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How do I estimate the abosolute and relative maximum and average errors in the total of the above rounded data?
If b2 - 4ac >0, the quadratic equation ax2 + bx +c = zero has two real solutions x1, x2 given by the typical: x1 = (-b + sqrt(b^2-4ac))/ (2a)
Use the method of characteristics to find the solution to (1) with initial condition u(x,0) = f(x).
Explain the following in your own words: (a + b)2 ¹ a2 + b2. Give a numerical example to illustrate this.
Solve the following ?eigenvalue? problem: d2y/dx2+?2y(x)=0 0 < x <1
Explain why you cannot find f(x,y) such that ?f(x,y) = ( x2+3xy2, 2xy+y3+1).
Consider the heat equation ?u/?t= k(?2u/?x2) ,0=x=L t>0 .
Find the solution u(x,t) of the heat equation: ut = 1/2 uxx
The bending moment M at position x m from the end of a simply supported beam of length L m carrying a uniformly distributed load of w Kn m-1 .
Solve the following PDE: du/dt = d^2u / dx^2,u(x, 0) = sin^2(x), u(0, t) = 0, u(Pi, t) = 0,
Find the particular solution of the differential equation , (dy/dx) + ycos(x) = 6cos(x) w/ y(0) = 8
y'''-11 y'' + 18 y' = 0 w/ y(0) = 1, y'(0) = 3, y"(0) = 4
Calculate uxx, uyy and uxy and show that uxx and uyy are continuous in the whole disk, but that u?c2. Calculate f := - ?u.
an posses a nontrivial solution which vanishes at x=0 and x=1 only if ? is such that J1/4 (1/2v?)=0,and that corresponding to such a characteristic number ?k.
The population of a community is known to increase at a rate proportional to the number of people present at time t.
The problem that I'm having is that there is a nonconstant factor of (x^2+y^2+z^2)^(-1/2) appearing on the RHS of this equation, making it non-trivial to solve.
Suppose that 0
Use the Secant method to show that sequence below converges to vQ, where Q > 0, given "good" starting values x0 and x_1: xn+1 = (xnxn-1 + Q) / (xn + xn-1).
Suppose that y(x)' : f(x,y(x)) on the interval [x0, x1] with y (x0) = y0.
If you were to transform this PDE with the substitution S = Kex, where x is a variable and K a constant, what would be the resulting equation?
Assuming a drag coefficient of k=1/800 lb m/ft, how high does the arrow go? does your answer depend on the objects mass?
Show that for any constants c and d, |d| < 1, the equation x = c + d cos (x) = g(x) has a unique solution alpha.
Determine the flow Qt : R^2 into R^2 for the nonlinear system: x' =f(x) with f(x) = [ -x1 ]
Find the unique solution (and proof that it is unique) and the maximal interval of the initial value problem x' = x^3, x(0) = xo for any xo E R.
Why not just use Newton's Interpolatory Divided Difference formula to get an nth degree interpolating polynomial?