GREENBERG
VECTOR GEOMETRY
UNIT
COMPLEX NUMBERS
INTRO: is Unit is about complex numbers. Unlike real numbers, which ll a one-dimensional line (in
fact, we frequently say the real number line), the complex numbers ll an entire plane, the so-called complex p
1
Cash = $24,000 18,000 3,000 + 64,000 (46,100 500 2,400) = 23,800
Upon graduation from high school, William Nitter accepted a job as a plumbers assistant for a
large local plumbing company. After three years of hard work, William received a plumbing
lice
Accounting: A system for gathering data about an entitys economic activity, processing and
organizing that data to produce useful information about the entity, and communicating that
information to people who want to use it to make decisions
Entity: A eco
Confirming Pages
Investing and Financing Decisions
and the Accounting System
S
teve Ells is a classically trained chef who is often called one of the most innovative men
in the world of food. He is the founder, chairman of the board, and co-chief executiv
Unit 1
Psychology: The scientific study of behavior and mental processes
Origins
- Early philosophy 400 BC - Socrates/Plato/Aristotle mind, memory, self, mind/body
- Philosophers continue interest 1500s-1700s Descartes/Mill/Locke associationism
- Early me
Chapter 1 Key Terms
Integrity: The appropriateness of a corporations behaviour and its adherence to moral
guidelines acceptable to society such as honesty, fairness, and justice
Ethics of business: the rules, standards, codes, or principles that provide g
Chapter 1
Definition of Economics
-All economic questions arise because we want more than we can get
-Our inability to satisfy all our wants is called scarcity
-Because we face scarcity, we must make choices
-The choices we make depend on the incentives w
Lab Questions
P1-3:
a) A person considering making a donation to a charity: To understand how much money is
effectively and efficiently used in the charity
b) Members of a community group concerned about pollution by a local factory: find new
ways to redu
GREENBERG
VECTOR GEOMETRY
UNIT
COMPONENTS OF ACCELERATION AND CURVATURE
INTRO: In this Unit we will continue our study of the trajectory-aligned coordinate system T , N , B, in
particular how it may be used to decompose acceleration along a trajectory int
GREENBERG
VECTOR GEOMETRY
UNIT
LINES AND PLANES
INTRO: is Unit is about lines and planes: their equations, how they are determined by points and
vectors, and some additional facts about them. In the discussions of this Unit, x , y and z will be variables,
GREENBERG
VECTOR GEOMETRY
UNIT
VELOCITY, ACCELERATION AND PROJECTILES
INTRO: In this Unit we will study velocity and acceleration along trajectories, and, in particular, projectile problems.
. Vector Functions
In Units and we studied trajectories given by
GREENBERG
VECTOR GEOMETRY
UNIT
VARIABLE ACCELERATION, ARC LENGTH AND TANGENT VECTOR
INTRO: In this Unit we will introduce three di erent kinds of problems. First we will discuss variable
acceleration problems, which arise in problems with time-dependent f
GREENBERG
VECTOR GEOMETRY
UNIT
CROSS PRODUCT IN R
INTRO: In this Unit we will introduce the cross product along with a number of applications, and we
will compare the dot product and the cross product.
. Determinants
For those students who have never deal
GREENBERG
VECTOR GEOMETRY
UNIT
VECTOR SPACES
INTRO: is Unit is on vector spaces and on the dot product of a pair of vectors in the vector spaces R
and R . First, though, some preliminary remarks.
. Abstract Vector Spaces
Nearly all students will have alre
GREENBERG
VECTOR GEOMETRY
UNIT
ALGEBRA, TRIGONOMETRY PRELIMINARIES
INTRO:
etry.
is Unit will brie y touch on a smorgasbord of topics from elementary algebra and trigonom-
. Review of Some Basic Algebra
Solving equations
Di culty with algebra skills is a f
GREENBERG
VECTOR GEOMETRY
UNIT
PARAMETRIC EQUATIONS
INTRO: We study parametric equations, their relationship to Cartesian equations and their graphs. We
will also study points of intersection of two trajectories, and collision points.
. Parametric Equatio
GREENBERG
VECTOR GEOMETRY
UNIT
POLAR COORDINATES, GRAPHING
INTRO: We will study polar coordinates, a system for labeling points in a plane in a manner di erent
from Cartesian coordinates. Polar coordinates play an essential role in problems which have a s
77
Chapter 3 - Solutions
r
1. A vector a can be represented in the magnitude-angle notation (a, ), where
a ax2 a 2y
is the magnitude and
a
tan 1 y
ax
r
is the angle a makes with the positive x axis.
(a) Given Ax = 25.0 m and Ay = 40.0 m, A ( 25.0 m)