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CALCULUS TOPICS

Limits

 Basic Limit Information

Calculating Limits by Factoring and Cancelling

Calculating Limits by Getting Common Denominators

Calculating Limits by Expanding and Cancelling

Calculating Limits by Multiplying by a Conjugate

Calculating Limits by using: limit x--> 0 [sin(x)/x] = 1

Calculating Limits Involving Absolute Value

Infinite Limits

The Squeeze Theorem For Limits

 Limits at Infinity (See also Improper Integrals for More Examples!)

 Basic Limit at Infinity Example and 'Shortcut' Information

Limit at Infinity Example with Radicals Present - Two Examples


Limits - L'Hospital's Rule

Indeterminate Quotients - Basic Idea and Examples

Indeterminate Products - Basic Idea and Examples

Indeterminate Differences - Basic Idea and Examples

Indeterminate Powers - Basic Idea and Examples

 

Continuity

Continuity - Basic Idea and Types of Discontinuities

Continuity - Examples of Finding Discontinuities of Piecewise Functions
 

 Derivatives

Basic Derivative Formulas

Basic Derivative Examples

Sketching the Derivative of a Function

Finding the Equation of a Tangent Line

Find the Linearization at a Point

Finding the Derivative Using the Definition of the Derivative

 Derivatives Using the Product Rule

More Examples Using the Product Rule

 Derivatives Using the Quotient Rule

More Examples Using the Quotient Rule

 Derivatives Using the Chain Rule

More Chain Rule Examples

Chain Rule - Harder Example # 1

Chain Rule - Harder Example # 2

Chain Rule - Harder Example # 3

 More Complicated Derivative Examples

More Complicated Derivative Examples - Part 2

Using the Product and Chain Rule to Find a Derivative - Then Factoring and Simplifying

 Derivatives Using Implicit Differentiation

Derivatives Using Implicit Differentiation - More Examples #1

Derivatives Using Implicit Differentiation - More Examles #2

Related Rates Problems and Implicit Differentiation

Related Rates Involving a Cone

Related Rates - A point moving on a graph

Related Rates - With Trigonometry

Related Rates - Baseball Diamond Example

Logarithmic Differentiation - Basic Idea and Example

Logarithmic Differentiation Example 2

Derivatives Involving Logarithmic Functions - ln(x), log (x), etc.

Properties of Logarithms - Logarithmic Functions (algebra stuff!!)

Derivatives involving Exponential Functions - e^x, a^x, etc

Derivatives Involving Inverse Trigonometric Functions

Inverse Trigonometric Derivative Example 1

Inverse Trigonometric Derivative Example 2

Inverse Trigonometric Derivative Example 3

More Examples Involving Inverse Trig Functions

Finding Partial Derivatives

The General Chain Rule - Part 1

The General Chain Rule - Part 2

Newtons Method

Where a Function is Increasing and Decreasing , Finding Local Maximums and Local Minimums

What does it mean for a function to be increasing/decreasing? What is a local maximum and a local minimum? Basic Idea

Finding Critical Numbers - Example 1

Finding Critical Numbers - Example 2cr

Using the First Derivative to find where a funtion is increasing/decreasing and where the local maximums and minimums occur- 2 basic examples

Using the First Derivative to find where a funtion is increasing/decreasing and where the local maximums and minimums occur - Harder Example

Lagrange Multipliers - Finding Maximums or Minimums

Using the Second Derivative to Find Local Maximums and Local Minimums

Using the Second Derivative to Find Where a Function is Concave Up/Concave Down

Optimization Problem #1

Optimization Problem #2

Optimization Problem #3

Finding Local Maximums, Local Minimums and Saddle Points - Example 1

Finding Local Maximums, Local Minimums and Saddle Points - Example 2

Curve Sketching Using Calculus - Part 1 of 2

Curve Sketching Using Calculus - Part 2 of 2

Directional Derivatives

Differentials and Approximations



Integration Techniques / Antiderivatives

 Summation Notation

 The Definite Integral - Understanding the Definition

Approximating a Definite Integral Using Rectangles

Trapezoidal Rule to Approximate a Definite Integral

Simpson's Rule to Approximate a Definite Integral

Simpson's Rule and Error Bounds

Calculating a Definite Integral Using Riemann Sums - Part 1


Calculating a Definite Integral Using Riemann Sums - Part 2

 Basic Integration Formulas - turn down your volume, I was too close to the mic! : )

 Basic Antiderivate Examples - Indefinite Integral

More Basic Integration Problems

 Basic Definite Integral Example

 Indefinite Integral - U-substitution

 Definite Integral - U-substitution

More Integration Using U-Substitution

More Complicated U-Substitution Problems

Integration Involving Inverse Trigonometric Functions

 Integration By Parts - Indefinite Integral

 Integration By Parts - Definite Integral

More Integration By Parts Examples

Using Integration Parts Twice

Using Integration By Parts - A "Loopy" Example

Trigonometric Integrals - Part 1 of 6

Trigonometric Integrals - Part 2 of 6

Trigonometric Integrals - Part 3 of 6

Trigonometric Integrals - Part 4 of 6

Trigonometric Integrals - Part 5 of 6

Trigonometric Integrals - Part 6 of 6

 Trigonometric Substitution - Example 1 Part 1 (the last part is cut off, but finished in the next video!

Trigonometric Substituion - Example 1 Part 2 

Trigonometric Substitution - Example 2

Trigonometric Substitution - Example 3 Part 1

Trigonometric Substitution - Example 3 Part 2

Partial Fractions - The Different Types of Partial Fraction Decompositions / How to Decompose a Rational Function

Partial Fractions - How to Determine the Coefficients of a Partial Fraction Decomposition

A Complete Partial Fractions Problem

A Complete Partial Fractions Problem Using a Rationalizing Substitution

Calculating Double Integrals Over Rectangular Regions

Calculating Double Integrals Over General Regions

Reversing the Order of Integration - Example 1

Reversing the Order of Integration - Example 2

Finding Areas in Polar Coordinates

Double Integral using Polar Coordinates - Part 1

Double Integral using Polar Coordinates - Part 2

Double Integral using Polar Coordinates - Part 3

Evaluating a Triple Integral

Evaluating a Triple Integral in Spherical Coordinates

Line Integrals - Evaluating a Line Integral

Using Integration to Solve First Order Linear Differential Equations

Finding Centroids/Centers of Mass - Part 1

Finding Centroids/Centers of Mass - Part 2

Improper Integrals

Basic Improper Integral Examples and Information

Example of a More Complicated Improper Integral using L'Hospitals Rule

Improper Integral Example with Infinity in the Upper and Lower Limit

Improper Integral with an Infinite Discontinuity at an Endpoint

Improper Integral with an Infinite Discontinuity in the Middle of the Interval


Volumes of Revolution

Calculating Volumes of Revolution using the Disk/Washer Method - Rotating Regions about a Horizontal Line (for ex., the X-axis)

  Calculating Volumes of Revolution using the Disk/Washer Method - Rotating Regions about a Vertical Line (for ex., the Y-axis)

Calculating Volumes of Revolution Using the Disk/Washer Method


Work Problems

Finding the Work To Empty a Tank Full of Water


Polar Coordinates / Parametric Curves

Polar Coordinates - The Basics

Polar Coordinates - Basic Graphing

Parametric Curves - Basic Graphing

Parametric Functions - Finding First Derivatives

Parametric Functions - Finding Second Derivatives

Parametric Curves - Calculating Areas

Graphing a Polar Curve - Part 1

Graphing a Polar Curve - Part 2


Arc Length /Surface Area

Arc Length

Finding Surface Area - Part 1 of 2

Finding Surface Area - Part 2 of 2


 Sequences and Series

What is a Sequence? Examples Showing Convergence or Divergence

More Examples of Showing Sequences Converging or Diverging

 What is a Series? Discusses Geometric Series and the Test for Divergence

Geometric Series - Finding the Fraction Representation of a Rational Number Written as a Decimal

 More Examples of Geometric Series and the Test for Divergence (Part 1)

 Part 2 of the Above Video That Got Cut Off! (Part 2)

Telescoping Series

Showing A Series Diverges - Using Partial Sums

Basic Idea of the Integral Test for Series

Example 1 using the Integral Test for Series

Example 2 using the Integral Test for Series

Example 3 Using the Integral Test for Series

 Basic Idea of the Limit Comparison Test and Direct Comparison Test for Series

 Two Basic Examples: One using the Direct Comparison Test, One using the Limit Comparison Test

 More Examples using the Direct Comparison Test and the Limit Comparison Test

 Alternating Series, Basic Idea and Example

More Alternating Series Examples

Using The Alternating Series Estimation Theorem

Ratio Test to Determine if a Series Converges - Example 1

Ratio Test to Determine if a Series Converges - Example 2

Root Test for Series

Power Series for Functions by Manipulating the Power Series Representation for 1/(1-x)

Power Series - Finding the Interval of Convergence

Differentiating and Integrating Power Series to Derive New Power Series Expressions

Multiplying and Dividing Power Series

Taylor and MacLaurin Series - Example 1

Taylor and MacLaurin Series - Example 2

Taylor's Remainder Theorem aka Taylor's Inequality

The Binomial Series - Example 1

The Binomial Series - Example 2 - There is a small mistake at the very end! The power should be (2n+1)


 Differential Equations

Solving Separable First Order Differential Equations

Solving First Order Linear Differential Equations (there is a small mistake that is noted during the video)

Solving Exact Differential Equations

Homogeneous Second Order Linear Differential Equations


 Vectors

Finding the Magnitude or Length of a Vector

Calculating the Dot Product Between Two Vectors

Cross Product - Finding the Cross Product of Two Vectors

Torque - An Application of the Cross Product

Tangent Plane Approximations

Finding the Domain of a Vector Function

Finding the Limit of a Vector Function

Finding the Scalar Equation of a Plane

Directional Derivatives

The Gradient Vector - Notation and Definition

The Jacobian

AP/AB Calculus Videos

AB Calculus - Sample Questions 1 and 2

AB Calculus - Sample Questions 3 and 4

AB Calculus - Sample Questions 5 and 6

AB Calculus - Sample Questions 7 and 8

AB Calculus - Sample Questions 9 and 10

AB Calculus - Sample Questions 11 and 12

AB Calculus - Sample Questions 13 and 14

AB Calculus - Sample Questions 15 and 16

AB Calculus - Sample Questions 17 and 18

AB Calculus - Sample Questions 19 and 20

AB Calculus - Sample Questions 21 and 22

AB Calculus - Sample Questions 23 and 24

AB Calculus - Sample Questions 25 and 26

AB Calculus - Sample Questions 27 and 28


AP/BC Math Videos

BC Calculus - Sample Questions 1 and 2

BC Calculus - Sample Questions 3 and 4

BC Calculus - Sample Questions 5 and 6

BC Calculus - Sample Questions 7 and 8

BC Calculus - Sample Questions 9 and 10

BC Calculus - Sample Questions 11 and 12

BC Calculus - Sample Questions 13 and 14

BC Calculus - Sample Questions 15 and 16