General Calculus II

Further expand your understanding of the principles of calculus, like the techniques of integration and logistic models. After completing the course, you will be able to solve integration problems using different techniques of integration.

What you’ll learn

  • Students can complete in as little as 30 days.
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General Calculus II

$79

Plus membership

3 Credits

All courses include:

eTextbooks

2 to 3-day turnaround for grading

Multiple chances to improve your grade

On-demand tutoring & writing center

Student support 7 days a week

$79

Plus membership

3 Credits

All courses include:

eTextbooks

2 to 3-day turnaround for grading

Multiple chances to improve your grade

On-demand tutoring & writing center

Student support 7 days a week

General Calculus II

$79

Plus membership

3 Credits

About This Course

|
ACE Approved 2021

Expand on what you learned in General Calculus I with our online General Calculus II course, which covers the techniques of integration, application of integration, exponential and logistic models, parametric equations and polar coordinates, sequence and series, and vector and geometry.

download syllabus

What You'll Learn

Apply L’ Hôpital’s rule to find the limits of different indeterminate forms

Compute hyperbolic functions at the given point

Use hyperbolic identities

Compute the derivatives of hyperbolic functions

Solve integration problems using different techniques of Integration: Integration table, u-substitution, trigonometric functions, partial fraction, trigonometric substitution, and Trapezoidal rule

Apply integral calculus to compute average value of function, volumes, arc lengths, surface of revolution, work, and moments & centers of mass

Use various tests to determine the convergence and divergence of sequences and series

Apply Taylor and Maclaurin series for polynomial approximations

Demonstrate convergence and divergence of power series

Solve homogeneous differential equations

Use differential equations to solve ‘Growth and Decay’ problems

Solve problems based on eliminating the parameters, conversion between polar and cartesian forms, spirals and circles, polar coordinate system, and rose curve

Sketch parametric and polar curves

Apply differentiation and integration to parametric equations and polar functions

Apply dot product and cross product to vectors in R2 and R3

Apply differentiation to vector functions

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Course Details

MAT251

|

General Calculus II

After successfully completing our online General Calculus II course, you will be able to solve integration problems using different techniques of integration, such as integration table, u-substitution, trigonometric functions, partial fraction, trigonometric substitution, and trapezoidal rule.

Prerequisites

General Calculus I is a required prerequisite for General Calculus II. If you enroll, the assumption is made that you have previously completed General Calculus I for credit with a passing score.

Topic Subtopics
Introduction
  • Welcome to Calculus II
  • Review: Calculus I in 20 minutes
Math Fun
  • An Introduction to Paradoxes
  • Paradoxes and Air Safety
  • Newcomb’s Paradox
  • Zeno’s Paradox
  • Fibonacci Numbers
  • The Golden Ratio
Other Indeterminate Forms
  • 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
  • Defining the Hyperbolic Functions
  • Hyperbolic Identities
  • Derivatives of Hyperbolic Functions
Techniques of 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
  • Finding the Average Value of a Function
  • Finding the Volumes Using CrossSectional 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
  • 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)
  • 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
  • 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
  • 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
  • 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

Your score provides a percentage score and letter grade for each course. A passing percentage is 70% or higher.

Assignments for this course include:

  • 4 Graded Exams
  • 1 Graded Midterm
  • 1 Graded Final


This course does not require a text.


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Helpful resources:

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Do You Have to Take Math in College?

Tips to Help College Students to Succeed in an Online Math Course

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