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
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