1. Given f(x,y,z)=x^2y^3z^6, in what direction is F(x,y,z) increasing most rapidly at the point P(1,-1,1). What is the rate of increase? 2. Locate and classify the critical points of the function h(x,y) = x^2 -4x+4xy+y^2-16y.
Differential Equations. See attached file for full problem description. Problem #2 only.
1. Formulate a boundary value problem modeling heat conduction in a thin bar of length , if the left end is kept at temperature zero and the right end is insulated. The initial temperature in the cross section at is . 2. Formulate a boundary value problem for the motion of an elastic string of length , fastened at both e ...continues
1. (a) Solve the given equation by the method of characteristic curves. (b) Check your answer by plugging it back into the equation. See attached file for full problem description.
Differential Equations. See attached file for full problem description.
See attached file for full problem description. Solve by Eigenfunction.
See attached file for full problem description.
See attached file for full problem description.
Partial Differential Equations Problems
1) Let A(x,y) be the area of a rectangle not degenerated of dimensions x and y, in a way that the rectangle is inside a circle of a radius of 10. Determine the domain and the range of this function. 2) The wave equation (c^2 ∂^2 u / ∂ x^2 = ∂^2 u / ∂ t^2) and the heat equation (c ∂^2 u / ∂ ...continues
Partial differential equation problem
According to the ideal gas law, the pressure, the temperature and the volume of a gas are related by PV = kT (k is a constant). Show the following: (attached)
