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. 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.

This Course Includes:

Proctored Exams

48 hours grading turn-around

Live technical and student support

Free transcription to your destination school

150+ partner college and universities with direct articulation

Online Course

General Calculus II +$79.00

Proctoring (included)

Tutoring (included)

General Calculus II

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General Calculus II

Course Content from ThinkWell

Course Number: MAT251 Download Course Syllabus

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Content Rating

This Course Includes:

Proctored Exams
48 hours grading turn-around
Live technical and student support
Free transcription to your destination school
150+ partner college and universities with direct articulation

Self Paced
Mathematics
Content by ThinkWell

Online Course

General Calculus II +$79.00

Proctoring (included)

Tutoring (included)

Credits 3

Plus Membership [?]

Add to Cart

Course Objectives

Upon successful completion of this 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.

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
Other Indeterminate Forms	Indeterminate Form	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 Derivatives of Hyperbolic Functions Hyperbolic Identities
Techniques of Integration	Integration using tables 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
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 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	Alternating Series The Alternating Series Test Estimating the Sum of an Alternating Series 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
Sequences and Series (continued)	The Alternating Series 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	Alternating Series The Alternating Series Test Estimating the Sum of an Alternating Series 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 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

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.

This course does not require a text.

StraighterLine provides a percentage score and letter grade for each course. 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

Final Proctored Exam

The final exam is developed to assess the knowledge you learned taking this course. All students are required to take an online proctored final exam in order complete the course and be eligible for transfer credit.

Learn more about Proctored Exams

9/5/14 by neerav.thakkar

it was good

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9/1/14 by ksims214

this course on this site covered lots of information that my college did not cover. i think it requires too much.

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7/7/14 by jdsdog10

The lectures in this course were very well put together. They are made so that one can easily understand the subject.

Content Rating
Overall Rating

7/7/14 by jdsdog10

The lectures in this course were very well put together. They are made so that one can easily understand the subject.

Content Rating
Overall Rating

5/9/14 by neerav.thakkar

it was good

Content Rating
Overall Rating

1/9/14 by ksims214

this course on this site covered lots of information that my college did not cover. i think it requires too much.

Content Rating
Overall Rating

Load More Reviews

Course Objectives

Upon successful completion of this 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.

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
Other Indeterminate Forms	Indeterminate Form	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 Derivatives of Hyperbolic Functions Hyperbolic Identities
Techniques of Integration	Integration using tables 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
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 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	Alternating Series The Alternating Series Test Estimating the Sum of an Alternating Series 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
Sequences and Series (continued)	The Alternating Series 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	Alternating Series The Alternating Series Test Estimating the Sum of an Alternating Series 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 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