Beginning Partial Differential Equations 3rd Edition by Peter V. O'Neil

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Beginning Partial Differential Equations

PDF Free Download | Beginning Partial Differential Equations 3rd Edition by Peter V. O’Neil

Contents of Beginning Partial Differential Equations

  • First Ideas
  • Two Partial Differential Equations
  • The Heat, or Diffusion, Equation
  • The Wave Equation
  • Fourier Series
  • The Fourier Series of a Function
  • Fourier Sine and Cosine Series
  • Two Eigenvalue Problems
  • A Proof of the Fourier Convergence Theorem
  • The Role of Periodicity
  • Dirichlet’s Formula
  • The Riemann-Lebesgue Lemma Proof of
  • Solutions of the Heat Equation
  • Solutions on an Interval [ , L]
  • Ends Kept at Temperature Zero
  • Insulated Ends
  • Ends at Different Temperatures
  • A Diffusion Equation with Additional Terms
  • One Radiating End
  • A Nonhomogeneous Problem
  • The Heat Equation in Two Space Variables
  • The Weak Maximum Principle
  • Solutions of the Wave Equation
  • Solutions on Bounded Intervals
  • Fixed Ends
  • Fixed Ends with a Forcing Term
  • Damped Wave Motion
  • The Cauchy Problem
  • d’Alembert’s Solution
  • Forward and Backward Waves
  • The Cauchy Problem on a Half Line
  • Characteristic Triangles and Quadrilaterals
  • A Cauchy Problem with a Forcing Term
  • String with Moving Ends
  • The Wave Equation in Higher Dimensions
  • Vibrations in a Membrane with Fixed Frame
  • The Poisson Integral Solution
  • Hadamard’s Method of Descent
  • Dirichlet and Neumann Problems
  • Laplace’s Equation and Harmonic Functions
  • Laplace’s Equation in Polar Coordinates
  • Laplace’s Equation in Three Dimensions
  • The Dirichlet Problem for a Rectangle
  • The Dirichlet Problem for a Disk
  • Poisson’s Integral Solution
  • Properties of Harmonic Functions
  • Topology of Rn
  • Representation Theorems
  • A Representation Theorem in R
  • A Representation Theorem in the Plane
  • The Mean Value Property and the Maximum Principle
  • The Neumann Problem
  • Existence and Uniqueness
  • Neumann Problem for a Rectangle
  • Neumann Problem for a Disk
  • Poisson’s Equation
  • Existence Theorem for a Dirichlet Problem
  • Fourier Integral Methods of Solution
  • The Fourier Integral of a Function
  • Fourier Cosine and Sine Integrals
  • The Heat Equation on the Real Line
  • A Reformulation of the Integral Solution
  • The Heat Equation on a Half Line
  • The Debate over the Age of the Earth
  • Burger’s Equation
  • Traveling Wave Solutions of Burger’s Equation
  • The Cauchy Problem for the Wave Equation
  • Laplace’s Equation on Unbounded Domains
  • Dirichlet Problem for the Upper Half Plane
  • Dirichlet Problem for the Right Quarter Plane
  • A Neumann Problem for the Upper Half Plane
  • Solutions Using Eigenfunction Expansions
  • A Theory of Eigenfunction Expansions
  • A Closer Look at Expansion Coefficients
  • Bessel Functions
  • Variations on Bessel’s Equation
  • Recurrence Relations
  • Zeros of Bessel Functions
  • Fourier-Bessel Expansions
  • Applications of Bessel Functions
  • Temperature Distribution in a Solid Cylinder
  • Vibrations of a Circular Drum
  • Oscillations of a Hanging Chain
  • Did Poe Get His Pendulum Right?
  • Legendre Polynomials and Applications
  • A Generating Function
  • A Recurrence Relation
  • Fourier-Legendre Expansions
  • Zeros of Legendre Polynomials
  • Steady-State Temperature in a Solid Sphere
  • Spherical Harmonics
  • Integral Transform Methods of Solution
  • The Fourier Transform
  • Convolution
  • Fourier Sine and Cosine Transforms
  • Heat and Wave Equations
  • The Heat Equation on the Real Line
  • Solution by Convolution
  • The Heat Equation on a Half Line
  • The Wave Equation by Fourier Transform
  • The Telegraph Equation
  • The Laplace Transform
  • Temperature Distribution in a Semi-Infinite Bar
  • A Diffusion Problem in a Semi-Infinite Medium
  • Vibrations in an Elastic Bar
  • First-Order Equations
  • Linear First-Order Equations
  • The Significance of Characteristics
  • The Quasi-Linear Equation
  • End Materials
  • Notation
  • Use of MAPLE
  • Numerical Computations and Graphing
  • Ordinary Differential Equations
  • Integral Transforms
  • Special Functions
  • Answers to Selected Problems

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