International Journal of ChemTech Research
CODEN (USA): IJCRGG
ISSN : 0974-4290
Vol.6, No.10, pp 4497-4503, September 2014
RACE 2014 [12th 13th July 2014]
Recent Advances in Chemical Engineering
Fabri
The Visibility and the Interpretation of Social Reality
(Felipe Criado)
1. For the greater part of pre-history human action did not significantly alter the surrounding
environment.
2. There is the fac
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2150
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ADJACENT BUILDING LN.
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2650
B
C I S T E R N
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D E C K
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R O O F
5820
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FIRE WALL
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2113
Integer
Programming
Integer Linear Programming
Integer Linear Programs (ILP or IP) are linear
programs in which some or all the variables are
restricted to integer or discrete values.
Linear Program
RESISTIVE CIRCUITS
EE 1 Basic Electrical Engineering
Asst. Prof. Adrian Augusto M. Sumalde
Department of Electrical Engineering
College of Engineering and Agro-Industrial Technology (CEAT)
University
COURSE OUTLINE AND
POLICIES
EE 1 Basic Electrical Engineering
2nd Semester A.Y. 16-17
Lecture-GH (W 4-6 PM, EE Auditorium)
EE 1 - Basic Electrical Engineering
Faculty-in-Charge
Asst. Prof. Adrian Augu
Example 4.5
Production Process Models
Background Information
Repco produces three drugs, A, B and C, and can
sell these drugs in unlimited quantities at unit prices
$8, $70, and $100, respectively.
Pr
Assignment
The uniform beam weighing 3000 lbs is to be
supported by the three rods, the lower ends of
which were initially at the same level.
Determine the stress felt by the aluminum (E
= 10 x 106 ps
ES 13: Mechanics of Deformable Bodies I
Lecture No. 19
Beam Deflections using
Area-Moment Method (AMM)
Euler-Bernoulli Equation
Moment-Area Theorems
Area-Moment Method (AMM)
Moment Diagram by-Parts
Ma
Analytic
Geometry
MATH 36 A
MATHEMATICAL ANALYSIS I
Lecture 15
18 March 2015
Limits &
Continuity
Derivatives
Applications of
Derivatives
Integration
1
CHAPTER 3
THE DERIVATIVE AND DIFFERENTIATION
Outl
Unit 3
Applications of the
Definite Integral
Unit 3.1
Volume of Solids of
Revolution
Unit 3.1.1
Volume of Solids of
Revolution
(Using Disks)
Solid of Revolution
A solid of revolution is a solid obtain
Print this file using A4 and write your solutions on it.
EXERCISE 10
Center of Mass
Week 13 MATH 37 X
Due on November 3, 2016 in the lecture class
NAME:_ RECIT SECTION:_ SCORE:_
SET-UP only. All or no
Unit 5.5
Equations of Lines
and Planes
Plane in Space
A plane in space is determined by a point
P x0 , y0 , z0 in the plane and a vector N that
is orthogonal to the plane.
This orthogonal vector N is
Unit 3.1.2
Volume of Solids of
Revolution
(Using Cylindrical Shells)
Consider the region that lies under the curve
y f x , above the x-axis and between the
lines x a and x b.
Subdivide the region into
Unit 5.3
Dot Product
Dot Product
If A a1, a2 and B b1, b2 , then the dot
product of A and B is given by
A B a1b1 a2b2
If A a1, a2 , a3 and B b1, b2 , b3 , then
A B a1b1 a2b2 a3b3
Example 5.3.1
Perform
Unit 3.4.2
Center of Mass
of a Plane Region
n
x
m x
i 1
n
i i
m
i 1
i
mi xi moment of mass of the ith particle
with respect to the origin
n
M 0 mi xi moment of mass of the system
i 1
with respect to t
4.3
AREA
of
POLAR
REGIONS
1
Area of a sector of a circle.
1 2
A r
2
Consider the shaded region below.
Note: It is assumed here that r f 0.
Subdivide , into n subintervals of equal length.
Interva
Unit 5
Vectors and the Space
1
Unit 5.1
The Three Dimensional
Coordinate System
2
xy plane:
z0
xz plane:
y0
yz plane:
x0
P x, y , z
z
y
x
Plotting Points in 3D
For P x, y, z ,
1. Locate the point x,
Unit 4.2
Graphs of Polar Equations
Graph of a Polar Equation
The graph of a polar equation F r, 0,
consists of all points r , whose coordinates
satisfy the equation.
Lines
Form: C
Graph: line passing
Unit 5.2
Vectors
Vector
A vector is used to indicate a quantity that has
both magnitude and direction.
Velocity indicates speed magnitude and
direction
positive/negative .
Q
P
CD
AB
Vector in Plane a
Unit 3.3
Area of a Surface of
Revolution
Surface of Revolution
A surface of revolution is formed when a curve
is revolved about a line.
SA 2 rh
SA r1 r2 l
Consider the surface obtained by revolving th
Unit 3.4.3
Center of Mass
of a Solid of Revolution
xy plane:
xz plane:
yz plane:
z0
y0
x0
Consider a system of n particles with masses
m1, m2 , , mn located at the points x1, y1, z1 ,
x2 , y2 , z2 ,
Unit 4
Polar Coordinate System
Unit 4.1
Cartesian and Polar
Coordinate System
Polar Coordinate System
A polar coordinate system consists of a horizontal
ray called the polar axis.
The initial point of
4/10/2015
MATH 36 A
Analytic
Geometry
MATHEMATICAL ANALYSIS I
Lecture 16
27 March 2015
Limits &
Continuity
Derivatives
Applications of
Derivatives
Integration
1
CHAPTER 3
THE DERIVATIVE AND DIFFERENTI
4/10/2015
MATH 36 A
Analytic
Geometry
MATHEMATICAL ANALYSIS I
Lecture 17
08 April 2015
Limits &
Continuity
Derivatives
Applications of
Derivatives
Integration
1
CHAPTER 3
THE DERIVATIVE AND DIFFERENTI
Unit 5.6
Cylinders and
Quadric Surfaces
Traces
A trace of a surface is a curve of intersection
of the surface with planes parallel to the
coordinate planes.
Cylinders
A cylinder is a surface that cons
Unit 3.2
Length of an Arc
Consider the graph of y f x where f is
continuous and a x b.
y f x
a
b
Length of an Arc
If f ' is continuous on a, b , then the length
of the curve y f x , a x b is
L
b
a
1 f
3/18/2015
MATH 36 A
Analytic
Geometry
MATHEMATICAL ANALYSIS I
Lecture 14
18 March 2015
Limits &
Continuity
Derivatives
Applications of
Derivatives
Integration
1
CHAPTER 3
THE DERIVATIVE AND DIFFERENTI
Unit 3.4
Center of Mass
Unit 3.4.1
Center of Mass
of a Rod
The rod will balance if m1d1 m2d2
m1d1 m2d2
m1 x x1 m2 x2 x
m1x m1x1 m2 x2 m2 x
m1x m2 x m1x1 m2 x2
m1x1 m2 x2
x
m1 m2
In general, in a syst