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MATH 2552M1-M4
NAME
Midterm 2
GT ID NUMBER
11/16/16 (Wed), 2:05-2:55
Circle Your Section Below
.
M1 TA: Tongzhou Chen
This exam consists of 5 problems.
Do not use any books and notes except one sheet
of note of letter size handwritten by yourself.
Turn

MATH 2552F&K
NAME
Midterm 1
GT ID NUMBER
10/5/16 (Wed)
Circle Your Section Below
.
This exam consists of 5 problems.
Do not use any books and notes except one sheet
of note of letter size handwritten by yourself.
Turn in this note sheet with your test.

MATH 2552F&G
NAME
Quiz 2
GT ID NUMBER
10/18/16
SECTION
This quiz consists of 3 problems.
Do not use any books and notes except one sheet of note of letter size (front & back)
handwritten by yourself. Turn in this note sheet with your test.
Do not use c

MATH 2552M&G
NAME
Quiz 1
GT ID NUMBER
9/13/16
SECTION
This quiz consists of 3 problems.
Do not use any books and notes except one sheet of note of letter size (front & back)
handwritten by yourself. Turn in this note sheet with your test.
Do not use ca

MATH 2552G&M
NAME
Quiz 3
GT ID NUMBER
11/08/16
SECTION
This quiz consists of 3 problems.
Do not use any books and notes except one sheet of note of letter size (front & back)
handwritten by yourself. Turn in this note sheet with your test.
Do not use c

POJECT CHOSEN
Chapter 3, Page 199, Project 1: Estimating Rate Constants for an Open Two-Compartment
Model
My group and I decided to work on Project 1, Chapter 3 of the textbook, as after a lot of
discussion we found that the project was fairly challenging

Second Order Homogeneous Linear ODEs
with Constant Coefficients
Xu-Yan Chen
Diff Eqs:
ay + by + cy = 0
(a 6= 0 and a, b, c are real constants)
Things to explore:
General solutions
Initial value problems
Graph solutions y vs t
Phase portraits in the (y, y

Second Order Nonhomogeneous Linear
Differential Equations with Constant
Coefficients:
the method of undetermined coefficients
Xu-Yan Chen
Second Order Nonhomogeneous Linear Differential
Equations with Constant Coefficients:
a2 y (t) + a1 y (t) + a0 y(t) =

2D Homogeneous Linear Systems with
Constant Coefficients
distinct nonzero real eigenvalues
Xu-Yan Chen
Systems of Diff Eqs:
where ~x(t) =
d~x
= A~x
dt
x1 (t)
, A is a 2 2 real constant matrix
x2 (t)
Things to explore:
I
General solutions
I
Initial value

Nonhomogeneous Linear Systems of
Differential Equations:
the method of variation of parameters
Xu-Yan Chen
Nonhomogeneous Linear Systems of Differential
Equations:
d~x
= A(t)~x + ~f (t)
()nh
dt
Nonhomogeneous Linear Systems of Differential
Equations:
d~x

MATH 2552G&M
Practice Problems for Midterm 1
Fall 2016
TIME: October 5 (Wednesday)
PLACE: Howey (Physics) L2
COVERAGE: Lectures & Recitations of 08/22-09/29
EXAM POLICY: Bring your Georgia Tech ID. No calculator. No books. No notes, except for
one for

MATH 2552, Diff Eqs, Xu-Yan Chen
Worksheet Solutions, 04/11
[1] Use the Laplace transform to solve y (t) + y(t) = f (t), y(0) = 1, y (0) = 2, where
20 cos(3t)
t < 23 ,
f (t) =
0
t 32 .
Solution:
Re-express f (t) to get ready for L:
f (t) = [1 u(t 23 )]20

Math 2552 Section F2
A note on Partial Fractions
50
.
(s+3)(s2)3
In this note, we complete the partial fraction decomposition of
B
C
50
A
D
+
+
=
+
.
3
2
(s + 3)(s 2)
s + 3 s 2 (s 2)
(s 2)3
using two methods. Both methods start in the same way:
To find ou

MATH 2552, Diff Eqs, Xu-Yan Chen
Worksheet Solutions, 03/07
[1] Solve y + 5y + 6y = 7e4t 6tet + sin(3t).
Solution:
The
general solutions of given nonhomog diff eq are given by y = yp + yc , where
yp is a particular solution of the nonhomog eq, and
the c

Math 2552 - EXAM 1
Name:
Section M
Signature:
I commit to uphold the ideals of honor and
integrity by refusing to betray the trust bestowed upon me as a member of the Georgia
Tech community.
You will have 50 minutes to complete this closed book,
no notes,

2D Homogeneous Linear Systems with
Constant Coefficients
perturbed systems
Xu-Yan Chen
Recall basics of ~x = A~x
Eigenvalues & (generalized) eigenvectors of A
solution formulas, dynamics, stability/instability,.
Recall basics of ~x = A~x
Eigenvalues & (

2D Homogeneous Linear Systems with
Constant Coefficients
repeated eigenvalues
Xu-Yan Chen
Systems of Diff Eqs:
where ~x(t) =
d~x
= A~x
dt
x1 (t)
, A is a 2 2 real constant matrix
x2 (t)
Things to explore:
I
General solutions
I
Initial value problems
I
Ge

2D Homogeneous Linear Systems with
Constant Coefficients:
a zero eigenvalue a line of equilibria
Xu-Yan Chen
Systems of Diff Eqs:
where ~x(t) =
d~x
= A~x
dt
x1 (t)
, A is a 2 2 real constant matrix
x2 (t)
Things to explore:
I
General solutions
I
Initial v

2D Homogeneous Linear Systems with
Constant Coefficients
complex eigenvalues
Xu-Yan Chen
Systems of Diff Eqs:
where ~x(t) =
d~x
= A~x
dt
x1 (t)
, A is a 2 2 real constant matrix
x2 (t)
Things to explore:
I
General solutions
I
Initial value problems
I
Geo

MATH 2551 QUIZ 5 - LECTURE G
TA:
YOUR FULL NAME:
(1) Find the equations of the tangent plane and the parametric equations of the normal
line at the point P0 (0, 1, 2) on the surface
cos(x) x2 y + exz + yz = 4.
You must simplify your equations for the nal

MATH 2551 QUIZ 4 - LECTURE G
TA:
YOUR FULL NAME:
(1) Show that the limit
x2 + y 2
xy
(x,y)(0,0)
lim
does not exist.
1
MATH 2551 QUIZ 4 - LECTURE G
(2) Find the value of the partial derivative
z
x
2
at the point (3, 1, 1), if the equation
xz + y ln z z + 4

MATH 2551 QUIZ 3 - LECTURE G
TA:
YOUR FULL NAME:
(1) A particle moves along a path with acceleration vector
a(t) = 4e2t + 6t2 3 sin 3t k, t > 0.
Assuming that the particle started with a velocity of 2 + k at the point (0, 1, 0),
nd the position vector o

MATH 2551 QUIZ 2 - LECTURE G
TA:
YOUR FULL NAME:
(1) Determine the parametric equations of the line segment between the points P (2, 3, 2)
and Q(0, 2, 1).
(2) Find the angle between the planes 5x + y z = 10 and x 2y + 3z = 1.
1
MATH 2551 QUIZ 2 - LECTURE

MATH 2551 QUIZ 1 - LECTURE G
TA:
YOUR FULL NAME:
(1) Consider the following triangle:
(a) Find the angle .
(b) Find the area of the triangle ABC.
1
MATH 2551 QUIZ 1 - LECTURE G
2
For each of the
(2) Consider the two vectors ~u = 2 + + k and ~v = 2 + 5
+

MATH 2552, Section F, Exam 1, September 26, 2016
You must SHOW all your work, unsupported answer will get zero points.
Each question must be solved within that paper (front and back).
You MUST write your section and name on ALL papers to be handed in.
Sec

MATH2552F1-F4
Practice Problems for Lectures of 3/15-4/26
Spring 2016
FINAL EXAM: May 3 (Tuesday) 2:50pm-5:40pm, Howey L1 (not your recitation room)
COVERAGE: The whole semester.
The following practice problems only cover lectures of 3/15-4/26, while th