Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510/CS 522
Homework 1
September 8, 2005
1. Consider the oating point number system consisting of all numbers .d1 d2 e ,
where = 3, 1 e 1, 0 < d1 < 3, and 0 d2 < 3. Write down in rational form
all of the positive numbers in this system. What is the larg
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510 / CS 522 HW #6
Due Thursday November 3rd
A 5th problem will be added after lecture on Thursday 10/27
1. Find the discrete least squares polynomials of degrees 1, 2, and 3 for the following data: x =[1, 1.1, 1.3,
1.5, 1.9, 2.1], y =[1.84,
Pm1.96, 2.
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510 / CS 522 HW #5
Due in class Thursday 10/6
1. Consider the problem of finding a quadratic polynomial p(x) for which
p(xo ) = yo ,
p0 (x1 ) = y10 ,
p(x2 ) = y2
with xo 6= x2 and cfw_yo , y10 , y2 the given data points. Assuming that the nodes xo , x
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510 / CS 522 HW #4
Due in class Thursday 9/29
1. Recall the Vandermonde matrix X as defined in class, and define:
1
xo
x2o
xno
.
.
.
Vn (x) = det .
1 xn1 x2n1
xnn1
1
x
x2
xn
(a) Show that Vn (x) is a polynomial of degree n and that its roots are xo ,
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510 / CS 522 HW #3
Due Thursday September 22nd In Class
1. Write a code for Newtons Method to find the root of the following function:
f (x) = x3 x 3
The code should be set up as follows:
Initialize function and derivative, initialize starting guess x
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
Written Homework #1
Due by the end of class lecture on Thursday, September 8th. Please write your answers clearly and
show all work. You will be required to have a printed out version of code as well as submit a file
containing code for all of the homewor
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510 / CS 522 HW #2
Due Thursday September 15th by 5:30 pm
1. If a polynomial, f (x), has an odd number of real zeros in the interval [a, b] and each of the zeros is
of odd multiplicity, then f (a)f (b) < 0 and the bisection method will converge to one
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510/CS 522
Homework 7
November 10, 2005
1. (a) One can show that if G : I 1 I 1 is Lipschitz continuously dierentiable near
R
R
1
x I such that x = G(x ) and G (x ) = 0, then for x0 near x , the xedpoint
R
iterates cfw_xn converge quadratically to x
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510/CS 522
Homework 8
November 17, 2005
These two problems involve using the MATLAB spline command. Typing help
spline or doc spline in MATLAB will tell you enough about its usage to do this
exercise and also provide several helpful examples.
1. This p
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510/CS 522
Homework 6
November 3, 2005
For the following problems, you will have to download codes from the MFiles link
on the course web page. To use them, you will have to create Mles or otherwise
provide MATLAB codes to evaluate the necessary func
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MIDTERM EXAM
MA 510/CS 522
October 20, 2005
In working the following exam, you may use your class notes and any books you like.
However, do not consult or collaborate with anyone. Be sure to show your work.
1. (10 points) Suppose a system function for ex
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510/CS 522
Homework 4
October 6, 2005
1. Suppose A I mn , m n, and A = QR, where Q I mn is orthogonal, i.e.,
R
R
nn
T
Q Q = I, and R I
R
is upper triangular and nonsingular. Show the following:
(a) Qv
2
= v
2
for all v I n .
R
(b) 2 (A) = 2 (R).
Recall
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510/CS 522
Homework 2
September 15, 2005
1. Write a code to solve a linear system Ax = b using Gaussian elimination with
partial pivoting. Use it to solve the system Ax = b, where
1 2 1
2
1 2 2 , b = 5.
A=
2 1 1
0
Hand in your code and output.
Note:
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510/CS 522
Homework 3
September 22, 2005
1. Consider the simple static system illustrated. This consists of 13 rigid members
connected at 8 joints, each of which allows free rotation. All horizontal and vertical
members are of length one; all diagonal
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510/CS 522
FINAL EXAM
December 8, 2005
The following problems are worth 20 points apiece. In working them, you may use
your class notes and any books you like. However, do not consult or collaborate with
anyone. Be sure to show your work.
1. For our Ne
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
MA 510/CS 522
Homework 5
October 13, 2005
2
1. For c > ln(0.9), the function F (x) = ec(x 1) 0.9 satises F (0) < 0 < F (1) and
2
thus has a zero x in (0, 1). Since F (x) = 2cxec(x 1) > 0 for x (0, 1), this is the
only zero of F in (0, 1).
a. With c = 1, u
Numerical Methods for Calculus and Differential Equations
MA MA 510/CS

Fall 2005
Numerical Methods
MA 510/CS 522
FALL 2016
Instructor: Professor Sarah Olson
Office Location: 302 Stratton Hall
Office Hours: Tuesday 121, Wednesday 23
Email: sdolson@wpi.edu
Phone: x4940 (Please email if I do