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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 Multiplying by a Conjugate

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

Basic Limit at Infinity Example and 'Shortcut' Information

Limits - L'Hospital's Rule

Indeterminate Products - Basic Idea and Examples

Indeterminate Differences - Basic Idea and Examples

Indeterminate Powers - Basic Idea and Examples

Derivatives

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? Wh at 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

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





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







