Partial Differential Equation Unit 2 Quiz

What theorem is associated with the Cauchy problem?

• Fourier theorem

• Goursat theorem

• Riemann theorem

• Cauchy-Kowalewsky theorem

What type of equation is the homogeneous wave equation?

• Cubic

• Linear

• Non-linear

• Quadratic

What is the initial boundary value problem concerned with?

• Initial conditions and boundary conditions

• Non-homogeneous conditions

• Only initial conditions

• Only boundary conditions

What type of boundary conditions are considered non-homogeneous?

• Variable boundary conditions

• Constant boundary conditions

• Fixed boundary conditions

• Zero boundary conditions

What is a finite string with fixed ends an example of?

• A non-linear problem

• An initial value problem

• A homogeneous equation

• A boundary value problem

What type of wave equation includes external forces?

• Cylindrical wave equation

• Non-homogeneous wave equation

• Homogeneous wave equation

• Spherical wave equation

Which method is associated with solving certain types of partial differential equations?

• Riemann method

• Laplace method

• Newton method

• Euler method

What does the Goursat problem involve?

• Only boundary conditions

• Non-linear equations

• Only initial conditions

• Initial and boundary conditions

What type of wave equation describes waves radiating outward in three dimensions?

• Spherical wave equation

• Non-homogeneous wave equation

• Cylindrical wave equation

• Homogeneous wave equation

What type of wave equation describes waves in a cylindrical shape?

• Cylindrical wave equation

• Non-homogeneous wave equation

• Homogeneous wave equation

• Spherical wave equation