AMath 350
Assignment #8
Fall 2013
Solutions
1. Following the hint, we have
Z1
Z
(x x2 ) dx =
e
0
1
0
=e
Now, letting u = x
1
2
2
e (x x) dx =
1
4
Z
1
e (x
Z
1
0
h
x
e(
12
2
)
1
4
i
dx
12
2
) dx.
0
, this becomes
e
1
4
Z
1
2
e
u2
du
e
u2
du.
1
2
and since
AMath 350
Assignment #2
Fall 2013
SOLUTIONS
1. (Are the given equations separable, linear, neither, or both?)
a) Not separable, but linear.
b) Separable, but not linear.
c) Both.
d) Neither.
e) Both.
f) Separable, but not linear.
2.
a) Find the solution t
AMath 350
Assignment #2
Winter 2014
SOLUTIONS
1. (Are the given equations separable, linear, neither, or both?)
a) Not separable, but linear.
b) Separable, but not linear.
c) Both.
d) Neither.
e) Both.
f) Separable, but not linear.
2.
a) Find the solution
AMath 350
Assignment #2
Winter 2015
SOLUTIONS
1. (Are the given equations separable, linear, neither, or both?)
a) Not separable, but linear.
b) Separable, but not linear.
c) Both.
d) Neither.
e) Both.
f) Separable, but not linear.
2.
a) Find the solution
Rewrite the DE IN INCREMENTAL form
To keep
In the game, need to get 2nd degree, Taylor polynormial for
Eleiminate stochetic term in *'
As a writer make portfolio , with value
Theory of Linear Systems of ODEs (n  dimensions)
The E/U ( existence and uniqueness) theorem
If A(x) and F(x) arecontinuous on I, then there exists unique solution of the IVP
Ch5 partial dierential equations (PDE)
Method of "partial integration"
Recall from last lecture
The number of BCs depends on the order of the PDE
EX. wave equation vibrating string
Assgn 5 due on MONDAY 22 feb
Midterm
Tue feb 28
6:308:00
Mc 4041 4042 4059
Topics for midterm chapters 13 inclusive
Assgn 15 inclusive
Include exceptional cases
Finance application
Existence and uniqueness
First order,
General
Homogenous
Susbtitut
Final Exam on
Web, april 12, 911:30 PAC
midterm test
Tue Feb 28,
6:30  8:00 PM
Mc4041, 4042, 4059
TA's OH tomorrow moved to 2 4 pm in MC 6342
Assignment 4 due monday

Topics for midterm
Chapters 1  3 inclusive
Assgn 2  5

Last time: cases 3 for
Method of undetermined coecient for non homogeneous DEs
With const coecient and special F(x),
Method fails if F(x) is contained in yh(x), general silution of associated homogeneous DE,
Oce hours:
TA: Thurs 1:00  3:00 PM, MC 6496
Zoran: Mon 4 PM  5 PM, MC 6128
Classification of DEs
1. # of variables
A. One dependent, one independent variables
2.
B. One dependent, two or more independent variables (PARTIAL DE (PDE)
C. TWO OR MORE UNKN
Recall Example: continuously compounded Interest
Value of investment: V(t), given in units:
(Square bracket denotes unit => [V] = dollars, [t] = year,
R = annual interest rate, usually in units of %/year
[r] = 1/year (8%/year) > 0.08 / year
Dierenical
Solution of a ODE
Ex. Verify that indicated function is solution of given ODE
DEF : Finding a solution of a DE subject to a set of Initial conditions at one point x = x0,
constitutes Initial Value problem (IVP)
DEF: Finding ga solution of a DE subject ot
Last time:
General SOlution at nth order ODE
Contains n arbitrary constants, C1, c2, . Cn
a particular soln, we need n initial conditions IG at some x = x0; y(x0) = y1 ,.
THM: Existence & Uniqueness
At solution for a 1st  order I.V.P
If f(x,y)
Se