UNIT-I
UNIT-1 Syllabus :
What is modeling? Object Oriented Thinking, History of UML Building Blocks of UML, OCL: what & why,
expression syntax Introduction to OMG standards MDA, XMI, UML 2.0. RUP emphasizing Inception,
Elaboration, Construction, Transitio
Wright 1
Felix Wright
Mrs. De La Torre
English 9 H/Period 2
3 October 2014
Journals 1-4: _Frankenstein_
1. Do you like your book so far? Explain.
So far I like the book Frankenstein, by Mary Shelley, because of the descriptive detail the
author gives of t
CALCULATIONS:
1. Single Unknown Number
Our groups single unknown numbers were #2 and #3.
2. Identity of the Single Unknown
The #2 single unknown was KBr and the #3 single unknown was KI.
3. Justification
The single unknown #2 solution looked very similar
ELECTORAL COLLEGE SHOULD BE ELIMINATED
Hello my name is Felix Wright. I am on the prop side of this argument.
We stand on four major grounds.
thepossibilityofelectingaminoritypresident
theriskofsocalled"faithless"Electors,
thepossibleroleoftheElectoralCol
THE EMBEDDING CAPACITY OF 4-DIMENSIONAL SYMPLECTIC
ELLIPSOIDS
arXiv:0912.0532v2 [math.SG] 31 Jan 2010
DUSA MCDUFF AND FELIX SCHLENK
Abstract. This paper calculates the function c(a) whose value at a is the inmum
of the size of a ball that contains a sympl
SYMPLECTIC EMBEDDINGS OF 4-DIMENSIONAL ELLIPSOIDS
DUSA MCDUFF
Abstract. We show how to reduce the problem of symplectically embedding one 4dimensional rational ellipsoid into another to a problem of embedding disjoint unions
of balls into appropriate blow
Symplectic forms
Joel Kamnitzer
March 24, 2011
1
Symplectic forms
We assume that the characteristic of our eld is not 2 (so 1 + 1 = 0).
1.1
Denition and examples
Recall that a skew-symmetric bilinear form is a bilinear form such that
(v, w) = (w, v) for a
arXiv:1409.2385v1 [math.SG] 8 Sep 2014
Symplectic embeddings of 4-dimensional ellipsoids
into polydiscs
Max Timmons, Priera Panescu and Madeleine Burkhart
Abstract
McDu and Schlenk have recently determined exactly when a fourdimensional symplectic ellipso
SYMPLECTIC EMBEDDINGS AND CONTINUED
FRACTIONS: A SURVEY
arXiv:0908.4387v2 [math.SG] 14 Oct 2009
DUSA MCDUFF
Abstract. As has been known since the time of Gromovs Nonsqueezing Theorem, symplectic embedding questions lie at the heart of symplectic geometry.
arXiv:math/0506191v1 [math.SG] 10 Jun 2005
Quantitative symplectic geometry
K. Cieliebak, H. Hofer, J. Latschev and F. Schlenk
February 1, 2008
A symplectic manifold (M, ) is a smooth manifold M endowed with a nondegenerate and closed 2-form . By Darbouxs
Precalculus
Fall 2012
OCC
5.1 Angles and Their Measurements
Definition: Degree Measure
The degree measure of an angle is the number of degrees in the intercepted arc of a circle centered at the
vertex. The degree measure is positive if the rotation is _an
Precalculus
Spring 2012
OCC
8.1 Systems of Linear Equations in Two Variables
Method I: Graphing
Method II: Substitution
Ex: Solve each system by graphing
Ex: Solve each system by substitution
Method III: Addition
Ex: Solve each system by addition.
Types o
11.1 Sequences
Sequences:
A function whose domain is the set of counting numbers: 1,2,3,4,
Sequences can be infinite or finite.
It represented by its nth term, an.
Sometimes listed as a set, in set notation: cfw_an
Ex: Find all terms of the sequence
Math 180 Class Work Name:
Evaluateeach limit. \ 3_ as? -\f\
(3+h)1 31 hm 3W z \m aw :v\m gm.)
. z -" as j
1 m h has \A Wm M b?
, M L
\(\N 3/9)
. \
z \W SLI = "'"
Wm 729% 56
, \
x25x+6 = - dwe " K
x5 #15 (X 5080 \Nm
WW /-
l W) W W \m_
XIS'
\nn am»
W
Math 180 Class Work Sections 4.2, 4.3
a»
1. The graph of f is shown. Evaluate (approximate) each of the following integrals by interpreting them in
terms of area.
2'. Write the integral as the limit of a sum, and then evaluate the integral, interpreti
Math 180 Class Work 4 Name: 8
Sections 2.3, 2.4, 2.5, 2.6
J};
1. Find the equations of the tangent line and normal line to the curve y = 1
x +
at the point
(4) 0140'
tangent Knew
normal Knew
_ I: .1 "1- . &.5 _._."*2x iii-J-
mmh (KHZX ML 25; T ._. Ni 2
3.1 MAXIMUM AND MINIMUM VALUES
3.1 Maximum and Minimum Values
Some of the most important applications of differential calculus are
optimization problems, in which we are required to find the optimal (best)
way of doing something. These problems can be red
Math 180 5.1, and 5.2 Class Work Name:
'1. Sketch the region enclosed by the given curves and find its area. )6 = 2y2, and x = 4 + yz.
my X 5
5 V1.1
2. The region enclosed by the curves y = x and y = x2 is rotated about the X-axis. Find the
volume of t
Precalculus
Fall 2012
OCC
9.1 Solving Linear Systems Using Matrices
Matrices
A matrix with m rows and n columns has size m n (read m by n).
o The number of rows is always given first.
A square matrix has an equal number of rows and columns.
Ex: Determine
Precalculus
Fall 2012
OCC
3.1 Quadratic Functions and Inequalities
Two Ways to Write Quadratic Functions:
Standard Form
Vertex Form
Ex: Rewrite the function in the form ( )
(
)
and sketch its graph
( )
Theorem: Quadratic Functions
The graph of any quadrat
Math 170
Precalculus
Fall 2012
1.1 Equations in One Variable
Linear Equation
Using properties of equalities:
a.
b.
c.
d.
Addition property of equality
Subtraction property of equality
Multiplication property of equality
Division property of equality
Ex. S
5.1 AREAS BETWEEN CURVES
5.1 Areas Between Curves
In chapter 5 we defined and calculated areas of regions that
lie under the graphs of functions. Here we use integrals to
find areas of regions that lie between the graphs of two
functions.
Consider the reg
Precalculus
Fall 2012
OCC
2.1 Functions
Functions: a relationship between sets, such that each member of the first set corresponds to exactly
one member of the second set. The first set is called the _ and the second set is called
the _.
Functions will pa
Precalculus
Fall 2012
OCC
4.1 Exponential Functions and Their Applications
Exponential Function
f(x) = ax, a > 0 and a 1.
Ex: Let ( )
a. f(3/2)
, ( )
, and ( )
( ) . Find the following values.
b. g(3)
c. h(-2)
Domain of an Exponential Function
The domain
Precalculus
Fall 2012
Chapters 3 & 4 Review
OCC
No work no credits
Find all real and imaginary solutions.
1) x4 + 81x2 = 0
1)
Discuss the symmetry of the graph of the polynomial function.
2) f(x) = x3 - x
2)
State the domain of the rational function.
x-4
Precalculus
Fall 2012
Ch 8 & 9 Review
No work no credits!
OCC
9) Michael's bank contains only nickels, dimes,
and quarters. There are 48 coins in all, valued
at $3.80. The number of nickels is 4 short of
being three times the sum of the number of
dimes an