EXPERIMENT 205
HOOKES LAW
Carl Joshua A. Marcial, 2013103785, BSCE - 2
CEGE Department
[email protected]
ABSTRACT
The experiment is all about the law of Robert Hooke which is the Hookes Law. Hookes Law
states that Within the elastic limit of
CALCULUS 3
1ST Quarter
AY 2014-2015
SEQUENCES
Sequence
A sequence is a succession of numbers formed
according to some fixed rule. Mathematically, it is a
function whose domain is the set of positive integers.
Example: 1, 4, 9, 16, 25, having the rule that
WORK
MATH22-1
CALCULUS 2
OBJECTIVES
At the end of the lesson, the student is expected
to:
find the work done by a constant force.
find the work done by a variable force.
find the work done in pumping liquid out of the
container.
WORK
Work measures the
VOLUME OF SOLIDS WITH KNOWN
CROSS-SECTION
MATH22-1
Calculus2
The method of cross section is a way of computing the
volume of a solid that is described in terms of its cross
sections (or slices) in planes perpendicular to a fixed
reference line ( such as t
TRANSCENDENTAL FUNCTIONS
MATH22-1
CALCULUS 2
OBJECTIVES
At the end of the lesson, the students are
expected to:
use the Log Rule for Integration to integrate
rational functions.
integrate exponential functions.
integrate trigonometric functions.
integrate
VOLUME OF REVOLUTION
MATH22-1
CALCULUS 2
OBJECTIVES
At the end of the lesson, the student should be able
to:
define what a solid of revolution is.
find the volume of solid of revolution using disk
method.
find the volume of solid of revolution using the
w
THE THEOREM OF PAPPUS
OBJECTIVES
At the end of the lesson, the student is expected
to:
use the Theorem of Pappus to find the surface
area of revolution.
use the Theorem of Pappus to find the volume
of a solid of revolution.
THEOREMS OF PAPPUS
THEOEM 1:
EXPERIMENT 201
WORK, ENERGY AND POWER
Carl Joshua A. Marcial, 2013103785, BSCE-2
CEGE Department
[email protected]
ABSTRACT
This experiment aims to illustrate the connection among work, energy, and power. The laboratory
equipments used in the
MATH22-1
CALCULUS 2
MATHEMATICS
Mathematics is a collective term for
the branches of learning that have
grown out of the ancient discipline of
geometry and arithmetic.
CALCULUS
That branch of analysis which investigates
the infinitisimal changes of consta
SURFACE AREA OF REVOLUTION
MATH22-1
CALCULUS 2
DEFINITION OF SURFACE OF REVOLUTION
If the graph of a continuous function is
revolved about a line, the resulting surface is a
surface of revolution.
The area of a surface of revolution is derived
from the
THE DIFFERENTIALS
MATH22-1
CALCULUS 2
Week 1 Day 1 The Differentials (Calculus Early Transcendentals Larson 5th Edition, page 272-
Week 1 Day 3
GENERAL OBJECTIVE
At the end of the lesson the students are expected to:
THE DIFFERENTIALS
Find dy given the fo
THE DEFINITE INTEGRAL
MATH22-1
CALCULUS 2
Week 2 Day 3 The Differentials (Calculus Early Transcendentals Larson 5th Edition, page 272-
OBJECTIVES
At the end of the lesson, the students are
expected to:
define and interpret definite integral.
identify an
TECHNIQUES OF
INTEGRATION
OBJECTIVES
At the end of the lesson, the student should be able
to:
find an antiderivative using integration by parts.
use trigonometric substitution to solve an integral.
use algebraic substitution to solve an integral.
use reci
PLANE AREAS
MATH22-1
Calculus 2
OBJECTIVES
At the end of the lesson, the student should be
able to:
find the area of a plane region.
evaluate a definite integral using the
Fundamental Theorem of Calculus
find the area of a region between two curves
using
SPACE COORDINATES AND
SURFACES
Math 14
Plane and Solid Analytic Geometry
OBJECTIVES:
At the end of the lesson, the student is expected to be
able to:
define space coordinates.
plot points of space coordinates.
write and sketch the graphs of space coord
VECTORS IN THE PLANE
MATH23-1
1ST Quarter
AY 2014-2015
VECTORS IN THE PLANE
Scalar quantity a physical quantity such as
length, temperature, or mass that can be
specified in terms of a single real number, its
magnitude.
Vector quantity (or simply vector
MAPUA INSTITUTE OF TECHNOLOGY
Department of Physics
E201: WORK, ENERGY, AND POWER
MARCIAL, Carl Joshua A.
[email protected]/2013103785/BSCE-2
PHY11L-B2 Group 2
SCORE
Computation (10)
=
Data Sheet (5)
=
Results and Discussion (25)
=
Conclusion
DYNAMICS OF
ROTATION
SAMPLE PROBLEMS:
3.A merry-go-round has a radius of 2.50 meters and
moment of inertia of 2100 kg-m2 about a vertical
axle through its center and turns with negligible
friction.
A) A child applies an 18.0 N force tangentially to
the ed
Elasticity
Definition
property by virtue of which a body returns to its original size
and shape when the forces that deformed it are removed.
Elastic Behavior
Alightlydeformedmaterialwillrecoveritsoriginal shape
afterthestressisremoved.Elasticbehavioroccu
SEATWORK
WORK, POWER AND ENERGY/IMPULSE AND MOMENTUM
Instructions: Solve the following problems. Strictly use one bond paper per
problem. Summarize the answer/s.
1. A 2.0-kg wooden block slides down an inclined plane 1.0 m high and 3.0 m
long. The block s
HOMEWORK (Strictly use one bond paper per problem. Summarize all final answers.)
1. Two blocks M1 and M2 are connected by a massless wire
which has been passed through a pulley as shown in the
figure. The pulley is a disk of mass m and radius r. What is
t
LEVEL CURVES AND LEVEL
SURFACES
MATH23-1
1ST Quarter
AY 2014-2015
LEVEL CURVES
The intersection of the horizontal plane = with
the surface = (, ) is called the contour curve of
height c on the surface. The vertical projection of this
contour curve into th
PARTIAL DERIVATIVES
MATH23-1
1ST Quarter
AY 2014-2015
If f is a function of two or more independent
variables and all but one of these independent
variables are held fixed, then the derivative of
f with respect that one remaining independent
variable is c
LINES AND PLANES IN SPACE
MATH23-1
1ST Quarter
AY 2014-2015
Lines in space
Just in the plane, a straight line in space is determined by any two points that lie
on it.
z
L
0
v ai bj ck
r0
Then another point P( x, y, z ) lies on
the line L if and only if v
DIRECTIONAL DERIVATIVES and
GRADIENTS
MATH23-1
1ST Quarter
AY 2014-2015
The partial derivatives of a function gives
the instantaneous rates of change of that
function in directions parallel to the coordinate
axes. Directional derivatives computes the rate
VECTOR-VALUED FUNCTION
MATH23-1
1ST Quarter
AY 2014-2015
Vector-valued function
A parametric curve C in the plane is a pair of functions
y g (t )
and
x f (t )
that gives x and y as continuous function of the real number
t (the parameter) in some interval
FUNCTIONS OF SEVERAL
VARIABLES
MATH23-1
1ST Quarter
AY 2014-2015
A function f of two variables, x and y, is a rule
that assigns a unique real number f(x,y) to each
point (x,y) in some set D in the xy-plane.
A function f of three variables, x, y, and z, is