MATH 441
SECTION G13
Practice Problems for Midterm I
Coverage: Sections 1.11.3, 2.12.6.
Problem 1. Find the value of y0 for which the solution of the initial value problem
y y = 1 + 3 sin(t), y(0) = y0
remains nite as t .
Ans: y0 = 5/2.
Problem 2. (a) Sol
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MATH 441, HOMEWORK 2
DUE FRIDAY, JUNE 24 AT 6PM
PROFESSOR XU
To
(1)
(2)
(3)
(4)
submit your homework, log in to the course Moodle and click "Submit Homework [number]".
Click "Add submission".
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MATH 441, HOMEWORK 5
DUE FRIDAY, JULY 15 AT 6PM
PROFESSOR XU
To
(1)
(2)
(3)
(4)
submit your homework, log in to the course Moodle and click "Submit Homework [number]".
Click "Add submission".
Drag and drop your PDF file(s) to the area inside the dotted li
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Zongyuan Wang
MATH 441 F/G SP15: Differential Equations (Xu, S)
Dashboard College of Liberal Arts and Sciences MATH (Mathematics) Spring 2015
MATH 441 F/G SP15 General Un-confuse your minds Midterm 2 solutions, the easy way
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IMPORTANT FACTS ABOUT THE
FUNDAMENTAL MATRIX
Since a solution matrix X(t) is a fundamental matrix for the linear homogeneous
system x = A(t)x provided det X(t) 6= 0, it is easy to see that if C is any n n
non-singular matrix then X(t) C is also a fundamen
MATH 441, HOMEWORK 3
DUE FRIDAY, JULY 1 AT 6PM
PROFESSOR XU
To
(1)
(2)
(3)
(4)
submit your homework, log in to the course Moodle and click "Submit Homework [number]".
Click "Add submission".
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MATH 441, HOMEWORK 4
DUE FRIDAY, JULY 8 AT 6PM
PROFESSOR XU
To
(1)
(2)
(3)
(4)
submit your homework, log in to the course Moodle and click "Submit Homework [number]".
Click "Add submission".
Drag and drop your PDF file(s) to the area inside the dotted lin
MATH 441, HOMEWORK 1
DUE FRIDAY, JUNE 17 AT 6PM
PROFESSOR XU
To
(1)
(2)
(3)
(4)
submit your homework, log in to the course Moodle and click "Submit Homework [number]".
Click "Add submission".
Drag and drop your PDF file(s) to the area inside the dotted li
MATH 441, HOMEWORK 6
DUE FRIDAY, JULY 22 AT 6PM
PROFESSOR XU
To
(1)
(2)
(3)
(4)
submit your homework, log in to the course Moodle and click "Submit Homework [number]".
Click "Add submission".
Drag and drop your PDF file(s) to the area inside the dotted li
MATH441 Guide and Practice Exam I
Study guide
1. Direction fields. (This part is not in the textbook.) Sketch the direction field of the DE
y 0 = f (x, y) using the isocline method and sketch integral curves. Use properties of integral curves
to obtain qu
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MATH 441 Homework #2
due 02/04/2016 in class
1. (a) Use the Euler method and the step size h = .1 on the IVP y 0 = t y, y(0) = 1, to calculate
an approximate value of y(t) for t = .1, .2, .3. (Make a table as in the class). Is your answer for
y(.3) too hi
MATH 441 Homework #1 (modified 01/25/2016)
due 01/28/2016 in class
1. (a) Verify that y = xa solves the differential equation x2 y 00 = 2y if the constant a satisfies the
equation a2 a 2 = 0. Thus get the two solutions x2 and x1 . Note that the first is v
MATH 441 Homework #4
due 02/18/2016 in class
1. At that points of the (t, y) plane does the hypothesis of the existence and uniqueness theorem
(stated formally in the class notes) fail for the following equations?
(a) y 0 = sin(ty)
(b) y 0 = t1/3 y 3
(c)
MATH 441 Homework #9
due 04/28/2016 in class
1 0
1. Let A
. Calculate eAt three ways:
2 1
(a) directly, from its definition as an infinite series;
(b) by expressing A as a sum of simpler matrices, as in Notes;
(c) by solving the system by elimination so
MATH 441 Homework #7
due 04/14/2016 in class
1
1
1. Solve the system x1
x in two ways:
0 1
(a) Solve the second equation, substitute for y into the first equation, and solve it.
(b) Eliminate y by solving the first equation for y, then substitute into th
Fundamental Matrices, Matrix Exp &
Repeated Eigenvalues Sections 7.7 & 7.8
Given fundamental solutions
G
dx
G
G
G
x1 ,., xn of the ODE
= Ax
dt
we put them in an nxn matrix
,
G
G
(t ) = ( x1 ,., xn )
with each of the solution vectors being a column.
We ca