Laplace Equation

Laplace Equation. See attached file for full problem description.

Integral

PDE - Integral. See attached file for full problem description.

Boundary Value Problem

Boundary Value Problem. See attached file for full problem description.

Solving Differential Equations : Boundary Value Problem and Separation of Varaiables

Please see the attached file for the fully formatted problems.

Laplace's Equation and Separation of Variables

Using separation of variables, solve Laplace's equaton inside a 60 degree wedge of radius a, subject to boundary conditions: u(r,0) = 0 u(r,pi/3) = 0 u(a,θ) = f(θ)

Partial Differential Equatons : Homogeneous Heat Conduction

8. Use separation of variables to find the solution, in the form of an infinite series, of the homogeneous heat conduction problem with mixed boundary conditions: Ehi 02u PDE: .… BCs: .… ICs: .… Proceed as follows: (a) Assume u(x, t) = (x)G(t) and derive the ODEs satisfied by q(x) and G(t). (b) Solve the ODEs for q(x) and ...continues

Partial Differential Equations : Boundary Value Problem

Please see the attached file for the fully formatted problems.

Partial Differential Equations : Show that the drag force is zero for a uniform flow past a cylinder with circulation.

10. Show that the drag force is zero for a uniform flow past a cylinder with circulation.

Poisson's Equation and the Maximum Principle for Laplace's Equation

Please see the attached file for the fully formatted problem.

Backward Heat Equation

Please see the attached file for the fully formatted problems.