**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