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MAT251: General Calculus II
General Calculus II
Course Text
● This course does not require a text.
Course Description and Objectives This course is designed to acquaint students with the principles of Calculus like techniques of integration; application of integration; exponential and logistic models; parametric equations and polar coordinates; sequence and series; and vector and geometry. Upon successful completion of the course, students will be able to:
● Understand other Intermediate forms and how to solve the problems with different intermediate forms.
● Understand hyperbolic function and hyperbolic identities, learn how to find derivative of hyperbolic function.
● Understand techniques of Integration and learn how to solve - Integration using table 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 take General Calculus I or its equivalent before enrolling in General Calculus II. Concepts learned in General Calculus I are necessary in order to successfully complete General Calculus II.
Important Terms In this course, different terms are used to designate tasks:
● Proctoring: all final exams require proctoring which can be completed conveniently from your home. A webcam is required.
● Tutoring: memberships include online tutoring for students to access with any content/subject related questions in the place of faculty. If your tutor is not able to answer your questions please contact a student advisor.
● Exam: A graded online test.
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MAT251: General Calculus II
● Exercises: ungraded practice exercises and quiz questions.
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
Course Topics and Objectives Chapter Topics Subtopics
An Introduction to Calculus II
● Introduction ● Welcome to Calculus II ● Review: Calculus I in 20 minutes
Math Fun
● Paradoxes ● Sequences
● An Introduction to Paradoxes ● Paradoxes and Air Safety ● Newcomb’s Paradox ● Zeno’s Paradox ● Fibonacci Numbers ● The Golden Ratio
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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
● 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 ● 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
Substitution Strategy ● Trigonometric Substitution Involving a
Definite Integral: Part One ● Trigonometric Substitution Involving a
Definite Integral: Part Two ● Deriving the Trapezoidal Rule ● An Example of the Trapezoidal Rule
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MAT251: General Calculus II
Applications of Integral Calculus
● The Average Value of a Function
● Finding Volumes Using Cross-Sections
● Disks and Washers ● 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
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 ● 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
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MAT251: General Calculus II
● Absolute and Conditional Convergences
● The Ratio and Root Test
● Polynomial Approximations of Elementary Functions
● Taylor and Maclaurin Polynomials
● Taylor and Maclaurin Series
● Power Series ● Power Series
Representations of Functions
● Absolute and Conditional Convergence ● The Ratio Test ● Examples of the Ratio Test ● The Root Test ● 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 ● 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 Parametric Equations
● Understanding Polar Coordinates
● Polar Functions and Slope
● Polar Functions and Area
● An Introduction to Parametric Equations
● Sketching a Parametric Curve ● The Cycloid ● Eliminating Parameters ● Derivatives of Parametric Equations ● Finding the Slopes of Tangent Lines in
Parametric Form ● Graphing the Elliptic Curve ● The Arc Length of a Parameterized
Curve
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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
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
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Training Design Proposal
Imagine that you are tasked with the development and delivery of a two-day training workshop for 100 managers on how to use effective feedback skills when delivering one-on-one performance reviews to employees.
In an 800 to 1,000 word paper (excluding the title and reference page), construct a proposal that identifies three specific learning objectives, a discussion of the content the training would entail, methods to be used (e.g. lecture, case study, role play), and the instructional media and equipment required and explains why. Specify the logistical arrangements, such as type of room setup, that can enhance or undermine the content and interaction between participants. Assess the impact that room set up has upon communication within the group.
Take into consideration:
· Length of workshop (2 days)
· Number of trainees (100)
· Learning objective (developing effective feedback skills)
Your introductory paragraph must include a clear and concise description of the training. Tables, graphs and charts may be used. APA formatted headings should be used to organize and identify each section of your paper. An Abstract is not required. Your paper must be formatted according to APA style as outlined in the Ashford Writing Center. Your paper must also include citations and references from the Blanchard and Thacker (2013) text and at least three additional scholarly sources.
The paper
· Must be 800 to 1,000 words, double-spaced in length (excluding the title and reference pages) and formatted according to APA style as outlined in the Ashford Writing Center.
· Must include a separate title page with the following:
· Title of paper
· Student’s name
· Course name and number
· Instructor’s name
· Date submitted
· Must use at least three scholarly sources in addition to the course text from the Ashford University Library.
· Must document all sources in APA style as outlined in the Ashford Writing Center.
· Must include a separate references page that is formatted according to APA style as outlined in the Ashford Writing Center.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
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