Notes from Trigonometry
Steven Butler
Brigham Young
University
Fall 2002
Contents
Preface
1 The
1.1
1.2
1.3
1.4
1.5
vii
usefulness of mathematics
What can I learn from math? .
Problem solving techniques . . .
The ultimate in problem solving
Take a break .
COST CONCEPTS RELEVANT TO
DECISION MAKING
General Cost Terms
Classifying Costs for Financial Statements
Volume Index and Cost Behaviors
General Cost Terms
Manufacturing Costs
Direct Row Materials: These are any materials that are
used in the final pro
Engineering Economics
Introduction
Types of Business Organization
Propriatorship: Owned by ONE individual
No Legal and Organizational cost
Earning is taxed at the owners personal tax, (low)
Disadvantage: Difficult to raise fund. Can not
issue stocks a
Econ280
Lecturer: Prof. Dr. aziye Gazioglu
Time 11.40-12.30 Monday
Presentation %10
Written Work %25
Week5
Oct13-17
Interest Rates and Economic Equivalance
Erdem Korkmaz
A Emre Koska
Sinan Yldrm
Week6
Oct20-24
Annual Equivalant-worth Analysis
Yasin zal
Bu
2 Financial Statements
2 Financial Statements
Assets
Liabilities & Stockholders equities
Liabilities: the money the campany owes
Stock holders equities: the portion of the
assets of the campany provided by investors
Econ280, Prof Dr, Saziye Gazioglu,
3 Time Value of Money and
interest
Interest Rate and Economic
Equivalance
Time Value of Money and interest
Simple Interest:
The interest is only applied to the principle
amount
F=P+I=P(1+iN)
Compound Interest: Interest earning
generates its earning
F=
Second Order Dierential Equations
First Order Dierential Equations
Separable:
Solution:
Linear:
M (x) dx =
N (y ) dy
Characteristic Eqn: a r2 + b r + c = 0
Solution depends on the type of roots:
r = r1 , r2
(real, not repeated)
y = c1 e r 1 x + c2 e r 2
Common Derivatives and Integrals
Common Derivatives and Integrals
Derivatives
Basic Properties/Formulas/Rules d ( cf ( x ) ) = cf ( x ) , c is any constant. ( f ( x ) g ( x ) ) = f ( x ) g ( x ) dx d n d ( c ) = 0 , c is any constant. ( x ) = nxn-1 , n is
METU
Northern Cyprus Campus
Math 219
Dierential Equations
Last Name :
:
Name
Student No:
Dept./Sec. :
: 17 : 40
Time
Duration : 100 minutes
5 QUESTIONS ON 4 PAGES
1
2
3
II. Exam
4
17.04.2009
Signature
TOTAL 100 POINTS
5
EACH PROBLEM - 20 POINTS.
Question
Math 219
Dierential Equations
Last Name :
:
Name
Student No:
II. Exam
Dept./Sec. :
: 17 : 40
Time
Duration : 120 minutes
6 QUESTIONS ON 5 PAGES
1
2
3
4
Question 1 (20 pts.)
5
02.12.2008
Signature
TOTAL 100 POINTS
6
Consider the dierential equation
y (4) y
Contents
xix
xxi
Preface to the second edition
Preface to the rst edition
1
1.1
Preliminary algebra
Simple functions and equations
1
1
Polynomial equations; factorisation; properties of roots
1.2
Trigonometric identities
10
Single angle; compound-angles;
Estimating Profit from
Production
ECO 280 Presentation
Orhan Ata BAYMAN
1544535 MECH
Calculation of Operating Income
Project Revenue: Income earned by a
business as a result of providing products or
services to customers. Revenue comes from
sales of merc