Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
24 Cards in this Set
- Front
- Back
|
"well defined"
|
established way of solving, not subject to debate
|
|
|
Mathematics
|
the study of patterns
|
|
|
A calculus
|
any formal system
-a system that in theory could be executed entirely by a computer with no common sense and acting without regard to the meaning of the underlying symbols. |
|
|
The calculus
|
1. Differential: the study of change / rate of change
2. Integral: Integral calculus |
|
|
What did Hippasus do?
|
Hippasus discovered irrationality, specificially that root 2 is irrational. According to legend he was drowned by pythagoreans who believe in perfect order = music
|
|
|
System
|
A set of anything such that the components work together.
|
|
|
Definition
|
A bidirectional conditional statement.
|
|
|
Who discovered the calculus?
|
Newton and Leibniz (individually) discovered the calculus. We use Leibniz' notation.
|
|
|
Metamathematics
|
The mathematics of mathematics
|
|
|
Kurt Gödel
|
Incompleteness theorem: any complete system of mathematics will be inconsistent.
|
|
|
Proposition
|
"a concept"/"a statement", a statement about mathematical concepts
|
|
|
Don't forget WLOG!
|
Without Loss of Generallity
|
|
|
What is a calculator's normal tolerance / highest possible tolerance (machine)?
|
10^-5 and 10^-99
|
|
|
Neighborhood
|
A neighborhood of width ε about x=c, where ε>0 and ε, x is a member of set R, is an open interval (c-ε,c+ε)
|
|
|
Punctured δ-neighborhood
|
A punctured δ-neighborhood of q is a member of set R is a δ-neighborhood excluding q itself, i. e.,
(q-δ,q) U (q, q+δ) |
|
|
What are DeMorgan's Laws?
|
~(PUQ)⇔~P∩~Q
~(P∩Q)⇔~PU~Q |
|
|
What is the formal definition of limit as x approaches -∞?
|
L = lim as x approaches -∞ f(x) iff ∀ε>0 ∃ D∈R: ∀x<D,|f(x)-L|<ε
|
|
|
Definition of derivative
|
lim as h approaches 0 of [ f(x+h) - f(x) ] / h
|
|
|
Integral
|
Accumulation of rates of change
|
|
|
Adaptive Quadrature
|
Adaptive = step size can adapt, Quadrature = calculation of area (in squares)
Calculator uses this method to find integrals |
|
|
Necessary and sufficient
|
⇔ aka definition
If A=>B is true, then B is necessary and A is sufficient. |
|
|
Explain the importance of y = C+AcosB(x-D)
|
1. The sinusoidal axis is along the line y=c
2. The amplitude equals |A| 3. The period equals 2π/|B| 4. The phase displacement equals D |
|
|
Antiderivative
|
The function f is an antiderivative of function g iff f'(x)=g(x) for all values of x in their domains.
|
|
|
Differential Equation
|
Any equation that contains a derivative.
|
