Show, for any three-dimensional vectors , , , that
Lists and Matrices
Problem 2. Display the following matrix in matrixform.
Problem 3. Define the function
f(x) = x - 2 tanh(x). Find
the three real roots(use FindRoot), xr, of f(x) and check that one of the
non-zero roots satisfies f(xr)=0.
Problem 4. Define
x(t) = Cos[ t] , y(t) = Sin[t], z(t) = t.
Do a parametric plot of
What sort of motion is this ?
Ordinary differential equations
Problem 5. An ideal pendulum (
m = 1 kg, l=2m)
oscillates in air. The drag coefficient of
air is b=0.001. Consider a small amplitude
initial displacement of 1 cm and initial velocity of zero.
Solve the linear differential equation for this problem.
Partial differential equations
Problem 6. Show that y (x,t) = A Cos(x - v t) solves the wave equation