Solving Differential Equations
y'=ty^3 with y(0)= -1 over [-3/4, 3/4] Having trouble solving for y
Vectors and Gradients : Direction of Most Rapid Increase; Critical Points
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.
Gradients and Vectors : Rate of Maximum Increase
Find the direction in which f(x,y,z) = ze^(xy) increases most rapidly at the point (0,1,2) What is the maximum rate of increase?
Partial Differentials Equations : Gradient of the Function
Find the gradient ∇g of the function g(x, y) = r^5, where r = sqrt (x^2 +y^2). Hint: introduce a new variable, u = x2 + y2. Express g(x, y) in terms of u and use the chain rule to find dg/dx and dg/dy.
Systems of Equations and Reduced Row Echelon Form
2. A computer manufacturer produces three models of hardware: a desktop, a laptop, and a server. The production times for the desktop are 0.5 hours of assembly and 0.1 of packag- ing. For the laptop, it takes 1.0 hours of assembly and 0.6 hours of packaging. The server requires 1.5 hours of assembly and 1.2 hours of packaging ...continues
Partial Differential Equations : Characteristic Curves
1.(a) Solve the given equation by the method of characteristic curves. (b) Check your answer by plugging it back into the equation. x ∂u/∂x + y ∂u/∂y = 0 See attached file for full problem description.
Solving Partial Differential Equations
Please see the attached file for the fully formatted problems.
See attached file for full problem description. Solve by Eigenfunction.
Partial Differential Equations : Neumann and Dirichlet Problems
Please see the attached file for the fully formatted problems.
Partial Differential Equations : Heat Equations
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
