Linearization of a function. Attachments in Word.
The distance l from a point at a height h above the Earth's surface to the horizon can be approximated using Pythagoras' theorem by the expression: (Please see the attachment below) (a) Find an expression which serves as a linear approximation for l at h=1000 m. (b) Give two assumptions you think have been made in deriving ...continues
Solve an IVP ODE using the method of variation of parameters
Solve an IVP ODE using the method of variation of parameters
In an unmanaged tract of forest area, hardwood and softwood trees compete for the available land and water. The more desirable hardwood trees grow more slowly, but are more durable and produce more valuable timber. Softwood trees compete with the hardwoods by growing rapidly and consuming the available water and soil nutrients ...continues
wave equation using dirchlet boundary conditions
Utt means second derivative with respect to t Uxx means second derivative with respect to x The answer must meet all of the Boundary and other conditions. Please check your answer to make sure it is correct. It is extremely important. Solve: Utt = Uxx, 0 < x < pi, t > 0 U(0,t) = 0, U(pi,t) = 0 U(x,0) = 0, Ut ...continues
Utt means the second derivative with respect to t Uxx means the second derivative with respect to x Utt = 4Uxx, -(inf) < x < (inf), t > 0 U(x,0) = x, Ut(x,0) = xe^(-x^2) for -(inf) < x < (inf) Please use D'Alembert's Formula and show all work. If there is Fourier series, please show how you got eigenvalues and eige ...continues
Wave equation with mixed boundary conditions
Uxx means second derivative with respect to x Uyy means second derivative with respect to y Uxx + Uyy = 0, 0 < x < pi, 0 < y < 1 Ux(0,y) = 0 = U(pi,y), 0 < y < 1 U(x,0) = 1, U(x,1) = 0, 0 < x < pi Please show all work including how eigenvalues and eigenvectors are derived. Thank you
Elliptic Boundary Value Problem
Uxx means second derivative with respect to x Uyy means second derivative with respect to y Uxx + Uyy = 0, 0 < x < pi, 0 < y < pi U(x,0) = 0, U(x,pi) = 1, 0 < x < pi U(0,y) = 0, U(pi,y) = 1 0 < y < pi I know the problem has to be broken into 2 seperate problems using U = V + W with zero conditions on 3 sides fo ...continues
Ellipctic Boundary Value problem using laplace and polar cordinates
(lap) means the laplacian Vrr means the second derivative of V with respect to r V(theta theta) means the second derivateive of V with respect to theta Solve: (lap)V(r,theta)= Vrr+(1/r)Vr+(1/r^2)V(theta theta)=0 0 < r < 1, -(pi) < theta < pi V(1,theta) = {1, -(pi/2) < theta < (pi/2) {0, elsewhere Pl ...continues
Linear Partial Differential Equation (I) Linear Homogeneous Partial Differential Equation with Constant Coefficients Problem 1: Find the General solution of the equation r = a2t. ...continues
Linear Partial Differential Equation (II) Non- Homogeneous Linear Partial Differential Equation with Constant Coefficients Problem: Find the solution of the equation (D2 – D’2 + D – ...continues
