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 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
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
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
Math 309 Section F
Fall 2015
Midterm
October 27, 2015
Time Limit: 50 Minutes
Name (Print):
Student ID:
This exam contains 7 pages (including this cover page) and 6 problems. Check to see if any pages
are missing. Enter all requested information on the top
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
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
Math 309
Worksheet to Review Eigenstu
Winter 2016
1
Denitions. Suppose A is an n n matrix, x is nonzero vector, and is a scalar. If
A x = x,
(1)
we say is an eigenvalue of A and that x is an eigenvector of A (correpsonding to the
eigenvalue ). Finding eig
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
3
2
2
2
4
4
1 1 = 2 = 2.
A = 1
2 4 1
0
0
2
1 is an eigenvector of A,
Math 309 B&C Course Calendar
Note: This calendar is a rough guideline and Will change throughout the quarter.
Week
Jan.4-Jan.8
Jan.11-Jan.15
Jan.18-Jan.22
Jan.25-Jan.29
Feb.1-Feb.5
Feb.8-Feb.12
Feb.15-Feb.19
Feb.22-Feb.26
Monday
Intro/7.1
7.3
NO CLASS
7.7
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 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 20: August 8
Lecturer: Lucas Van Meter
20.1
The Laplace Equation
The last type of partial differential we equation we will study is called the Laplace equation (or potential
equation). In two dimensions it is
uxx +
Homework 5
Math 309
Summer 2016
Due August 5th
Name:
Solution: KEY: Do not distribute!
Directions:
This homework is due on August 5th in class. No late homework will be accepted.
Do all of the concept review problems. These problems are meant to give yo
309: Linear Analysis
Summer 2016
Lecture 19: August 5
Lecturer: Lucas Van Meter
19.1
Non-homogeneous Heat Equation
In this variation we suppose that the ends of the bar are held at a fixed temperatures T1 and T2 . The system
then becomes
ut = 2 uxx
u(0, t
Homework 1
Math 309
Summer 2016
Due June 1st
Name:
Solution: KEY: Do not distribute!
Directions:
This homework is due on June 8th in class. No late homework will be accepted.
Do all of the concept review problems. These problems are meant to give you pr
309: Linear Analysis
Summer 2016
Lecture 17: August 1
Lecturer: Lucas Van Meter
17.1
Sine and Cosine Series
Suppose we have a function defined on an interval 0, L then we can.
Consider the function
f (x) = 1 x
on the interval 0 x 1. Turning this into an e
Math 309 Section F
Fall 2015
Midterm
October 30, 2015
Time Limit: 50 Minutes
Name (Print):
Student ID:
This exam contains 7 pages (including this cover page) and 6 problems. Check to see if any pages
are missing. Enter all requested information on the top
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
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
Math 309 B&C
QUIZ 1
Winter 2016
1
Student ID Number:
Name:
t et
have an inverse?
t2 et
Calculate the determinant of P (t), we have
1. (a) When does the matrix P (t) =
detP (t) = (t t2 )et .
Its invertible if and only if the determinant is nonzero. So when
Math 309 G
Name:
QUIZ 1
Spring 2015
1
Student ID Number:
1. (a) Solve the given system of equations
x1 2x2 x3 = 2
2x1 + x2 + 3x3 = 1
x1 + 4x2 + 3x3 = 4
(b) Determine whether the following set of vectors are linearly independent or not. If
they are linearl
309: Linear Analysis
Summer 2016
Lecture 18: August 3
Lecturer: Lucas Van Meter
18.1
Warm up
On the interval 0 x 1 find a sine series for the functions f (x) = 1.
18.2
Summary of results so far
Last time we showed that the system
ut = 2 uxx
u(0, t) = 0, u
Math 309 Section F
Fall 2015
Midterm
October 30, 2015
Time Limit: 50 Minutes
Name (Print):
Student ID:
This exam contains 14 pages (including this cover page) and 6 problems. Check to see if any pages
are missing. Enter all requested information on the to
Homework 1
Math 309
Summer 2016
Due June 1st
Name:
Solution: KEY: Do not distribute!
Directions:
This homework is due on June 1st in class. No late homework will be accepted.
Do all of the concept review problems. These problems are meant to give you pr
309: Linear Analysis
Summer 2016
Lecture 21: August 10
Lecturer: Lucas Van Meter
21.1
A Dirichlet Problem on a circle
What if the boundary we consider is a circle? If we use coordinates r and this means our boundary
condition is
u(a, ) = f ().
Note that w
Math 309 Section F
Fall 2015
Midterm
October 27, 2015
Time Limit: 50 Minutes
Name (Print):
Student ID:
This exam contains 13 pages (including this cover page) and 6 problems. Check to see if any pages
are missing. Enter all requested information on the to