Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Section 10.1: Solutions of Dierential Equations
An (ordinary) dierential equation is an equation involving a function and its derivatives. That is, for functions P (x0 , x1 , . . . , xn ) and Q(x0 , . . . , xn ) of n + 1 variables, we say that the functio
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Taylor Polynomials and Series
Probability
Term
random variable
expected value
(or mean)
standard
deviation
Definition
Application
continuous:
=E ( X )= X F PDF ( X) dX
( X ) = V ( X )
1
CRV = (a+ b)
2
1
( X CRV )=
(ba)
12
V ( X )= ( X )2 F PDF ( X ) dX
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Math 126 Lecture Notes
Steven D. Hoehner
sdh60@case.edu
November 14, 2013
These notes come primarily from the texts College Mathematics and Additional Calculus Topics, 12th edition, by Barnett, Ziegler, and Byleen. Occasionally I will provide additional m
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Seminole State Homepage


Calculus I
Calculus II
Calculus Homepage
ExamplesApplication Problems
Example 15: Exponential Population Growth Example
Exponential Population Growth
The population of a country is growing at a rate that
is proportional to the
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Math 126
TakeHome Exam 3
Due July 14, 2014
Answer the questions in the spaces provided on the question sheets. If you
run out of room for an answer, continue on the back of the page. You may
use your books or course notes, as well as calculators. All oth
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
NEWTONS LAW OF COOLING OR HEATING
Let
T = temperature of an object,
M = temperature of its surroundings, and
t = time.
If the rate of change of the temperature T of the object is directly proportional to the
difference in temperature between the object an
Math and Calculus Applications for Life, Managerial, and Social Sci II
MATH 126

Summer 2014
Solutions to Exercises on Newtons Law of Cooling
S. F. Ellermeyer
1. A thermometer is taken from a room that is 20 C to the outdoors where
the temperature is 5 C. After one minute, the thermometer reads 12 C.
Use Newtons Law of Cooling to answer the follo