DIFFERENTIATION OF
EXPONENTIAL FUNCTIONS
OBJECTIVES:
apply the properties of exponential functions
to simplify differentiation;
differentiate functions involving exponential
functions; and
solve problems involving differentiation of
exponential functio
THE DIFFERENTIALS
The derivative of a function can often be used to
approximate certain function values with a surprising
degree of accuracy. To do this, the concept of the
differential of the independent variable and the
dependent variable must be introd
DIFFERENTIATION OF
LOGARITHMIC
FUNCTIONS
OBJECTIVES:
differentiate and simplify logarithmic
functions using the properties of logarithm,
and
apply logarithmic differentiation for
complicated functions and functions with
variable base and exponent.
TRANS
Differential Equations
Long Quiz 2
3rd Quarter SY 2014-2015
February 27, 2015
1. Determine whether the equation (2xy tan y)dx + (x2 x sec2y)dy = 0 is exact. If it is exact, find the
solution. (15 points)
2. Find the solution for (xy + 1)dx + x(x + 4y 2)dy
An Introduction to Organic Reactions:
Acids and Bases
Acid-Base Reactions
The Brnsted-Lowry Definitions
In 1923 the Danish chemist Johannes Brnsted (1879-1947) and the
English chemist Thomas Lowry (1874-1936) independently proposed
that acids and bases be
Chap. 5 part II
Alkenes and Alkynes II:
Addition Reactions
Solomons, Chapter 8
Chapter 5: Structure and Preparation of Alkenes:
Elimination Reactions
Alkenes (olefins) are hydrocarbons that contain a carbon-carbon
double bond and are said to be "unsaturat
Chapter 5
Aromatic Compounds
Aromatic Compounds
Aromatic compound: A term used to classify
benzene and its derivatives containing 6membered rings with 3 double bonds
Arene: An aromatic hydrocarbon
Aryl group: A group derived from an aromatic
compound b
Organic Chemistry, 6h Edition
L. G. Wade, Jr.
Chapter 6
Alkyl Halides: Nucleophilic
Substitution and Elimination
Classes of Halides
Alkyl: Halogen, X, is directly bonded to sp3
carbon.
Vinyl: X is bonded to sp2 carbon of alkene.
Aryl: X is bonded to sp
Titrimetric Methods;
Precipitation Titrimetry
Lecture 5
Titration
Based on a reaction between the analyte
and a standard reagent known as the
titrant.
The end point is signaled by an indicator
color change or a change in an
instrumental response.
Widel
Chapter 3
EXPERIMENTAL
ERRORS
1
Other Common Analytical Terms
1. Precision refers to reproducibility of repetitive measurements
of equivalent analyte solutions (e.g. aliquots)
Often expressed as (absolute) standard deviation, s,
or relative standard devi
Stereochemistry
Compounds which have the same molecular formula and
the same sequence of covalently bonded atoms, but
different spatial orientations of those atoms.
Conformational stereoisomers those that interconvert
easily at room temperatures through
Chapter 5: Structure and Preparation of Alkenes:
Elimination Reactions
Alkenes (olefins) are hydrocarbons that contain a carbon-carbon
double bond and are said to be "unsaturated."
molecular formula CnH2n
5.1: Alkene Nomenclature (please read and understa
Organic Compounds:
Alkanes and Their
Stereochemistry
Based on McMurrys Organic Chemistry, 7th edition
Objectives of discussion
Alkanes are unreactive, but provide useful vehicle to
introduce important ideas about organic compounds
Alkanes will be used t
Precipitimetry
CHM 112
MAPUA Institute of Technology
11/21/2015
dcapodaca_2Q2012-13
1
Precipitation methods
Are those in which a desired constituent is
precipitated from solution by means of a
standard solution of precipitating agent
May be direct or in
Redox Methods
Oxidimetry and Reductimetry
Titration of an oxidizing agent with a standard
solution of a reducing agent or the titration of a
reducing agent with a standard solution of an
oxidizing agent
Oxidation the increase in the positive direction
o
Special Theory of
RELATIVITY
FRAMES OF REFERENCE
Inertial Frame of Reference
A frame of reference where Newtons Laws of Motion
hold true.
A frame of reference that is at rest or moving with
constant velocity is an inertial frame of reference.
Non-inertial
THE FEASIBILITY OF A MEAL PLAN SYSTEM IN
MIT
Set-eral universities In the U|'|".EI:I States include meal plane for their students. A meal plan
includes a set number of meals each term_. each plan includes e specific set of meals and a
speciﬁed amount that
CE141
HYDROLOGY
ENGR. CRIS EDWARD F. MONJARDIN
Index Card
Course / Section
Name
Program / year
Student Number
Contact number
Guardian
Guardians Contact number
Signature
COURSE DESCRIPTION
A course designed to provide conceptual
understanding of the hydro
LIGHT AND
GEOMETRIC OPTICS
The Nature of Light
1678
Christiaan
Huygensproposed
the
wave
theory which states that light was
made up of waves vibrating up and
down perpendicular to the direction
of travel of light.
1704 Isaac Newton, proposed the
corpuscula
DIFFRACTION AND
INTERFERENCE
INTERFERENCE
Interference refers to a situation when two or more
waves overlap in space.
Principle of Superposition
when two or more waves
overlap,
the
resultant
displacement at any point and
any instant is found by adding
th
MAGNETIC FIELD AND
MAGNETIC FORCES
MAGNETISM: Properties of Magnets
1. If a permanent bar magnet is free to rotate, one end
would point north this is the north pole or N-pole.
to north
pole
2. Like poles of two magnets repel and unlike poles attract.
3. I
INTRODUCTION TO UNIT
HYDROGRAPHS
A unit hydrograph shows the temporal change in
flow, or discharge, per unit of runoff. In other words,
how the flow of a stream will be affected over time
by the addition of one unit of runoff. The unit
hydrograph is a us
SOURCES OF
MAGNETIC FIELD
28.1 Magnetic Field of a Moving Charge
Consider a charge q moving with a constant velocity v.
The location of the charge at any given instant is called
the source point.
The point P where the magnetic field due to the charge is
b
Evapotranspiration
Evapotranspiration is the sum total of water returned to the
atmosphere from surface and ground (soil) water, ice, snow, and
vegetation.
Evaporation
It is understood to be a cooling process because heat is
removed from the surface whe