Solution Techniques for Elementary Partial Differential Equations, Second Edition

Ordinary Differential Equations: Brief RevisionFirst-Order Equations Homogeneous Linear Equations with Constant Coefficients Nonhomogeneous Linear Equations with Constant Coefficients Cauchy-Euler Equations Functions and OperatorsFourier SeriesThe Full Fourier Series Fourier Sine Series Fourier Cosine Series Convergence and Differentiation Sturm-Liouville ProblemsRegular Sturm-Liouville Problems Other Problems Bessel Functions Legendre Polynomials Spherical HarmonicsSome Fundamental Equations of Mathematical PhysicsThe Heat Equation The Laplace Equation The Wave EquationOther EquationsThe Meth. Read more... Abstract: Ordinary Differential Equations: Brief RevisionFirst-Order Equations Homogeneous Linear Equations with Constant Coefficients Nonhomogeneous Linear Equations with Constant Coefficients Cauchy-Euler Equations Functions and OperatorsFourier SeriesThe Full Fourier Series Fourier Sine Series Fourier Cosine Series Convergence and Differentiation Sturm-Liouville ProblemsRegular Sturm-Liouville Problems Other Problems Bessel Functions Legendre Polynomials Spherical HarmonicsSome Fundamental Equations of Mathematical PhysicsThe Heat Equation The Laplace Equation The Wave EquationOther EquationsThe Meth Incorporating A Number Of Enhancements, Solution Techniques For Elementary Partial Differential Equations, Second Edition Presents Some Of The Most Important And Widely Used Methods For Solving Partial Differential Equations (pdes). The Techniques Covered Include Separation Of Variables, Method Of Characteristics, Eigenfunction Expansion, Fourier And Laplace Transformations, Green’s Functions, Perturbation Methods, And Asymptotic Analysis. New To The Second Edition New Sections On Cauchy–euler Equations, Bessel Functions, Legendre Polynomials, And Spherical Harmonics A New Chapter On Complex Variable Methods And Systems Of Pdes Additional Mathematical Models Based On Pdes Examples That Show How The Methods Of Separation Of Variables And Eigenfunction Expansion Work For Equations Other Than Heat, Wave, And Laplace Supplementary Applications Of Fourier Transformations The Application Of The Method Of Characteristics To More General Hyperbolic Equations Expanded Tables Of Fourier And Laplace Transforms In The Appendix Many More Examples And Nearly Four Times As Many Exercises This Edition Continues To Provide A Streamlined, Direct Approach To Developing Students’ Competence In Solving Pdes. It Offers Concise, Easily Understood Explanations And Worked Examples That Enable Students To See The Techniques In Action. Available For Qualifying Instructors, The Accompanying Solutions Manual Includes Full Solutions To The Exercises. Instructors Can Obtain A Set Of Template Questions For Test/exam Papers As Well As Computer-linked Projector Files Directly From The Author. Content: Front cover Contents Foreword Preface to the Second Edition Preface to the First Edition Body Chapter 1: Ordinary DifferentialEquations: Brief Review Chapter 2: Fourier Series Chapter 3: Sturm-Liouville Problems Chapter 4: Some Fundamental Equationsof Mathematical Physics Chapter 5: The Method of Separation of Variables Chapter 6: Linear Nonhomogeneous Problems Chapter 7: The Method ofEigenfunction Expansion Chapter 8: The Fourier Transformations Chapter 9: The Laplace Transformation Chapter 10: The Method of Green's Functions Chapter 11: General Second-Order LinearPartial DifferentialEquations with TwoIndependent VariablesChapter 12: The Method of Characteristics Chapter 13: Perturbation and Asymptotic Methods Chapter 14: Complex Variable Methods Answers to Odd-Numbered Exercises Appendix Bibliography Back cover