Amath 507
Homework Solution #1.6.4
Problem: Potential energy inside the earth
Use your results from Exercise 1.6.3 and integrate over shells of appropriate
radii to show that the potential energy of a
Amath 507
Homework Solution #1.6.3
Problem: Potential energy due to a spherical shell
The gravitational potential energy between two point masses, M and m, separated by a distance r is
GMm
,
(3.1)
r
w
Amath 507
Homework Solution #1.6.1
Problem: Descent time down a cycloidal curve
Show that the descent time down the cycloidal curve
x( ) = a + R ( sin ) , y( ) = y a R (1 cos )
(1.1)
is
T =
R
,
g b
(
AMATH 352: Problem set 1 Solutions
April 11, 2016
Class management questions
(1pt each: 4pts) Thank you for answering!
1
Linearity
In class, I showed you what the definition of linearity was (its also
AMATH 423/523
1
Mathematical Analysis in Biology and Medicine
Winter, 2016
Introduction
1.1
The philosophy of the course
Probability is the logic of science1 ; statistics is a tool for making discover
University of Washington
AMATH 301 Winter 2016
Instructor: Dr. KingFai Li
Week5
Optimization
1D example
f x x 4 10 x sin x 2
f = @(x) x.^4 + 10*x.*sin(x.^2);
x = linspace(2,3,100);
plot(x,f(x);
[xm
University of Washington
AMATH 301 Winter 2016
Instructor: Dr. KingFai Li
Week 3
1. Fixedpoint iteration
Purpose: Find the roots of F x 0
1. Rewrite F x 0 into the form of x G x . i.e. if x is a sol
University of Washington
AMATH 301 Winter 2016
Instructor: Dr. KingFai Li
Week 2
Solving Systems of Linear Equations
Given a set of equations,
x1 x2 2
2 x1 5 x2 7
First check the determinant: (1)(5)
%Question 1
t = 2;
X = hilb(t);
A1 = [];
while cond(X, inf) < 1e16
A1 = [A1, cond(X, inf)];
t = t + 1;
X = hilb(t);
end
A1 = A1.';
save('A1.dat', 'A1', 'ascii');
A2 = [];
for t = 2:11
z = ones(t,
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Name:
Student number:
QUIZ 3
1. If A Rmn , A = QR is the QR factorization of matrix A, which of the following statements
are true
(a) QT Q = In , where In is the identity matrix of size n.
ANS: True.
Name:
Student number:
QUIZ 1
1. True of False
(a) If S1 and S2 are subspaces of Rn of the same dimension, then S1 = S2 .
1
0
ANS: False. Counter example span
= span
0
1
(b) If S = span(u1 , u2 , u1 +
Name:
Student number:
QUIZ 3
1. True of False
(a) Suppose f : R22 R
a11
a21
f
a12
a22
= a11 a12 a21 + a22 ,
then f is a linear function R22 R.
ANS: True.
For any A, B R22 ,
f (A + B)
f
a11 + b11
a21 +
% Hw3_ex1
% Yuqi Wu
clear all
% part a
A = [6,3,1; 5,2,2; 4,1,3];
gA = 0.0;
for i = 1:size(A,1)
for j = 1:size(A,2)
gA = gA + A(i,j)*(1)^(i+j);
end
end
save A.dat A ascii
save gA.dat gA ascii
%
Homework 7  Due on March 14th, 2014 (due before 12:30
40 points)
The rst two exercises should be submitted online via Dropbox. Instructions of submission are on
the Catalyst webpage. For Exercise 1
Homework 6  Due on Friday Mar. 7th, 2014 (due before 12:30
40 points)
The rst two exercises should be submitted online via Dropbox. Instructions of submission are on
the Catalyst webpage. For Exerci
% Homework 2, exercise 1
%
% Learn how to use norm and dot
%
% Yuqi Wu
clear all
% create the vector x
x = [exp(2); 4+sqrt(2); pi; log(5); 3];
norm_X_1 = norm(x,1);
save Norm_X_1.dat norm_X_1 ascii
Homework 5  Due on Wednesday Feb. 26th, 2014 (due before
12:30 40 points)
The rst two exercises should be submitted online via Dropbox. Instructions of submission are on
the Catalyst webpage. For Exe
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AMATH 352

Final Exam
December 12th 2013
Name:
Signature:
Show all your work! I)etail
work! (losid book, no
your
notes. 110
o:alculator.
) I) points) True or false. iio flxplaliatiol
Homework 4  Due on Monday Feb. 10th, 2014 (due before
12:30 40 points)
The rst two exercises should be submitted online via Dropbox. Instructions of submission are on
the Catalyst webpage. For Exerci
Homework 3  Due on Monday Feb 3rd , 2014 (due before 12:30
40 points)
The rst two exercises should be submitted online via Dropbox. Instructions of submission are on
the Catalyst webpage. For Exerci
Homework 2  Due on Jan. 24th, 2014 (due before 12:30 40
points)
The rst two exercises should be submitted online via Dropbox. Instructions of submission are on
the Catalyst webpage. For Exercise 1 an
Homework 1  Due on Jan. 17th, 2015 (due before 12:30 40
points)
The rst two exercises should be submitted online via Dropbox. Instructions of submission are on
the Catalyst webpage. For Exercise 1 an