potential Equation; 4.1 Potential Equation; 4.2 Potential in a Rectangle; 4.3 Further Examples for a Rectangle; 4.4 Potential in Unbounded Regions; 4.5 Potential in a Disk; 4.6 Classification and Limitations; Miscellaneous Exercises; Chapter 5. Higher Dimensions and Other Coordinates5.1 Two-Dimensional Wave Equation: Derivation; 5.2 Three-Dimensional Heat Equations: Vector Derivation; 5.3 Two-Dimensional Heat Equation: Solution; 5.4 Problems in Polar Coordinates; 5.5 Bessel's Equation; 5.6 Temperature in a Cylinder; 5.7 Vibrations of a Circular Membrane; 5.8 Some Applications of Bessel Functions; 5.9 Spherical Coordinates; Legendre Polynomials; 5.10 Some Applications of Legendre Polynomials; Miscellaneous; Chapter 6. Laplace Transform; 6.1 Definition and Elementary Properties; 6.2 Partial Fractions and Convolutions; 6.3 Partial Differential Equations6.4 More Difficult Examples; Miscellaneous Exercises; Chapter 7. Numerical Methods; 7.1 Boundary Value Problems; 7.2 Heat Problems; 7.3 Wave Equation; 7.4 Potential Equation; 7.5 Two-Dimensional Problems; Miscellaneous
• Sommario/riassunto: This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.Provides students with exercises that skillfully illustrate the techniques used in the text to solve science and engineering problemsNearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercisesMany exercises based on current engineering