List of Figures

• 15.1. Illustration of change of basis.
• 17.1. Laminar viscous flow in a long duct.
• 18.1. An example Laplace equation problem.
• 18.2. An example heat equation problem.
• 18.3. An example wave equation problem.
• 18.4. An improperly posed Laplace problem.
• 18.5. An improperly posed wave equation problem.
• 19.1. Chopping a one-dimensional function up into spikes.
• 19.2. Contribution of one spike to the solution.
• 19.3. Approximation of the spike by an infinitely narrow one.
• 19.4. Green's function solution of an example one-dimensional Poisson equation.
• 19.5. Approximate Dirac delta function left and true one right.
• 19.6. One of the spikes of which an arbitrary two-dimensional function consists.
• 19.7. Sketch of the problem to be solved.
• 19.8. Region of integration for the Green's function integral.
• 19.9. Example finite domain $\Omega$ in which the Poisson or Laplace equation is to be solved.
• 19.10. Temperature distributions involved in the solution process.
• 19.11. Region of integration of the integral for the infinite-space solution. Note that $\delta\Omega$ is a bounding surface of both dark grey domain $\Omega$ and of the light grey exterior region.
• 20.1. Characteristics of the partial differential equation of problem 5.30.
• 20.2. Given the value of $u$ at a single point on a characteristic line, $u$ can be found at every point on that line.
• 20.3. Region where $u$ is determined by an initial condition given on the line $x+y=1$.
• 20.4. Characteristics of Burgers' equation for an example initial condition intersect.
• 20.5. Profiles at times $t = 0$, .5, 1, and 1.3 show wave steepening leading to a multiple-valued solution for times greater than $t=1$.
• 20.6. Correct solution of Burgers' equation.
• 20.7. Correct profiles for Burgers' equation.
• 20.8. Incorrect expansion shock solution to Burgers' equation.
• 20.9. Correct expansion fan solution to Burgers' equation
• 22.1. Acoustics in a pipe.
• 22.2. Dependent variables.
• 22.3. Heat conduction in a bar.
• 22.4. Heat conduction in a bar.
• 22.5. Heat conduction in a bar.
• 22.6. Heat conduction in a bar.
• 24.1. Viscous flow next to a moving plate
• 24.2. Viscous flow next to a moving plate
• 24.3. Supersonic flow over a membrane.
• 24.4. Supersonic flow over a membrane.
• 24.5. function f-bar.
• 24.6. function f-bar again.
• 24.7. Supersonic flow over a membrane.
• 24.8. Problem for v.
• N.1. Spherical coordinates of an arbitrary point P.