Assignment 3 Solutions
Robotics 811, Fall 2013
1.
Consider the function f (x) = sinh x over the interval [2, 2].
(a)
What is the Taylor series expansion for f (x) around x = 0 ?
In the Taylor series expansion for f (x) around x = 0, the derivative alterna
Assignment 5 Solutions
Robotics 811, Fall 2013
1.
Consider a plane curve y (x) over the interval [x0 , x1 ], with specied endpoints y0 = y (x0 ) and y1 = y (x1 ). Assume that
y0 > 0 and y1 > 0 and that y (x) 0 for x0 x x1 . Now imagine rotating the curve
Assignment 1 Solutions
Robotics 811, Fall 2013
Problem 1 (Implement the P A = LDU decomposition algorithm directly yourself (in other words, do not just call a built-in Gaussian elimination algorithm
in MatLab, for instance). You may assume that the matri
Assignment 2 Solutions
Robotics 811, Fall 2013
1. Prove that the rst derivative p2 (x) of the parabola interpolating f (x) at x0 < x1 < x2 is
equal to the straight line which takes on the value f [xi1 , xi ] at the point (xi1 + xi )/2, for
i = 1, 2.
We us
Assignment 4 Solutions
Robotics 811, Fall 2013
Problem 1: Consider the following dierential equation over the interval [0, 1]:
dy
2
=2
,
dx
x (1 y )
with y (1) = 1.
(a) Obtain an exact analytic solution y (x) to the dierential equation.
dy
2
=2
dx
x (1 y
Assignment 1
Robotics 811, Fall 2015
DUE: Thursday, September 17, 2015
1. Implement the P A = LDU decomposition algorithm directly yourself (in other words, do
not just call a built-in Gaussian elimination algorithm in MatLab, for instance). You may
assum
Assignment 2
Robotics 811, Fall 2015
DUE: Thursday, October 1, 2015
1. Prove that the rst derivative p2 (x) of the parabola interpolating f (x) at x0 < x1 < x2 is
equal to the straight line which takes on the value f [xi1 , xi ] at the point (xi1 + xi )/2