CHAPTER 5 EXERCISES
1. Reconsider problem 4 of chapter four.
(a) Sketch the vector eld for this model. Determine the location of each
equilibrium in the state space. Can you tell from the vector eld w
U. Washington
AMATH 352 - Winter 2010
Homework 2 - Due on 01/22/10
The rst exercise should be submitted via Scorelator (4 attempts are available). Remember to use the command save with the ag -ascii t
CHAPTER 3 EXERCISES
1. (a) The following graph shows price (p) as a function of time (t). Over the first 5 days
price is nearly a linear function of time and falls about one cent per day. As time goes
Summary of some useful formulas
Taylor polynomial of degree k (Note typo in (7.7), (7.8) - sums start at j = 0): Pk (x) = 1 (j) f (x0 )(x - x0 ). j! j=0
k
Error in Taylor polynomial Pk (x): If f C
CHAPTER 4 EXERCISES
1. (a) The dynamical system equation is x' = F(x) where x = (x1, x2) and F = (f1, f2) with
f1(x1, x2) = r1*x1 - a1*x1^2 - b1*x1*x2
f2(x1, x2) = r2*x2 - a2*x2^2 - b2*x1*x2
and the s
AMATH 352 HW1
1. a) b) f = @(x) x .* cos(x) f= @(x) x .* cos(x) quad(f, 0, 1) ans = 3.817732902243389e-001 2. From script prob2.m :
true = .381773291; f = @(x) x .* cos(x); sprintf('%-10s %-23s %-15s
1. An automobile manufacturer makes a profit of $1,500 on the sale of a certain model.
It is estimated that for every $100 of rebate, sales increase by 15%.
(a) What amount of rebate will maximize pro
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
April 4th 2014
Homework 1
Homework 1 has been posted on the course webpage.
Written pa
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Feb. 10th 2014
Midterm Exam
Friday Feb. 14th in class
No notes, no calculator, no phon
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Feb. 7th 2014
Midterm Exam
Friday Feb. 14th in class
No notes, no calculator, no phone
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Feb 5th 2013
Range of a Matrix
Consider a matrix A Rmn
Denition
The range is the subspac
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Feb. 3rd 2014
Homework 4
Homework 4 will be posted later today, due Monday Feb. 10th.
R
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Feb. 19th 2014
Homework 5
Homework 5 will be posted this afternoon.
Due next Wednesday
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Feb 24th 2014
Homework 5
The due date of homework 5 is extended to Friday Feb. 28th
Ort
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Feb. 26th 2014
Gram-Schmidt process
Consider the basis vectors a1 , a2 , a3 . We want to
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Mar. 7th 2014
Homework 7
Homework 7 will be posted this afternoon
Due Friday March 14t
CHAPTER 2 EXERCISES
1. (a) Step 1: Ask the question.
Variables:
x = Blue whale population (whales)
y = Fin whale population (whales)
B = Blue whale population growth rate (whales / year)
F = Fin whale
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Feb. 28th 2014
Homework 6
Homework 6 will be posted later this afternoon
Due Friday Ma
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
March 31st 2014
Instructor
Dr. Yuqi Wu
Email: [email protected]
Oce: Lewis 116
Assistants
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Jan. 31st 2014
Review: Matrix-Matrix Multiplication
A Rmr and B Rr n , then we can dene
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Jan. 29th 2014
Review: Linear Functions
Denition
Consider U and V two real linear spaces
Applied linear algebra and numerical analysis
AMATH 352 - Winter 2014
Yuqi Wu
Department of Applied Mathematics
Jan. 27th 2014
Linear Functions
Recall what we mean by the notation
f : U V.
(1)
The fu
Name: SOLUTIONS
AMATH 352
Homework Set 7
Due: Monday, May 22nd, in class.
(1) In this problem, well think about systems that are given to us in factored form.
Let A Rmn , and suppose that we are given
Name: SOLUTIONS
AMATH 352
Homework Set 6
Due: Monday, May 15th, on canvas (by class time).
(1) In this exercise, fill in the gaps to our logistic regression derivation
(guided practice). We are given
Name: Solution Set
AMATH 352
Homework Set 2
Due: Monday, April 10th, online.
(1) There are two important methods we can use to find the root of f (x) = 0. The
first is called Newtons method. We take a
Name: Solutions
AMATH 352
Homework Set 5
Due: Monday, May 8th, on canvas (by class time).
(1) Compute the QR decomposition of the following matrix. You can either do it by
hand, showing the steps, or
Name: SOLUTIONS
AMATH 352
Homework Set 8
Due: Monday May 30th by 12:30pm on Canvas.
(1) Symmetric positive definite and positive semidefinite matrices.
(a) Let A Rm,n be any matrix. Show that AT A and
Name: Solution Set
AMATH 352
Homework Set 1
Due: Monday, January 11th, in class.
Matlab code can easily be pasted in a verbatim environment. Below, I paste the code to
compute the 150th term in a Fibo
Name:
AMATH 352
Homework Set 3
Due: Monday, April 24, in class.
(1) Compute the inverse to the following
1
A = 0
1
matrix (show your work):
0 1
0 1
1 0
(2) Matrix inversion.
(a) Show that a square mat
For Hw5, #5b, you solved the problem:
1
min kw vk2 + kvk1
v 2
where you were given w and and you found the vector v (I have changed the names of the
variables to better adapt to the variables that you
Name: Solutions
AMATH 352
Homework Set 4
Due: Monday, April 24th, online.
(1) Compute the inverse to the following
1
A = 0
1
matrix (show your work):
0 1
0 1
1 0
Start with matrix A and append the ide
Name: Solutions
AMATH 352
Homework Set 3
Due: Online, by class time, Monday April 17.
(1) On the first day in class, we saw that if you are interested in approximately solving
Ax = b,
it makes sense t