Concept & Example Videos for Calculus II 

 

If you have any questions, comments or corrections, please e-mail me. shawna.haider@slcc.edu

 

Applications of Integration

Concept Video - Volumes by Slicing 
Concept Video - Solids of Revolution and Finding Volumes Using the Washer Method

Example 1 – Finding Volume of Solid of Revolution Using the Disk Method 
Example 2– Finding Volume of Solid of Revolution Using the Washer Method
Example 3 – Finding Volume of Solid Rotated Around x-axis and then y-axis
Example 4 – Finding Volume of Solid Rotated Around a Line Other than x or y-axis

Concept Video - Finding Volumes Using the Shell Method

Example 1 – Finding the Volume of a Solid of Revolution Using the Shell Method Example 1
Example 2a- Finding the Volume of a Solid of Revolution Using the Shell Method Example 2
Example 2b - Finding the Volume of a Solid of Revolution Using the Shell Method When y = - 2
Example 3 - Finding the Volume of a Solid of Revolution Using Both Washer and Shell Methods
Example 4 – Finding the Volume of a Solid of Revolution About a Line Using the Washer Method

Which Method Washer or Shell?

Concept Video – Work
Example 1 – Computing work done moving an object with a variable force 
Example 2 – Computing work done raising a bucket from a well
Example 3 – Computing the work needed to stretch or compress a spring
Example 4– Computing the work needed to pump water out of a tank

 

Techniques of Integration

Concept Video - Integration by Parts Method 
Example 1 – Using Integration by Parts 
Example 2 – Using Integration by Parts Twice
Example 3 – Integration by Parts with Cycling Functions 
Example 4 – Integration by Parts to Find a Volume of Solid of Revolution
Example 5 – Integration by Parts Leading to Tabular Integration Algorithm (don’t miss this!)
Example 6 – Tabular Integration


Concept Video - Integrating Products of Trigonometric Functions Part 1 

Concept Video - Integrating Products of Trigonometric Functions Part 2
Example 1 – Integrate Powers of Sine 
Example 2 – Integrate Product of Sines and Cosines
Example 3a – Integrating Sine to the 6th Power Using Half Angle Formula 
Example 3b – Integrating Sine to the 6th Power Using Reduction Formula 


Concept Video - Integrating Using Trigonometric Substitution
Example 1 – Trigonometric Substitution 1
Example 2 – Trigonometric Substitution 2
Example 3 – Trigonometric Substitution 3
Example 4 – Trigonometric Substitution 4
Example 5 – Trigonometric Substitution 5


Concept Video - Using Partial Fractions to Evaluate Integrals With Linear Factors
Concept Video - Using Partial Fractions to Evaluate Integrals With Repeated Linear Factors
Concept Video - Using Partial Fractions to Evaluate Integrals With Quadratic Factor
Concept Video - Using Partial Fractions to Evaluate Integrals With Repeated Quadratic Factors and Using Substitution to Rationalize and Evaluate Rational Functions
Example 1 – Partial Fractions With Linear Factors
Example 2 – Partial Fractions With Repeated Linear Factors
Example 3 – Partial Fractions With a Quadratic Factor 
Example 4 – Partial Fractions With a Repeated Quadratic Factor
Example 5 – Using Substitution to Rationalize the Integrand

 

Concept Video - Integrating Using Tables 

 

Concept Video - Integrating Using Computer Algebra Systems


Integral Tables http://integral-table.com/ ~ http://eqworld.ipmnet.ru/en/auxiliary/aux-integrals.htm 

 

Online Integrator: http://integrals.wolfram.com/index.jsp 

Example 1 – Using Integral Tables 1
Example 2 – Using Integral Tables 2
Example 3 – Using Integral Tables 3
Example 4 – Using Integral Tables 4
 

Concept Video - Integration Strategies
Example 1 – Integration Strategies
Example 2 – Integration Strategies
Example 3 – Integration Strategies 
Example 4 – Integration Strategies 
Example 5 – Integration Strategies 
 

Concept Video - Improper Integrals : Type 1 – Infinite Limit of Integration
Concept Video - Improper Integrals: Type 2 – Unbounded Integrand (Infinite Range)
Example 1 – Integral With Infinite Upper Limit of Integration
Example 2 – Another Integral With infinite Upper Limit of Integration
Example 3 – Integral With Unbounded Integrand
Example 4 – Integral With Infinite Range
 

Additional Applications of Integration 

 

Concept Video - Length of a Curve 

Example 1 - Finding the Length of a Curve 1
Example 2 - Finding the Length of a Curve 2 
Example 3 - Finding the Length of a Curve 3
Example 4 - Finding the Length of a Curve 4 

 

Concept Video - Hyperbolic Functions

Concept Video - Finding the Surface Area of a Solid of Revolution

Example 1 - Finding the Surface Area of a Sphere
Example 2 - Finding the Area of a Surface of Revolution About the y-Axis

 

Content Video - Differential Equations and Modeling
Content Video - Graphs and Verifying Solutions to Differential Equations
Content Video - Direction Fields
Content Video - Playing With Direction Fields

Direction Field Interactive used in the video
http://www.cengage.com/math/discipline_content/stewartcalcet7/2008/14_cengage_tec/publish/deployments/transcendentals_7e/m9_2a.html

 

Example 1 – Sketching a Direction Field Example
Example 2 – Sketching a Direction Field Example 2

 

Concept Video - Separable Differential Equations
Example 1 – Solving a Separable Differential Equation Example 1
Example 2 – Solving a Separable Differential Equation Example 2
Example 3 – Solving the Logistic Equation Example 3
Example 4 – Solving the Solving a Separable DE Example 4

 

Polar and Parametric Equations

Concept Video - Polar Coordinates
Concept Video - Graphs of Polar Equations
Concept Video - Graphing Polar Equations
Example 1 – Sketch a region Defined in Polar Coordinates
Example 2 – Identify a Polar Curve by Converting to Rectangular Coordinates
Example 3 – Sketch a Polar Curve
Example 4 – Sketch a Polar Curve Given a Rectangular Curve 

 

Concept Video - Calculus and Polar Curves
Example 1 – Find the slope of a tangent to a polar curve
Example 2 – Find the horizontal and vertical tangents of a polar curve part 1
Example 2 – Find the horizontal and vertical tangents of a polar curve part 2
Example 3 – Determining interval of integration to find area of a polar curve
Example 4 – Finding the area of a rose
Example 5 – Finding Area of overlapping polar curves
Example 6 – Finding length of a cardioid

 

Concept Video - Graphing Parametric Equations
Example 1 – Parametric Graphing Given Graphs of x(t) and y(t)

 

Concept Video - Calculus and Parametric Equations
Example 2 – Graphing Parametric Equations Using Calculus
Example 3 – Finding Equation of Tangent Line With and Without Parameter
Example 4 – Finding the Speed of An Object Defined Parametrically
Example 5 – Finding the Length of a Curve or Distance Traveled Parametrically

 

Infinite Sequences and Series

Concept Video - Sequences
Concept Video - Part 2 - Limit of a Sequence
Concept Video - More About Sequences
Concept Video - Geometric Sequences
Example 1 – Sequences Example 1
Example 2 – Sequences Example 2
Example 3 – Sequences Example 3
Example 4 – Sequences Example 4

 

Concept Video - Infinite Series
Concept Video - Part 2 - More on Series and the Divergence Test
Example 1 – Series Example 1
Example 2 – Series Example 2
Example 3 – Series Example 3
Example 4 – Series Example 4

 

Concept Video - Integral Test
Concept Video - P-Series
Example 1 – Use the Integral Test to Determine Convergence
Example 2 – Use the Integral Test to Determine Convergence
Example 3 – Use the Integral Test to Determine Convergence
Example 4 – Determine Convergence of P-Series
Example 5 – Determine Convergence of P-Series

 

Concept Video - Comparison Tests
Example 1 – Use the Comparison Tests to Determine Convergence
Example 2 – Use the Comparison Tests to Determine Convergence
Example 3 – Use the Comparison Tests to Determine Convergence
Example 4 – Use the Comparison Tests to Determine Convergence
Example 5 – Use the Comparison Tests to Determine Convergence

 

Concept Video -Alternating Series
Example 1 – Use the Alternating Series Test to Determine Convergence
Example 2 – Use the Alternating Series Test to Determine Convergence
Example 3 – Use the Alternating Series Test to Determine Convergence
Example 4 – Use the Alternating Series Test to Determine Convergence
Example 5 – Use the Alternating Series Test to Determine Convergence

 

Concept Video - Absolute Convergence
Concept Video - Ratio and Root Tests
Proof of Ratio Test
Proof of Root Test


Example Videos: - Absolute Convergence Testing Example 1 
Absolute Convergence Testing Example 2 
Absolute Convergence Testing Example 3 
Applying the Ratio Test Example 1 
Applying the Ratio Test Example 2 
Applying the Root Test Example 1 
Applying the Root Test Example 2

 

Concept Video - Strategies for Testing Convergence
Example Videos:

Applying Strategies for Testing 

Applying Strategies for Testing 2

Applying Strategies for Testing 3

Applying Strategies for Testing 4

Applying Strategies for Testing 5

Applying Strategies for Testing 6 

Applying Strategies for Testing 7

Applying Strategies for Testing 8 

Applying Strategies for Testing 9

Applying Strategies for Testing 10

Applying Strategies for Testing 11

Applying Strategies for Testing 12 

 

Concept Video - Power Series Part 1
Concept Video - Power Series Part 2


Concept Video - Bessel Functions
Example Videos:
Finding the Radius and Interval of Convergence 1
Finding the Radius and Interval of Convergence 2 
Finding the Radius and Interval of Convergence 3 
Finding the Radius and Interval of Convergence 4 
Finding the Radius and Interval of Convergence 5 

 

Content Video - Representations of Functions as Power Series 
Example Videos:
Representing a Function as a Power Series and Finding Coefficients and Radius of Convergence Example 1
Representing a Function as a Power Series and Finding Coefficients and Radius of Convergence Example 2
Representing a Function as a Power Series and Finding Coefficients and Radius of Convergence Example 3
Representing a Function as a Power Series Using The Derivative 
Representing a Function as a Power Series Using The Integral - involves natural log 

 

Content Video - Part 1 – Taylor Polynomials
Content Video - Part 2 – Using Taylor Polynomials, Taylor’s Theorem, Taylor’s Inequality
Proof of Taylor’s Theorem 
Proof of Taylor’s Inequality 
Example Videos: 
Finding a 3rd Degree Taylor Polynomial Centered at 2
Finding a 4th Degree Taylor Polynomial Centered at 0
Finding a Taylor Polynomial and Estimating the Error using Taylor's Inequality
Finding a Taylor Polynomial and Using Alternating Series Estimating Theorem wrote 4! as 48 instead of 24 in video (sorry)

 

Content Video - Taylor and Maclaurin Series
Content Video - Binomial Series
Example Videos:
Finding a Taylor Series 
Representing a Function as a Maclaurin Series 
Finding a Taylor Series Centered at a
Finding a Maclaurin Series with an x factor in front
Using Series to Evaluate an Integral
Using Series to Evaluate a Limit
Find the Terms of a Binomial Series

 

Three Dimensional Systems, Vectors and Equations 

Content Video - 3D Coordinate System

 

Content Video - Vectors 
Example Videos: 
Finding magnitudes and Combining Vectors
Expressing a Vector in Standard Position Given Initial and Terminal Points
Using Vectors in an Application 

 

Content Video - Dot Product Introduction 
Content Video - Projection of Vectors and Work
Example Videos:
Find the angle between vectors
Find the scalar and vector projection of one vector onto another
Find the work done by a force applied in a given direction

 

Content Video - Cross Product 
Content Video - More on Cross Product 
Proof of Property 6
Proof of Property 7 
Example Videos:
Finding the Area of a Parallelogram and a Triangle in 3D
Finding the Volume of a Parallelepiped


Content Video - Equations of Lines
Content Video - Equations of Planes 

Shawna Haider                   Professor Mathematics                Salt Lake Community College

shawna.haider@slcc.edu