CE317 Computer Methods in Civil Engineering
Assignment
#1
Due date: 5 October
2002
1-
Consider the
function 
. Estimate
the value of the function at x = 0 from at its value at x = 1 using Taylor
Series. Find the minimum order of Taylor series that gives a true relative
error єt < 1%. (Hint: the limit of the value of
the function as x -> 0 is 1.)
2-
Consider the
function Ln x
a-
Estimate the
first derivative of the given function at x = 1 using the backward, forward and
centered finite difference with h = 0.2.
b-
Repeat part
(a) for the second derivative.
3-
The velocity
distribution of a fluid near a flat surface is given by the following table,
where v is the velocity and x is the distance from the surface:
|
X(m) |
v(m/sec) |
|
0.000 |
0.00000 |
|
0.001 |
0.00723 |
|
. |
. |
|
. |
. |
|
. |
. |
If α is the viscosity, the Newton’s law for the
shear stress is given by
Use the forward finite
difference to calculate the shear stress at the surface (x = 0). Assume
that α = 0.0011 N sec/m2.
4-
Use Mathematica
to generate Taylor series for the function f= x-cos(x) with x0 = 0
and n=5. Use the series to approximate f(1) and calculate the percent relative
errors.