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) = y
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MATH 441, HOMEWORK 2
DUE FRIDAY, JUNE 24 AT 6PM
PROFESSOR XU
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MATH 441, HOMEWORK 5
DUE FRIDAY, JULY 15 AT 6PM
PROFESSOR XU
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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
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
MATH 441, HOMEWORK 3
DUE FRIDAY, JULY 1 AT 6PM
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MATH 441, HOMEWORK 4
DUE FRIDAY, JULY 8 AT 6PM
PROFESSOR XU
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(4)
submit your homework, log in to the course Moodle and click "Submit Homework [number]".
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MATH 441, HOMEWORK 1
DUE FRIDAY, JUNE 17 AT 6PM
PROFESSOR XU
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(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 6
DUE FRIDAY, JULY 22 AT 6PM
PROFESSOR XU
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(1)
(2)
(3)
(4)
submit your homework, log in to the course Moodle and click "Submit Homework [number]".
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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
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
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
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 followi
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
MATH 441 Homework #6
due 03/17/2016 in class
1. Boyce and DiPrima, Section 3.2, #13, #14, #16.
2. Boyce and DiPrima, Section 3.2, #29, #36, #38.
3. Boyce and DiPrima, Section 3.4, #33, #34.
4. Boyce a
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 so
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 )