Homework 1
Math 309
Spring 2016
Due April 6th
Name:
Directions:
This homework is due on April 6th at 2:30 pm. No late homework will be accepted.
The homework can be turned in during class or in the math lounge in Pedelford C-wing.
The math lounge is at
Homework 6
Math 309
Spring 2016
Due May 18th
Name:
Directions:
No late homework will be accepted.
The homework can be turned in during class or in the math lounge in Pedelford C-wing.
The math lounge is at the end of the hallway on the left. There are m
Homework 3
Math 309
Spring 2016
Due April 20th
Name:
Directions:
No late homework will be accepted.
The homework can be turned in during class or in the math lounge in Pedelford C-wing.
The math lounge is at the end of the hallway on the left. There are
Math 309
1
Review sheet for Chapter 10
Section 10.1: Know how to solve a two-point boundary-value problem:
Solve the characteristic equation.
If the roots r1 , r2 are real, write a solution under the form X (x) = c1 er1 x + c2 er2 x and
determine the co
344
PROBLEMS
Chapter 7. Systems of First Order Linear Equations
In each of Problems 1 through 4 transform the given equation into a system of rst order
equations.
2. u + 0.5u + 2u = 3 sin t
1. u + 0.5u + 2u = 0
3. t 2 u + tu + (t 2 0.25)u = 0
4. u u = 0
5
Homework 4
Math 309
Summer 2016
Due July 29th
Name:
Solution: KEY: Do not distribute!
Directions:
This homework is due on July 29th in class. No late homework will be accepted.
Do all of the concept review problems. These problems are meant to give you
Differential equations
Math 307, Autumn 2016
University of Washington
c
2016,
Dr. F. Dos Reis
Review for the Final Exam
Exercise 1. Find the general solution of the given differential equation or initial value problem
1. (1p183) y 00 2y 0 3y = 3 e3t
2. (2
Differential equations
Math 307, Autumn 2016
University of Washington
c
2016,
Dr. F. Dos Reis
Review for Exam 1, Sections 2.1, 2.2, 2.3, 2.4, 2.5, 2.7,
3.1, 3.2, 3.3, 3.4, 3.5
Exercise 1. (close to 21p8) A pond initially contains 1,000,000 gal of water an
Math 309 G
QUIZ 1
Spring 2015
1
Student ID Number:
Name:
1. (a) Solve the given system of equations
x1 2x2 x3 = 2
2x1 + x2 + 3x3 = 1
x1 + 4x2 + 3x3 = 4
Start with the augmented matrix
1 2 1 2
2
1
3 1 ,
1 4
3 4
Subtracting 2 times the rst row from the seco
Math 309 D
Name:
QUIZ 1
Summer 2015
1
Student ID Number:
2
1. (a) Recall we say is an eigenvector of A if A = . Verify = 1 is an
0
3
2
2
1
4
1 .
eigenvector of the matrix A =
2 4 1
(b) Use (a), construct a solution to the system x = Ax.
Math 309 D
QUIZ 1
Dierential equations
Math 307, Autumn 2016
University of Washington
c
!2016,
Dr. F. Dos Reis
Homework 1
Last name:
First name:
Due at the beginning of the class on Wednesday October 5th, 2013.
1. For (a) and (b), determine whether the given function is a
Differential equations
Math 307, Autumn 2016
University of Washington
c
2016,
Dr. F. Dos Reis
Sections 3.5 Method of undetermined coefficients
1
Particular solutions
Exercise 1. Find the solutions to the differential equation
y 00 5y 0 + 6y = 1
Theorem 3.
Math 309 A
MIDTERM EXAM ANSWERS
Summer 2010
1 (6 points) What can you say about the eigenvalues of a 2 2 matrix A if the phase portrait of
x0 = Ax is a center? Sketch (any) phase portrait which is a center. Give an example of such
a matrix A.
Answers: The
Math 309A Midterm 1 (Winter 2011)
NAME _
Instructions: Show your work. You can leave radicals and fractions as they are
without converting to decimals. Note that some information is given so that you do
not ha
Math 309
Midterm 1
Instructions Write you name clearly at the top of the exam. Answer each
question below, showing you work. Please be as neat and organized as possible.
Problem 1. Consider the following order 3 differential equation:
y'" - 3y" + Ity' + y
309: Linear Analysis
Summer 2016
Lecture 3: June 24
Lecturer: Lucas Van Meter
3.1
Warm-up
Let V be a two dimension vectors space and choose a basis B1 = cfw_v1 , v2 . Let T : V V be a linear
transformation. Suppose that
a) Suppose that T (v1 ) = v1 + 2v2
309: Linear Analysis
Summer 2016
Lecture 1: June 20
Lecturer: Lucas Van Meter
1.1
Introductions
Things to do:
1. Cards with info;
2. Introduce myself;
3. Do name game;
4. Talk about the course;
5. Goals for quarter.
1.2
Linear Algebra Review
Question: If
309: Linear Analysis
Summer 2016
Lecture 2: June 22
Lecturer: Lucas Van Meter
2.1
Bases
Now that we have briefly recalled what a vector space and a linear transformation we can discuss one of
our main tools: bases (the plural of basis). So far what I want
309: Linear Analysis
Summer 2016
Lecture 7: July 6
Lecturer: Lucas Van Meter
7.1
Non-homogeneous equations
Solving non-homogeneous systems will be very similar to what we did in 307 to solve non-homogeneous
differential equations. The main idea is that th
ECON-201 A INTRODUCTORY MACROECONOMICS
PROBLEM SET-1
(Due to to submitted by the end of class on January 28th, Wednesday)
QUESTION-1: (2.5 pts each for a total of 10 pts)
a) What are the assumptions that are made in the circular flow diagram model?
b) Whi
Differential equations
Math 307, Autumn 2016
University of Washington
c
2016,
Dr. F. Dos Reis
Homework 6
Last name:
First name:
Due at the beginning of the class on Monday November 21st 2016.
1. Use the definition of the Laplace transform to find the Lapl
Differential equations
Math 307, Autumn 2016
University of Washington
c
2016,
Dr. F. Dos Reis
Homework #3 - Sections 2.4-2.7
Last name:
First name:
Section:
Due at the beginning of the class on Monday July 18th, 2015.
Exercise 1.
1. Find the general solut
Differential equations
Math 307, Autumn 2016
University of Washington
c
2016,
Dr. F. Dos Reis
Homework 2 - Sections 2.3
Last name:
First name:
Due at the beginning of the class on Wednesday October 12th, 2016.
You may use a calculator or a computer to sol