M427K Handout: Separable and Exact Equations
Salman Butt
January 267 2006
This handout describes the procedure used to solve two specic types of rst order differential
equations: separable and exact equations
SEPARABLE EQUATIONS
Observe that we can writ
Macroeconomics
Homework #2
Due Monday, September 19th
Please write your answers on the answer sheet given.
For questions (1) through (6), chose one of the graphs below.
A
B
C
D
1)
Consider the market for handmade acoustic guitars sold in the U.S. These gu
Blue Letter Bible
Daily Bible Reading Program
Chronological Plan
1-Year Plan. These readings are
compiled according to recent
historical research, taking into
account the order in which the
recorded events actually
occurred. This is a fantastic plan
to fo
Macroeconomics
Homework #1
Due Monday, September 12th
Please write your answers on the answer sheet at the end and hand in only this sheet.
You may hand in this assignment together, working in groups no larger than two.
1) The firm for which you work pays
1 Denitions
The positive integers are 1, 2, 3, 4, 5, 6, . . .
The nonnegative integers are 0, 1, 2, 4, 5, 6, . . .
The rational numbers are
E , a an integer, b an integer, b 75 0.
The real numbers are all possible decimal expansions.
The complex numbers a
1. Define the following:
The span of a set of vectors
The span of a set S of vectors is the collection of all possible (finite) linear combinations of
vectors in S, i.e. all vectors of the form 1'2 = 01171 +.+C;c17k where 17wa are in S
The null space of a
1 4
1. (12 pts) For the system Ic = |: 2 3 :|Jc
a) Find the general solution as a combination of real-valued solutions.
1;l 4 2 _
det =1222+5=(l1)+22=0,}i=1i21
2 32.
£=1+2i:
2 2' 4 2
A it] = I , 17 = (from first row)
2 2 21' 1 +1'
. 2 2
3c = away = e(cos
on the interval from [1.2]. (This is Problem 9 on page 393 of the book.)
Answer:
The formula for the arc length of a graph is
b
L=f x/1+[f(x)]2d$.
In our case we have
This gives us
83:4 + 16$8 + l
i 16594
i (49:4 + 1)2
_ 163:4
Thus, we get
4$4+
Name:
Pledge:
CRN:
Instructions: Please enter your NAME, ID NUMBER, FORM DESIGNATION, and, your CRN
on the op-scan sheet. The CRN should be written in the box labeled COURSE. Darken the
appropriate circles below your ID number and below the Form des
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