- 1.1: Functions in two dimensions, contours
- 1.2: Adding two standing waves
Chapter 2
- 2.1: Periodic functions in Maple - sine and cosine
- 2.1: - dealing with discontinuous functions
- 2.1: - using "floor" to make periodic functions
- 2.2: Representing functions with a Fourier series - Parabola
- 2.2: - linear function
- 2.2: - piecewise linear function
- 2.3: Fourier Transform over an Arbitrary Range - Parabola
- 2.3: - an odd function over symmetric limits
- 2.3: - an odd function over arbitrary limits
- 2.3: - Fourier series involving elements of the basis set - a caution
- 2.3: - harmonics of a plucked string
- 2.4: Expanding an even function with a cosine series
- 2.4: Expanding an even function with a sine series
- 2.6: A complex Fourier expansion
- 2.6: Example 1 from the text
Chapter 3
- 3.3: Animated waves on a string: parabolic
- 3.3: - Problem 3.3.2 in the text
- 3.3: - a problem with both f(x) and g(x)
- 3.5: Animated solutions of the heat transfer equation in one dimension: u=0 on the ends
- 3.5: - non-homogeneous boundary conditions
- 3.6: Heat equation: insulated ends
- 3.6: - both ends radiate - finding the values of mu
- 3.6: - both ends radiate - the animated solution - programming loops in Maple
- 3.7: Wave equation in two dimensions - Cartesian
- 3.7: - normal modes
- 3.9: Poisson's Equation - two-dimensional in Cartesian coordinates
- 3.9: - steady state 2-dimensional heat equation with a source
- 3.9: Another inhomogeneous equation
- rod with
internal heat source, time dependent
Chapter 4
- 4.2: Bessel functions of order zero
- 4.2: Oscillations on a drumhead - using J0
- 4.2: - Two-dimensional animation
- 4.2: - Normal modes
- 4.3: General circular drumhead problem - initial velocity is zero
- 4.3: Normal modes on a drumhead
- 4.3: Three normal modes summed together
- 4.4: Euler's Equation
- 4.4: Center-struck drum
- 4.4: Off-center drum
- 4.4: Heat transfer on a circular disk
- 4.5: Dirichlet problem on a cylinder
- 4.7: More on Bessel and Gamma functions
- 4.8: Bessel-Sine expansion of functions in r and theta
Chapter 5
- 5.1: Associated Legendre Polynomials - Maple's default phases
- 5.1: - Getting the usual phases
- 5.2: Graphing Associated Legendre Polynomials
- 5.2: Representing a function of theta with Legendre Polynomials
- 5.3: Two Maple procs to make spherical harmonics
- 5.3: Representing a function of theta and phi in terms of spherical harmonics
- 5.E: Spherical Bessel and Neumann functions
- 5.E: Hydrogen atom wavefunctions
- 5.E: Scattering of an electron from a hard sphere potential
Chapter 6
- 6.1: An insulated rod radiating at both ends
Chapter 7
- 7.1: Fourier integrals in Maple
- 7.1: Fourier transform of a sum of sine waves over an infinite range
- 7.1: - of a sum of sine waves restricted to a finite range
- 7.1: - and single slit scattering
- 7.1: - and scattering through irregular slits
- 7.1: The inverse Fourier transform
- 7.1: Gibb's phenomenon and windowing in Fourier transforms
- 7.2: Fourier transform - Truncated sine function
- 7.2: - Transform of a derivative
- 7.2: - Visualizing a convolution
- 7.2: - Inverse Fourier transform
- 7.3: Heat transfer on an infinite rod using Fourier transforms
Chapter 8
- 8.1: Some Laplace transforms
- 8.1: Using Maple's Laplace transforms
- 8.1: More examples of Laplace transforms
- 8.1: Problem 8.1.43 with Laplace transforms
- 8.2: Using Heaviside functions
- 8.2: Shifting a function along the t-axis
- 8.2: Laplace transforms of combinations of Heaviside functions
- 8.2: An oscillator with a piecwise continuous driving force
- 8.2: An oscillator with a Dirac function driving force
- 8.3: Changing variables in a Laplace transform
- 8.3: A heat transfer problem with a convolution
- 8.3: Another heat transfer problem
