Differential Equations with Applications and Historical Notes, 2nd Edition (I…

Description: About this productProduct InformationA revision of a much-admired text distinguished by the exceptional prose and historical/mathematical context that have made Simmons' books classics. The Second Edition includes expanded coverage of Laplace transforms and partial differential equations as well as a new chapter on numerical methods.Product IdentifiersPublisherMcGraw-Hill Higher EducationISBN-100070575401ISBN-139780070575400eBay Product ID (ePID)28770Product Key FeaturesFormatHardcoverPublication Year1991LanguageEnglishDimensionsWeight26.4 OzWidth6in.Height1.1in.Length9.1in.Additional Product FeaturesDewey Edition21Table of Content1. The Nature of Differential Equations. 2. First Order Equations. 3. Second Order Linear Equations. 4. Qualitative Properties of Solutions. 5. Power Series Solutions and Special Functions. 6. Fourier Series and Orthogonal Functions. 7. Partial Differential Equations and Boundary Value Problems. 8. Some Special Functions of Mathematical Physics. 9. Laplace Transforms. 10. Systems of First Order Equations. 11. Nonlinear Equations. 12. The Calculus of Variations. 13. The Existence and Uniqueness of Solutions. 14. Numerical Methods., Preface to the Second Edition Preface to the First Edition Suggestions for the Instructor 1 The Nature of Differential Equations. Separable Equations 1. Introduction 2. Gemeral Remarks on Solutions 3. Families of Curves. Orthogonal Trajectories 4. Growth, Decay, Chemical Reactions, and Mixing 5. Falling Bodies and Other Motion Problems 6. The Brachistochrone. Fermat and the Bernoullis 2 First Order Equations 7. Homogeneous Equations 8. Exact Equations 9. Integrating Factors 10. Linear Equations 11. Reduction of Order 12. The Hanging Chain. Pursuit Curves 13. Simple Electric Circuits 3 Second Order Linear Equations 14. Introduction 15. The General Solution of the Homogeneous Equation 16. The Use of a Known Solution to Find Another 17. The Homogeneous Equation with Constant Coefficients 18. The Method of Undetermined Coefficients 19. The Method of Variation and Parameters 20. Vibrations in Mechanical and Electrical Systems 21. Newton's Law of Gravitation and the Motions of the Planets 22. Higher Order Linear Equations. Coupled Harmonic Oscillators 23. Operator Methods for Finding Particular Solutions Appendix A. Euler Appendix B. Newton 4 Qualitative Properties of Solutions 24. Oscillations and the Sturm Separation Theorem 25. The Sturm Comparison Theorem 5 Power Series Solutions and Special Functions 26. Introduction. A Review of Power Series 27. Series Solutions of First Order Equations 28. Second Order Linear Equations. Ordinary Points 29. Regular Singular Points 30. Regular Singular Points (Continued) 31. Gauss's Hypergeometric Equation 32. The Point at Infinity Appendix A. Two Convergence Proofs Appendix B. Hermite Polynomials and Quantum Mechanics Appendix C. Gauss Appendix D. Chebyshev Polynomials and the Minimax Property Appendix E. Riemann's Equation 6 Fourier Series and Orthogonal Functions 33. The Fourier Coefficients 34. The Problem of Convergence 35. Even and Odd Functions. Cosine and Sine Series 36. Extension to Arbitrary Intervals 37. Orthogonal Functions 38. The Mean Convergence of Fourier Series Appendix A. A Pointwise Convergence Theorem 7 Partial Differential Equations and Boundary Value Problems 39. Introduction. Historical Remarks 40. Eigenvalues, Eigenfunctions, and the Vibrating String 41. The Heat Equation 42. The Dirichlet Problem for a Circle. Poisson's Integral 43. Sturm-Liouville Problems Appendix A. The Existence of Eigenvalues and Eigenfunctions 8 Some Special Functions of Mathematical Physics 44. Legendre Polynomials 45. Properties of Legendre Polynomials 46. Bessel Functions. The Gamma Function 47. Properties of Bessel functions Appendix A. Legendre Polynomials and Potential Theory Appendix B. Bessel Functions and the Vibrating Membrane Appendix C. Additional Properties of Bessel Functions 9 Laplace Transforms 48. Introduction 49. A Few Remarks on the Theory 50. Applications to Differential Equations 51. Derivatives and Integrals of Laplace Transforms 52. Convolutions and Abel's Mechanical Problem 53. More about Convolutions. The Unit Step and Impulse Functions Appendix A. Laplace Appendix B. Abel 10 Systems of First Order Equations 54. General Remarks on Systems 55. Linear Systems 56. Homogeneous Linear Systems with Constant Coefficients 57. Nonlinear Systems. Volterra's Prey-Predator Equations 11 Nonlinear Equations 58. Autonomous Systems. The Phase Plane and Its Phenomena 59. Types of Critical Points. Stability. 60. Critical Points and Stability for Linear Systems 61. Stability by Liapunov's Direct Method 62. Simple Critical Points of Nonlinear Systems 63. Nonlinear Mechanics. Conservative Systems 64. Periodic Solutions. The Poincar&IllustratedYesDewey Decimal515.3/5SeriesInternational Series in Pure and Applied MathematicsCopyright Date1991AuthorGeorge F. SimmonsEdition Number2Number of Pages640 PagesEdition DescriptionRevisedLc Classification NumberQa372.S49 1991Publication Date1991-01-01Lccn90-033686

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