BC Calculus Links

General Calculus Links:

College board AP BC site (the good one): http://apcentral.collegeboard.com/apc/members/exam/exam_information/232222.html

College board AP AB site (the good one): http://apcentral.collegeboard.com/apc/members/exam/exam_information/232050.html

Bookmark and utilize: http://patrickjmt.com/#calculus / https://www.youtube.com/user/patrickJMT/videos

Bookmark and utilize: https://www.khanacademy.org/math/differential-calculus

Bookmark and utilize:https://www.khanacademy.org/math/integral-calculus

Bookmark and utilize: https://www.youtube.com/user/TheIntegralCALC

Bookmark and utilize OR install the app: Calcchat.com: http://www.calcchat.com/book/Calculus-9e/ - Worked out solutions to all of the odd problems from your textbook.

All of Calculus 1 in 20 minutes: Part 1 / Part 2 

 

Specific Calculus Topic Links:

1.2 - Finding Limits from a Graph

1.2 - Finding Limits from Numerically

1.2 - Epsilon Delta Definition of a Limit

1.3 - Evaluating Limits Analytically 

1.3 - Squeeze Theorem for Limits

1.3 - Evaluating Limits by Direct Substitution

1.3 - Evaluating Limits by Cancellation

1.3 - Evaluating Limits by Rationalization

1.3 - Special Trigonometric Limits

1.3 - Intermediate Value Theorem

1.3 - Limits of Difference Quotients

1.4 - One Sided Limits

1.4 - Limit Definition of Continuity

1.4 - Intermediate Value Theorem

1.4 - The Greatest Integer (or Floor) Function

1.4 - Greatest Integer Function on the TI83/84

1.5 - Infinite Limits

3.5 - Limits at Infinity

 

2.1 - Limits Definition of the Derivative

2.1 - Definition of Differentiability

2.2-Basic Derivatives Using Power Rule (Patrick JMT)

2.2-Power Rule for Derivatives (Khan Academy, more videos listed at the left)

2.3-Product Rule for Derivatives

2.3-Quotient Rule for Derivatives

2.4 - Horizontal and Vertical Tangent Lines Using a Product Rule Example

2.4-Basic Chain Rule

2.4-Chain Rule with Product Rule, Ex1

2.4-Chain Rule with Product Rule, Ex2

2.5-Implicit Differentiation – Basic Idea and Examples

2.5-Implicit Differentiation – Extra Examples

2.5-Implicit Differentiation – More Examples

2.5-Implicit Differentiation and Second Derivatives

2.5 - Finding Horizontal and Vertical Tangent Lines Using Implicit Differentiation - Video 1

2.5 - Finding Horizontal and Vertical Tangent Lines Using Implicit Differentiation - Video 2

2.6 – Related Rates

2.6 - Related Rates FRQ's

 

3.1 – Finding Absolute Extrema

3.2 – Rolle’s Theorem

3.2 – Mean Value Theorem

3.2-Finding Increasing and Decreasing Intervals

3.3-Finding Relative (Local) Extrema

3.4-Finding Concavity Intervals 

3.4-Finding Inflection Points

3.4-Identifying Local Extrema with the SECOND Derivative Test

3.5 - Limits at Infinity

3.5 - Finding Horizontal Asymptotes

3.6 Curve Sketching with Calculus (Drawing Pretty, Pretty Pictures)

3.7 - Optimization with Calculus

3.7 - Optimization Example #1

3.7 - Optimization Example #2

3.7 - Optimization Example #3

3.9 - Tangent Line Approximation

3.9 - Differentials

3.9 - Differentials and Error Approximation

 

4.1 - Basic Indefinite Integration

4.1 - An Introduction to Indefinite Integration

4.1 - Initial Value Problems - Solving Basic Differential Equations with an Initial Condition

4.2 - LRAM - Left Riemann Sum

4.2 - RRAM - Right Riemann Sum

4.2 - MRAM - Midpoint Riemann Sum

4.2 - Trapezoidal Sum

4.3 - Basic Integral Properties

4.3 - Introduction to Definite Integrals

4.4 - Basic Definite Integrals

4.4 - Fundamental Theorem of Calculus

4.4 - The SECOND Fundamental Theorem of Calculus

4.4 - Average Value of a Function

4.4 - Accumulation Functions

4.4 - Net Change Theorem

4.4 - AP Motion Problems - Particle Motion

4.5 - Integration using u substitution

4.5 - Definite Integration using u substitution

4.5 - Integrals of Even and Odd Functions showing WHY

4.5 - Integrals of Even and Odd Functions showing HOW (greater depth with examples)

4.5 - Differential Equation with an Initial Condition, aka an Initial Value Problem

4.5 - Definite integral example, including u-substitution

4.6 - Trapezoidal Sum 

 

5.1 - Differentiation of Natural Logarithmic Functions

5.1 - Logarithmic Differentiation - An Application of Implicit Differentiation

5.1 Pre - Logarithm Properties

5.1 Pre - Solving Logarithmic Equations by Exponentiation

5.1 Pre - Solving Natural Logarithmic Equations by Exponentiation

5.2 - Integration Involving Natural Logarithmic Functions

5.3 - Derivatives of Inverses

5.3 Pre - Inverse Functions

5.4 - Derivatives of Exponential Functions with Base e

5.4 - Integration of Exponential Functions with Base e

5.5 - Derivatives of Log Functions with Bases Other than e

5.5 - Derivatives of Exponential Functions with Bases Other than e

5.5 - Integration of Exponential Functions with Bases Other than e

5.6 Pre - Inverse Trigonometric Functions

5.6 Pre - Solving Trigonometric Equations

5.6 - Derivatives of Inverse Trigonometric Functions

5.7 - Integration Involving Inverse Trigonmetric Functions

 

6.1 - Euler's Method

6.1 - Slope Fields

 

6.1 - Slope Field Generator to play with.

6.1 - Euler's Method Calculator to play with.

6.2 - Exponential Growth and Decay with Calculus

6.3 - Solving Differential Equations by Separation of Variables

6.3 - Verifying Solutions to Differential Equations

6.3 - Logistic Growth 

 

7.1 - Area Between Two Curves (integrating with respect to x)

7.1 - Area Between Two Curves (integrating with respect to y)

7.1 - Accumulation Functions

7.1 - Finding a Vertical Line that Splits a Region into Two Equal Parts - Basic

7.2 - Volume by Disks

7.2 - Volume by Washers

7.2 - Finding Volume when the Cross-Sectional Shape is Known (Square, Triangle, Rectangle, etc.)

7.3 - Finding Volume Using The Shell Method

7.3 - Video to go with Applet

7.3 Volume by Shells Applet / Other Calculus Applets from the Same Guy

7.4 - Arc Length

7.4 - Surface Area of a Volume of Revolution

7.5 - Work Integrals - Springs

7.5 - Work Integrals - Pumping Liquids

7.5 - Hooke's Law

 

8.1 - Long Division Before Integrating

8.1 - Completing the Square Before Integrating

8.1 Supplemental - Completing the square when a is not equal to 1

8.2 - Integration by Parts - Basic

8.2 - Integration by Parts - General

8.2 - Integration by Parts - Tabular Method

8.3 - Trigonometric Integrals

8.4 - Trigonometric Substitution

8.4 - Trigonometric Substitution

8.4 - Trigonometric Substitution - Full Lecture

8.4 - Specific Video 1 - Quick introduction to the topic with an expectation that students explore the topic further on their own as they work through homework.

8.4 - Specific Video 2 - More in depth introduction to the topic with detailed examples.

8.4 - Specific Video 3 - (Follow up to 8.4 - Specific Video 2)

8.5 - Easy - Partial Fractions with Linear Factors

8.5 - Partial Fractions

8.5 Supplemental - Solving Systems of Equations Using RREF

8.5 Supplemental - Solving Systems of Equations Using Inverse Matrices

8.6 - Integration Using a Table of Integrals

8.7 - L'Hopital's Rule

8.8 - Improper Integrals

 

9.1 - Introduction to Sequences

9.1 Pre - Solving Absolute Value Inequalities

9.1 - Squeeze Theorem and Absolute Value Theorem for Sequences

9.1-9.2 - Writing a Formula for the n-th Term of a Sequence

9.2 - Geometric Series

9.2 - nTH-TERM Test for Divergence

9.2 - Partial Sums of an Infinite Series

9.2 - Sum of a Telescoping Series

9.3 - The Integral Test

9.3 - p-series

9.4 - Limit Comparison Test

9.4 - Direct Comparison Test

9.5 - Alternating Series Test

9.5 - Alternating Series Error Bound

9.5 - Absolute Convergence vs. Conditional Convergence

9.6 - The Ratio Test (Common AP Topic)

9.6 - The Root Test (Rare AP Topic)

9.7 - WATCH THIS ONE FIRST!!!

9.7 - Taylor Polynomials and Taylor Series - Introduction Videos

9.7 - Taylor Polynomial Approximation

9.7 - Taylor Polynomials and Taylor Series - General

9.7 - Taylor Polynomials and Taylor Series - Full Lectures

9.7 - Lagrange Error Bound

9.8 - Finding the Interval of Convergence

9.8 - Radius of Convergence

9.8 - Interval of Convergence: Checking the Endpoints of the Interval

9.8 - Differentiation of Taylor Series

9.8 - Integration of Taylor Series

9.9 - Representation of Functions by GEOMETRIC Power Series

9.9 - Representation of Functions by Power Series

9.10 - Manipulating Known Taylor Series to Construct Taylor Series for Related Functions

9.10 - Finding Taylor Series Using Substitution

9.10 - Binomial Expansion with Taylor Series

9.10 - Multiplying Taylor Series Together

9.10 - Taylor Series - General

9.10 - Taylor Series - Full Lectures

 

9.1-9.10 - 114 Videos Covering all of Chapter 9

 

10.2 - Eliminating the Parameter

10.2 - Graphing Parametric Equations

10.2 - Parameterizing a Curve

10.2 Supplemental - Center Radius Form of a Circle

10.2 Supplemental - Completing the Square to Find the Equation of a Circle in Center Radius Form

10.2 Supplemental - Center Radii Form of an Ellipse

10.2 Supplemental - Center Radii Form of an Ellipse Derivation

10.2 Supplemental - Completing the Square to Find the Equation of an Ellipse in Center Radii Form

10.3 - Calculus in Parametric Coordinates

10.3 - Concavity with Parametric Coordinates

10.3 - Arc Length for Parametric Curves

10.3 - Surface Area for a Revolution in Parametric Coordinates

10.4 - Converting Between Polar Coordinates and Rectangular Coordinates

10.4 - Converting Between Polar EQUATIONS and Rectangular EQUATIONS

10.4 - Polar Graphs

10.4 - Polar Graphs on a TI Graphing Calculator

10.5 - Slope and Tangent Lines in Polar Coordinates

10.5 - Area Integrals in Polar Coordinates

10.5 - Area Bounded by TWO Polar Curves

10.5 - Arc Length in Polar Coordinates

10.5 - Surface Area in Polar Coordinates

 

11.1 - Adding Vectors

11.1 - Subtracting Vectors

11.1 - Magnitude of a Vector

11.1 - Finding a Unit Vector

11.3 - Dot Product of Two Vectors

11.3 - Finding the Angle Between Two Vectors

11.3 - Direction Cosines

11.3 - Projections of a Vector onto another Vector

11.4 - Cross Product