2. and u-substitution, integration by partial fraction, integration
by using trigonometric
substitution, how to solve numerical integration.
● Learn applications of integral – understand the average value
of function, understand
how to find - volume of revolution, surface of revolution and
arc length of functions.
● Understand Sequences and Series -learn monotonic, bounded
sequences and indefinite
series. Understand how to check convergence and divergence of
series, solve problems
based on Taylor and McLaurin series and convergence and
divergence of power series.
● Understand what differential equation is, learn how to solve
Homogeneous differential
equations, and solve growth and decay problems.
● Understand what are parametric equations and polar
coordinates.
● Understand vectors.
The topics covered under this course are other indeterminate
forms, the hyperbolic functions; the
techniques of integration; application of integral calculus;
sequences and series; differential
equations; parametric equations and polar coordinates; and
vectors and geometry.
Course Prerequisites
StraighterLine does not require prerequisites, however it is
highly recommended that students
4. Course Evaluation Criteria
StraighterLine provides a percentage score and letter grade for
each course. See Academic
Questions section in FAQ for further details on percentage
scores and grading scale. A passing
percentage is 70% or higher.
If you have chosen a Partner College to award credit for this
course, your final grade will be
based upon that college's grading scale. Only passing scores
will be considered by Partner
Colleges for an award of credit.
There are a total of 1000 points in the course:
Chapter Assessment
Points
Available
4 Graded Exam 1 125
6 Graded Exam 2 125
7 Midterm Exam 200
9 Graded Exam 3 125
11 Graded Exam 4 125
12 Final Exam 300
Total 1000
6. MAT251: General Calculus II
Other
Indeterminate
Forms
● Indeterminate Form
0 ⋅ ∞, ∞ - ∞
1∞ , 00, ∞0
● L’Hopital’s rule and Indeterminate
Products
● L'Hôpital's rule and Indeterminate
Differences
● L'Hôpital's rule and One to the Infinite
Power
● Another example of One to the Infinite
Power
● L'Hôpital's rule and zero to the zero
power
● L'Hôpital's rule and infinity to the zero
power
The Hyperbolic
Functions
● Hyperbolic Functions
7. ● Defining the Hyperbolic Functions
● Hyperbolic Identities
● Derivatives of Hyperbolic Functions
Techniques of
Integration
● Integration Using
Tables
● Integrals Involving
Powers of Sine and
Cosine
● Integrals Involving
Powers of Other
Trigonometric
Functions
● Integration by Partial
Fractions and
Repeated Factors
● An Introduction to
Trigonometric
Substitution
● Trigonometric
Substitution Strategy
● Numerical Integration
● An Introduction to the Integral Table
● Making u-Substitutions
8. ● An Introduction to Integrals with
Powers of Sine and Cosine
● Integrals with Powers of Sine and
Cosine
● Integrals with Even and Odd Powers of
Sine and Cosine
● Integrals of Other Trigonometric
Functions
● Integrals of Odd Powers of Tangent
and Any Power of Secant
● Integrals with Even Powers of Secant
and Any Power of Tangent
● Repeated Linear Factors: Part One
● Repeated Linear Factors: Part Two
● Distinct and Repeated Quadratic
Factors
● Partial Fractions of Transcendental
Functions
● Converting Radicals into Trigonometric
Expressions
● Using Trigonometric Substitution to
Integrate Radicals
● Trigonometric Substitutions on
Rational Powers
● An Overview of Trigonometric
10. ● Shells
● Arc Lengths and
Functions
● Surface of Revolution
● Work
● Moments and Centers
of Mass
● Finding the Average Value of a
Function
● Finding the Volumes Using
Cross-Sectional Slices
● An Example of Finding Cross-Sectional
Volumes
● Solids of Revolution
● The Disk Method along the y-Axis
● A Transcendental Example of the Disk
Method
● The Washer Method across the x-Axis
● The Washer Method across the y-Axis
● Introducing the Shell Method
● Why Shells Can Be Better Than
Washers
● The Shell Method: Integrating with
Respect to y
● An Introduction to Arc Length
● Finding Arc Lengths of Curves Given
11. by Functions
● Finding Area of a Surface of Revolution
● An Introduction to Work
● Calculating Work
● Hooke’s Law
● Center of Mass
● The Center of Mass of a Thin Plate
Sequences and
Series
● Sequences
● Monotonic and
Bounded Sequences
● Infinite Series
● Convergence and
Divergence
● The Integral Test and
p-Series
● The Direct
Comparison Test
● The Limit Comparison
Test
● The Limit of a Sequence
● Determining the Limit of a Sequence
● Monotonic and Bounded Sequences
● An Introduction to Infinite Series
● The Summation of Infinite Series
12. ● Geometric Series
● Telescoping Series
● Properties of Convergent Series
● The nth-Term Test for Divergence
● An Introduction to the Integral Test
● Examples of the Integral Test
● Using the Integral Test
● Defining p-Series
● An Introduction to the Direct
Comparison Test
● Using the Direct Comparison Test
● An Introduction to the Limit
Comparison Test
● Using the Limit Comparison Test
● Inverting the Series in the Limit
Comparison Test
Sequences and
Series
(continued)
● The Alternating
Series
● Alternating Series
● The Alternating Series Test
● Estimating the Sum of an Alternating
Series
Privacy Policy | Student Handbook
14. ● Polynomial Approximations of
Elementary Functions
● Higher-Degree Approximations
● Taylor Polynomials
● Maclaurin Polynomials
● The Remainder of a Taylor Polynomial
● Approximating the Value of a Function
● Taylor Series
● Examples of the Taylor and Maclaurin
Series
● New Taylor Series
● The Convergence of Taylor Series
● The Definition of Power Series
● The Interval and Radius of
Convergence
● Finding the Interval and Radius of
Convergence: Part One
● Finding the Interval and Radius of
Convergence: Part Two
● Finding the Interval and Radius of
Convergence: Part Three
● Differentiation and Integration of
Power Series
● Finding Power Series Representations
by Differentiation
● Finding Power Series Representations
by Integration
15. ● Integrating Functions Using Power
Series
Differential
Equations
● Solving a
Homogeneous
Differential Equation
● Growth and Decay
Problems
● Separating Homogeneous Differential
Equations
● Example of Newton’s Law of Cooling
● Change of Variables
● Exponential Growth
● Logistic Growth
● Radioactive Decay
Parametric
Equations and
Polar
Coordinates
● Understanding
Parametric Equations
● Calculus and
17. MAT251: General Calculus II
● Finding Arc Lengths of Curves Given
by Parametric Equations
● The Polar Coordinate System
● Converting between Polar and
Cartesian Forms
● Spirals and Circles
● Graphing Some Special Polar Functions
● Calculus and the Rose Curve
● Finding the Slopes of Tangent Lines in
Polar Form
● Heading toward the Area of a Polar
Region
● Finding the Area of a Polar Region:
Part One
● Finding the Area of a Polar Region:
Part Two
● The Area of a Region bounded by Two
Polar Curves: Part One
● The Area of a Region bounded by Two
Polar Curves: Part Two
● The Arc Length of a Polar Curve
● Area of surface of revolution in Polar
Form
18. Vectors and
the Geometry
of R² and R³
● Vectors and the
Geometry of R² and
R³
● Vector Functions
● Coordinate Geometry in Three
Dimensional Space
● Introduction to Vectors
● Vectors in R² and R³
● An Introduction to the Dot Product
● Orthogonal Projections
● An Introduction to the Cross Product
● Geometry of the Cross Product
● Equations of Lines and Planes in R³
● Introduction to Vector Functions
● Derivatives of Vector Functions
● Vector Functions: Smooth Curves
● Vector Functions: Velocity and
Acceleration
Review and
Final Exam
Review and Final Exam ● Review and Final Exam
19. Privacy Policy | Student Handbook
http://www.straighterline.com/privacy-policy
http://www.straighterline.com/student-handbook
Ewa 4
Vincent Ewa Topic: What do we
know about school discipline reform?
February 11, 2017
Article Review # 1
Bibliography entry:
Steinberg, Matthew P., and Johanna, Lacoe. "What do we know
about school discipline reform?." Education Next 17, no. 1
(Winter2017 2017): 44-52. Education Research Complete,
EBSCOhost.
Purpose: The U.S. Department of Education’s Office for Civil
Rights announced this spring that the number of suspensions
and expulsions in the nation’s public schools had dropped 20
percent between 2012 and 2014.
Authoraffiliations:
· Steinberg – The University Pennsylvanian’s Graduate School
of Education
· Lacoe - Researcher at Mathematica Policy Research
Summary:
According to the department of Education office for civil rights,
there has been a drop of suspensions and expulsions in public
schools between 2012 and 2014. There have been moves to
abolish the use of suspensions and expulsion by some policy
20. makers. Furthermore, there have also been complains that
suspensions and expulsions where used in a way that was not
fair and discriminative of other students. Others do also believe
that the abolishment of such punishment would result to a better
working environment. There has also been a push by politicians
including Barak Obamas government, which advocated for an
alternative kind of punishment for students found on the wrong
line of the school rules. This involved a joint venture by the
Department of Education and the Department of Justice who
eventually arrived on measures to improve the school climate
and the discipline among students. They also send a strict
warning of racism when it comes to disciplining of students at
school. It is evident also that the move for discipline reforms
has gone to the grassroots, which is the state and school district
levels. Example is the District of Colombia.
A critical look on the effects of this alternative ways of
suspension should be made. Various statistical reports have
brought out variety of evidences. Example is the documentation
in disparities in school in school discipline and race. In addition
is the statistical report by the National Centre for Education
show a downward trend in suspensions, student victimization
and reports of bullying. It also shows decline in suspensions and
expulsions. There has also been more that 30% if teachers
reporting of disruption to studies due to behavior and tardiness.
Evidence of exposure to extreme harsh conditions such has
students exposed to Hurricanes tend to be out of school for a
given time while dealing with the disaster. Finally, exposure to
disruptive peers tends to affect students later in their studies.
Statistics also show disproportionate rates of suspension
with it mainly affecting students of a specific race and also
students with disabilities. Most of these being racial especially
among the blacks in preschool, primary, middle and high
schools. This has also created gaps between blacks and whites
in suspension rates with it doubling between 1989 and 2010.
Russell Skiba and colleagues carried a study that proved this to
be right by far. They found out that blacks and Hispanics
21. received punishment for minor offences more than the white
students did. This is further questionable since black students
receive far much harsh punishment than the whites for offices
made. There has also been suspension targeting the disabled
with the rate of suspension in 2011 hitting twice those with no
disabilities. However critics have argued that there has been an
overuse of suspension instead of using other punishment
methods that are less harsh for minor offences. Furthermore,
advocates of reform agree that exclusion of punishment can lead
to adverse effects with evidence showing insubordination,
physical attacks and other offences such as drug and alcohol
use, and possession of firearms.
They finally arrive at the alternative measure of
exclusionary punishment. One would be program based
interventions where target program using the response to
intervention model to provide services to specific youth with
the aim of preventing problems as they arise. Further
adjustments are made when a student does not respond to a
given intervention by introducing more intense intervention. In
addition, policy based interventions are introduced. Here target
policies like early warning tend to improve behavior.
Furthermore, school level programs redefine how teachers and
school resource officers interact with students while school
level policies such as KIPP aim at setting high behavioral
expectations from all students.
Critique:
These article brought the under tone of school discipline and the
solution to the race and punishment in schools in United States.
The best way to punish a student brings a lot of headache to the
government, teachers and other education stakeholders. The
major challenge being the punishment given to students of
different races and those students with disabilities where
evidence from statistics show how others are other races gets
more punishment that can be rather harsher sometimes. The
decision to exclude punishment also brings adverse effects to
22. the learning environment hence resulting to other alternatives
that can help keep students behavior in check. These also
includes though measures to how institutions should deal with
students and at the same time respect all races and punish them
equally without showing a lighter hand to another race when it
comes to punishment.
