AP Calculus Videos

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Jim Bowen              Stillwater High School            Stillwater, Oklahoma

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Note:

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==================      Calculus Videos… Index:     ===================

Limits:

( Part 1 ) – Limits of Rational Functions

( Part 2 ) – Limits of Rational Functions

Limits by Rationalizing the Numerator

( Part 1 ) Understanding the Epsilon – Delta Definition of Limits

( Part 2 ) Epsilon – Delta Definition of Limits

The “Squeeze” Theorem for Limits

The Intermediate Value Theorem

Limit as X Approaches Infinity ( Part 1 )

Limit as X Approaches Infinity ( Part 2 ) ( Rational Functions )

Limit as X Approaches Infinity ( Part 3 ) ( Two Asymptotes & Radicals )

( Part 1 )  Graph Piecewise Defined Functions

( Part 2 )  Evaluate Piecewise Defined Functions

( Part 3 )  Limits of Piecewise Defined Functions

L’Hospital’s Rule ( Part 1 )  (  0 / 0  Form  )

L’Hospital’s Rule ( Part 2 )  (  oo / oo  Form  )

L’Hospital’s Rule ( Part 3 )  ( Repeated Application )

L’Hospital’s Rule ( Part 4 ) ( Mis-Application! )

Derivative Rules:

Basic Derivatives using the Power Rule

Equation of the Tangent Line using the Limit Definition

Find Equation of the Tangent and Normal Lines

Product and Quotient Rule ( Part 1 )

Product and Quotient Rule ( Part 2 )

Product and Quotient Rule ( Part 3 )

Basic Trig Derivatives

Chain Rule ( Part 1 )

Chain Rule ( Part 2 )

Chain Rule with Trig ( Part 1 )

Chain Rule with Trig ( Part 2 )

Implicit Differentiation

Logarithmic Differentiation

Derivatives of Ln

( Base e ) Exponential Function Derivatives

Exponential and Log Derivatives ( Base A )

( Part 1 ) Derivative of an Inverse Function

( Part 2 ) Derivative of an Inverse Function

( Part 3 ) Derivative of an Inverse Function

Bisection Method for Finding the Zeros of a Function

( Part 1 ) Newton’s Method for Finding the Zeros of a Function

( Part 2 ) Newton’s Method for Finding the Zeros of a Function

Inverse Trigonometric Function Derivatives ( Part 1 )

Inverse Trigonometric Function Derivatives ( Part 2 )

Curve Sketching:

Sketch First Derivative Graphs

Sketch Second Derivative Graphs ( Method 1 )

Sketch Second Derivative Graphs ( Method 2 )

( Part 1 ) Sketch Complete Graphs ( No Asymptotes )

( Part 2 ) Sketch Complete Graphs ( With Asymptotes )

( Part 1 ) Mean Value Theorem ( and Rolle’s Theorem )

( Part 2 ) Mean Value Theorem ( and Rolle’s Theorem )

Extreme Values ( Part 1 ) Maximum and Minimum

Extreme Values ( Part 2 ) Maximum and Minimum

( Part 1 ) Increasing and Decreasing Intervals

( Part 2 ) Increasing and Decreasing Intervals

( Part 3 ) Increasing and Decreasing Intervals

( Part 4 ) Increasing and Decreasing Intervals

( Part 1 ) Second Derivative & Concavity & Inflection Points

( Part 2 ) Second Derivative & Concavity & Inflection Points

( Part 3 ) Second Derivative & Concavity & Inflection Points

( Part 4 ) Second Derivative Test for Local Maximum or Minimum

Applications of Derivatives:

Average Velocity  vs  Instantaneous Velocity

Projectile Motion ( Example 1 )

Projectile Motion ( Example 2 )

Projectile Motion ( Example 3 )

Projectile Motion ( Example 4 )

Non “Projectile Motion” ( Example 5 )

Related Rates ( Part 1 )

Related Rates ( Part 2 )

Related Rates ( Part 3)

Related Rates “The Shadow Problem”

Related Rates with Trig ( Part 4 )

Related Rates with Trig ( Part 5 )

Related Rates with Trig ( Part 6 )

Optimization Problems ( Example 1 )

Optimization Problems ( Example 2 )

Optimization Problems ( Example 3 )

Integrals and Integration:

Sigma Notation ( Summation Formulas )

Riemann Sum ( Part 1 )

Riemann Sum ( Part 2 )

Midpoint Rule

Trapezoid Rule

Simpson’s Rule

Basic Integrals using the Power Rule ( Part 1 )

Basic Integrals using the Power Rule ( Part 2 )

Basic Integrals with Trig

Definite Integrals

Definite Integrals with Trig

Average Value using Integrals

Absolute Value using Integrals

U-Substitution ( Part 1 )

U-Substitution ( Part 2 ) with Trig

U-Substitution ( Part 3 ) Double Substitution

U-Substitution ( Part 4 ) Definite Integrals

U-Substitution ( Part 5 ) Final Examples

Area Between Curves ( Vertical Rectangles )

Area Between Curves ( Horizontal Rectangles )

Arc Length using Integrals

Surface Area using Integrals

Center of Mass ( Example 1 ) One Dimensional System

Center of Mass ( Example 2 )  2-D Point Mass System

Center of Mass ( Example 3 ) Planar Lamina

Center of Mass ( Example 4 ) Derive the Formulas

Center of Mass ( Example 5 ) One Function

Center of Mass ( Example 6 ) Two Functions Vertical Rectangles

Center of Mass ( Example 7 ) Derive the Horizontal Formulas

Center of Mass ( Example 8 ) Horizontal Rectangles

Natural Log Function Integrals ( Part 1 )

Natural Log Function Integrals ( Part 2 )

Natural Log Function Integrals ( Part 3 )

Natural Log Function Integrals ( Part 4 )

Six Basic Trig Integrals (Part 1 )

Six Basic Trig Integrals (Part 2 )

Six Basic Trig Integrals (Part 3 )

Exponential Function Integrals ( Base “e” ) ( Part 1 )

Exponential Function Integrals ( Base “e” ) ( Part 2 )

Exponential Function Integrals ( Bases other than “e” ) ( Part 1 )

Exponential Function Integrals ( Bases other than “e” ) ( Part 2 )

Inverse Trigonometric Function Integrals ( Part 1 )

Inverse Trigonometric Function Integrals ( Part 2 )

Applications of Integration:

Volume of Revolution ( Disk Method )

Volume of Revolution ( Volume of a Sphere )

Volume of Revolution ( Washer Method – Part 1 )

Volume of Revolution ( Washer Method – Part 2 )

Volume of Revolution ( Washer Method – Part 3 )

Volume of Revolution ( Shell Method – Part 1 )

Volume of Revolution ( Shell Method – Part 2 )

Volume of Revolution ( Shell Method – Part 3 )

Volume of Revolution ( Shell method – Part 4 )

Volume of Revolution ( Shell Method – Part 5 )

Volume of a Solid using Cross Sections (#1)

Volume of a Solid using Cross Sections ( #2 )

Volume of a Solid using Cross Sections ( #3 )

Volume of a Solid using Cross Sections ( #4 )

Volume of a Solid using Cross Sections ( #5 )

Volume of a Solid using Cross Sections ( #6 )

Integration by Parts:

Integration by Parts ( Part 1 )

Integration by Parts ( Part 2 )

Integration by Parts ( Part 3 )

Integration by Parts ( Part 4 )

Integration by Parts ( Part 5 )

Integration by Parts ( Part 6 )

Techniques of Integration:

Integration by Partial Fractions ( Part 1 ) Fraction Decomposition

Integration by Partial Fractions ( Part 2 ) Distinct Linear Factors

Integration by Partial Fractions ( Part 3 ) Distinct Linear Factors

Integration by Partial Fractions ( Part 4 ) Repeated Linear Factors

Integration by Partial Fractions ( Part 5 ) Quadratic Factors

Integration by Partial Fractions ( Part 6 ) Long Division

Trigonometric Integrals ( Part 1 ) ( Sine & Cosine )

Trigonometric Integrals ( Part 2 ) ( Sine & Cosine )

Trigonometric Integrals ( Part 3 ) ( Sine & Cosine )

Trigonometric Integrals ( Part 4 ) ( Sine & Cosine )

Trigonometric Integrals ( Part 5 ) ( Sine & Cosine )

Trigonometric Integrals ( Part 6 ) ( Secant & Tangent )

Trigonometric Integrals ( Part 7 ) ( Secant & Tangent )

Trigonometric Integrals ( Part 8 ) ( Secant & Tangent )

Trigonometric Integrals ( Part 9 ) ( Secant & Tangent )

Trigonometric Integrals ( Part 10 ) ( Secant & Tangent )

Integrals using Trigonometric Substitution ( Part 1 )

Integrals using Trigonometric Substitution ( Part 2 )

Integrals using Trigonometric Substitution ( Part 3 )

Integrals using Trigonometric Substitution ( Part 4 )

Integrals using Trigonometric Substitution ( Part 5 )

Integrals using Trigonometric Substitution ( Part 6 )

Integrals using Trigonometric Substitution ( Part 7 )

Integrals using Trigonometric Substitution ( Part 8 )

Improper Integrals ( Part 1 ) Infinite Limits

Improper Integrals ( Part 2 ) Infinite Limits

Improper Integrals ( Part 3 ) Infinite Limits

Improper Integrals ( Part 4 ) Infinite Limits

Improper Integrals ( Part 5 ) Infinite Limits

Improper Integrals ( Part 6 ) Infinite Limits

Improper Integrals ( Part 7 ) Infinite Limits

Improper Integrals ( Part 8 ) Infinite Discontinuity

Improper Integrals ( Part 9 ) Infinite Discontinuity

Improper Integrals ( Part 10 ) Infinite Discontinuity

Improper Integrals ( Part 11 ) Infinite Discontinuity

Infinite Series

A Review of Basic Arithmetic Sequences

A Review of Basic Arithmetic Series

A Review of Basic Geometric Sequences

( Part 1 ) Change Repeating Decimals into Fractional Form

( Part 2 ) Change Repeating Decimals into Fractional Form

Convergence of a Sequence ( Part 1 )

Convergence of a Sequence ( Part 2 )

Convergence of a Sequence ( Part 3 )

Convergence of a Sequence ( Part 4 ) ( with Factorials )

Convergence of a Sequence ( Part 5 ) “Squeeze Theorem”

Infinite Sequence and Series Graphs & Partial Sums

Nth Term Test for Divergence ( Infinite Series )

“Geometric Series” Test for Convergence ( Infinite Series )

“p-Series” Test for Convergence ( Infinite Series )

Integral Test for Convergence ( Part 1 ) ( infinite Series )

Integral Test for Convergence ( Part 2 ) ( infinite Series )

Direct Comparison Test for Convergence ( Infinite Series )

Limit Comparison Test for Convergence ( Part 1 ) ( Infinite Series )

Limit Comparison Test for Convergence ( Part 2 ) ( Infinite Series )

Limit Comparison Test for Convergence ( Part 3 ) ( Infinite Series )

Alternating Series Test for Convergence ( Part 1 ) ( Infinite Series )

Alternating Series Test for Convergence ( Part 2 ) ( Infinite Series )

Alternating Series ( Part 3 ) Remainder Estimation ( Infinite Series )

Absolute and Conditional Convergence ( Part 1 ) ( Infinite Series )

Absolute and Conditional Convergence ( Part 2 ) ( Infinite Series )

Understanding the Ratio Test ( Part 1 ) ( Infinite Series )

Ratio Test for Convergence Examples ( Part 2 ) ( Infinite Series )

Root Test for Convergence ( Part 1 ) ( Infinite Series )

Root Test for Convergence ( Part 2 ) ( Infinite Series )

Root Test for Convergence ( Part 3 ) ( Infinite Series )

Taylor Polynomial Approximation for Sin(x)  ( Infinite Series )

Taylor Polynomial for Sin(x)  ( not centered at x=0 )  ( Infinite Series )

Taylor Polynomial Approximation for Cos(x)  ( Infinite Series )

Taylor Polynomial Approximation for e^x  ( Infinite Series )

( Part 1 ) Taylor Polynomial for ln(x)   ( Infinite Series )

( Part 2 ) Taylor Polynomial for ln(1+x)  ( Infinite Series )

( Part 3 ) Taylor Polynomial – Compare  ln(x) with ln(1+x)   ( Infinite Series )

Taylor Polynomial Approximation for  1 / ( 1 – x )    ( Infinite Series )

( Part 1 )  Lagrange Remainder of a Taylor Polynomial  ( Infinite Series )

( Part 2 )  Lagrange Remainder of a Taylor Polynomial  ( Infinite Series )

( Part 3 )  Lagrange Remainder of a Taylor Polynomial  ( Infinite Series )

( Part 1 )  Power Series Interval of Convergence   ( Infinite Series )

( Part 2 )  Power Series Interval of Convergence   ( Infinite Series )

( Part 3 )  Power Series Interval of Convergence   ( Infinite Series )

( Part 4 )  Power Series Interval of Convergence   ( Infinite Series )

( Part 5 )  Power Series Interval of Convergence   ( Infinite Series )

( Part 1 ) Convert Rational Function to Geometric Power Series (Infinite Series)

( Part 2 ) Convert Rational Function to Geometric Power Series (Infinite Series) 

( Part 3 ) Convert Rational Function to Geometric Power Series (Infinite Series)

( Part 4 ) Convert Rational Function to Geometric Power Series (Infinite Series)

Find a New Power Series using Substitution  ( Infinite Series )

( Part 1 ) Multiplication of Power Series  ( Infinite Series )

( Part 2 ) Multiplication of Power Series  ( Infinite Series )

( Part 3 ) Multiplication of Power Series  ( Infinite Series )

( Part 1 ) Division of Power Series  ( Infinite Series )

( Part 2 ) Division of Power Series  ( Infinite Series )

( Part 1 ) Derivatives of Power Series  ( Infinite Series )

( Part 2 ) Derivatives of Power Series  ( Infinite Series )

( Part 1 )  Integration of Power Series  ( Infinite Series )

( Part 2 )  Integration of Power Series  ( Infinite Series )

( Part 3 )  Integration of Power Series  ( Infinite Series )

===================  End of Video List  =======================

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