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 profit? Use the five-step method, and model as
a one-varia
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 k+1 (Int[x0 , x]), then |f (x) - Pk (x)| = |f (k+
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 %-8s', 'tol', 'integral', 'error', 'f evals') for
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. The function f : U V
is a linear function if both of
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 state space is the set of all x satisfying x1 >= 0 and x
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 which of the
equilibria are stable?
The dynamical system
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
March 31st 2014
Instructor
Dr. Yuqi Wu
Email: yuqiwu@uw.edu
Oce: Lewis 116
Assistants
Teaching Assistant: Peng Zheng
Email: zhengp@uw.edu
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 part is due on Friday Apr. 11th in class.
Programming pa
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
Apr. 9th 2014
Review of Linear Space
A real linear space consists of a set of objects V along with two
operations + (addition) and (scalar mult
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
Apr. 11th 2014
Homework 2
Homework 2 will be posted on the course webpage this
afternoon
Due date: Friday Apr. 18th in class.
Review
real li
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
Apr. 7th 2014
Questions about Hw 1
Submit computing homework via Dropbx
Vector Norm
To measure the magnitude or the length of a vector, we use
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
April 14th 2014
Quiz 1
solution of Quiz 1 has been posted on the webpage, under
homework tab
Some common issues
Denitions
Review
Denition
Le
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
Apr. 18th 2014
Hoemwork 3
Homework 3 will be posted this afternoon
Due on Friday Apr. 25th.
Review Linear Functions
Denition
Consider U and V
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 by
the price curve flattens so that the rate of declin
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 population growth rate (whales / year)
T = Total popul
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 the product
C = AB, which will be a matrix in Rmn . An
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.
Range of a Matrix
Consider a matrix A Rmn
Denition
The r
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 subspace of all vectors produced by the matrix A
R(A) = cfw_Ax
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, scratchd paper will be
provided
Review all lecture s
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 phone, scratchd paper will be
provided
Review all lecture
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 in class.
Midterm
If you have questions about your mi
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
Orthogonal bases
Let V be a real linear space with an inn
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 Mar. 7th in class
Floating point arithmetic
Fact
Almost a
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 build the
sequence of orthonormal vectors q1 , q2 , q3
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 14th in class
GradeBook
Please double check your homework
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
Apr. 16th 2014
Gradebook
All the homework and quiz grade will be posted on the online
Gradebook
Please contact me if you nd an error
Review
D
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
Apr. 21st 2014
Homework 3
Few typos on Homework 3
Please download the updated version on course webpage
Review: Linear Functions
Denition
Con
Applied linear algebra and numerical analysis
AMATH 352 - Spring 2014
Yuqi Wu
Department of Applied Mathematics
May 30th 2014
Review: Counting the solutions
Consider a matrix A Rmn and a linear system Ax = b.
If b R(A), then the system has no solution.
/
AMath 352
Homework #2
Partial solutions
#1. (a) The absolute error is about 9 106 and the relative error about 5 102 , so wed
say theres 1 or 2 correct digits.
(b) The integral is nearly zero since the positive and negative parts of the sine function
near
AMath 352
Homework #1
Partial solutions
Please omplete the student survey available from the hw1 webpage (from the 352 webpage) if
you haven't done so already.
#2. Here's an m-le, whih is also at hw1/hw1prob2.m:
f = (x) x.*os(x);
true = sin(1) + os(1) - 1
10/10/2016 Lecture 6 Announcements:
Problem Set 1 Due Wednesday 10/12.
Quiz 1 Due Thursday 10/13.
Discussion board participation due Friday 10/14.
Last Time:
Machine numbers (clarification)
Direct methods for solving linear equations
Gaussian Eliminati
10/5/2016 Lecture 4 Announcements:
Problem Set 1 Due Wednesday 10/12. (updated some typos this morning)
Quiz 1 Due Thursday 10/13. (updated Q6 this morning)
Make sure email is working!
Last Time:
Things blowing up.
Numerical Error
Machine numbers
To