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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
• 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
• 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
• 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  