Differentiation of Inverse Functions
Assume that y = f(x) is a single-valued function of x in an interval (a, b) and the
derivative function dy
dx = f(x) exists and is different from zero in this interval. If the
inverse function x = f1(y) exists, then it

Differentiation of Parametric Equations
If x = x(t) and y = y(t) are a given set of parametric equations which define y as
a function of x by eliminating the parameter t and the functions x(t) and y(t) are
continuous and differentiable, then by the chain

Higher Derivatives
If the derivative function f(x) is the input to the operator box illustrated in
the figure 2-4, then the output function is denoted f(x) and represents a derivative
of a derivative called a second derivative. Higher ordered derivatives

First Derivative Test
The first derivative test for extreme values of a function tests the slope of the
curve at near points on either side of a critical point. That is, to test a given function
y = f(x) for maximum and minimum values, one first calculate

Maxima and Minima
Examine the curve y = f(x) illustrated in the figure 2-12 which is defined and
continuous for all values of x satisfying a x b. Start at the point x = a and move
along the x-axis to the point b examining the heights of the curve y = f(x)

Logarithmic Differentiation
Whenever one is confronted with functions which are represented by complicated
products and quotients such as
y = f(x) =
x2
3 + x2
(x + 4)1/3
or functions of the form y = f(x) = u(x)v(x), where u = u(x) and v = v(x) are complic

Concavity of Curve
If the graph of a function y = f(x) is such that f(x) lies above all of its tangents
on some interval, then the curve y = f(x) is called concave upward on the interval. In
this case one will have throughout the arc of the curve f(x) > 0

Simple Harmonic Motion
If the motion of a particle or center of mass of a body can be described by either
of the equations
y = y(t) = Acos(t
0) or y = y(t) = Asin(t 0) (2.61)
where A, and 0 are constants, then the particle or body is said to undergo a
si

Chapter 1
Sets, Functions, Graphs and Limits
The study of different types of functions, limits associated with these functions
and how these functions change, together with the ability to graphically illustrate
basic concepts associated with these functio

Learning algebra
Eugene, OR
October 17, 2009
H. Wu
*I am grateful to David Collins and Larry Francis for many corrections and
suggestions for improvement.
This is a presentation whose target audience is primarily mathematics teachers of grades 58. The mai

Conic Sections in Polar Coordinates
Place the origin of the polar coordinate system at the focus of a conic section
with the y-axis parallel to the directrix as illustrated in the figure 1-46. If the point
(x, y) = (r cos q, r sin q) is a point on the con

Now if the function f(x) is such that no two ordered pairs have the same second
element, then the function obtained from the set
S = cfw_ (x, y) | y = f(x), x X
by interchanging the values of x and y is called the inverse function of f and it is
denoted b

The
Foundations of Geometry
BY
DAVID HILBERT, PH. D.
PROFESSOR OF MATHEMATICS, UNIVERSITY OF GTTINGEN
AUTHORIZED TRANSLATION
BY
E. J. TOWNSEND, PH. D.
UNIVERSITY OF ILLINOIS
REPRINT EDITION
THE OPEN COURT PUBLISHING COMPANY
LA SALLE
ILLINOIS
1950
TRANSLAT

Variables, Constants, and Data Types
Primitive Data Types
Variables, Initialization, and Assignment
Constants
Characters
Strings
Reading for this class: L&L, 2.1-2.3, App C
1
Primitive Data
There are eight primitive data types in Java
Four of them repre