Limits

• Basic Limit Information
• Factoring and Cancelling
• Using Common Denominators
• Expanding and Cancelling
• Multiplying by a Conjugate
• Using limit x--> 0 sin(x)/x = 1
• The Sandwich (Squeeze) Theorem For Limits

Limits at Infinity

• Limit at Infinity Example and 'Shortcut'
• Limit at Infinity - Radicals Present

Continuity

• Continuity and Types of Discontinuities
• Discontinuities of Piecewise Functions

Derivative Rules

• Basic Derivative Formulas
• Basic Derivative Examples
• Finding the Equation of a Tangent Line
• Find the Linearization at a Point
• 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

Chain Rule

• MathTV Chain Rule 1
• MathTV Chain Rule 2
• MathTV Chain Rule 3
• 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 #1
• More Complicated Derivative Examples #2
• Using the Product and Chain Rules

Implicit Differentiantion

• Introduction
• Introduction Part 2
• Introduction Part 3
• Introduction Part 4
• Implicit Differentiation
• More Implicit Differentiation #1
• More Implicit Differentiation #2
• MathTV Implicit Differentiation

Related Rates

• MathTV Related Rates 1
• MathTV Related Rates 2
• MathTV Related Rates 3
• Related Rates Problems
• Related Rates Involving a Cone
• A point moving on a graph
• Related Rates - With Trigonometry
• Baseball Diamond Example
• Balloon & Bike
• Conical Pile of Sand
• Shadow of Falling Ball

Inverse Trig Function Rules

• Review of the Unit Circle
• Inverse Trig Derivatives
• Inverse Trig Derivative Ex. #1
• Inverse Trig Derivative Ex. #2
• Inverse Trig Derivative Ex. #3
• More Inverse Trig Examples

Inverse Functions & Logarithmic Differentiation

• Properties of Logarithms
• More Log Properties
• MathTV Logs and Exponentials
• Basic Logarithmic Differentiation
• MathTV Logarithmic Differentiation
• Logarithmic Differentiation Example 2
• Derivatives with ln(x), log(x), etc.
• Derivatives of Exponential Functions
• Derivatives with e^x, a^x, etc.

Linearization, Partial Derivates & Newton's Method

• Linearization
• Finding Partial Derivatives
• The General Chain Rule - Part 1
• The General Chain Rule - Part 2
• Newtons Method

Critical Points & Mean Value Theorem

• Basic Inc/Dec, Local Max/Min
• Finding Critical Points - Example 1
• Finding Critical Points - Example 2
• Mean Value Theorem

Max & Min

• Examples Using the First Derivative
• Another First Derivative Example
• Intervals of Increase/Decrease, Local Max/Mins
• Lagrange Multipliers
• Finding Local Max/Min/Saddle Points - Ex. #1
• Finding Local Max/Min/Saddle Points - Ex. #2

Sketching Curves

• Curve Sketching Using Calculus - Part 1 of 2
• Curve Sketching Using Calculus - Part 2 of 2

Concavity & The Second Derivative

• Second Derivative - Local Max/Min
• Concave Up/Concave Down

Optimization

• Light Through a Window
• Trapezoidal Trough
• Optimization Problem #1
• Optimization Problem #2
• Optimization Problem #3

Limits & L'Hospital's Rule

• Indeterminate Quotients
• Indeterminate Products
• Indeterminate Differences
• Indeterminate Powers

Basic Integration

• Summation Notation
• The Definite Integral Definition
• Approximating a Definite Integral
• Trapezoid Rule for Defininte Integrals
• Basic Integration Formulas
• Basic Indefinite Integral Examples
• More Basic Integration Problems
• Basic Definite Integral Example

U-Substitution

• Integration Using U-Substitution
• More Complicated U-Substitution Problems
• Indefinite Integral - U-substitution
• Definite Integral - U-substitution
• Integration with Inverse Trig Functions

Integration By Parts

• 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

• 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

Trig Substitutions

• Trig Substitution - Example 1 Part 1
• Trig Substitution - Example 1 Part 2
• Trig Substitution - Example 2
• Trig Substitution - Example 3 Part 1
• Trig Substitution - Example 3 Part 2

Partial Fractions

• How to Decompose a Rational Function
• Determine the Coefficients
• A Complete Partial Fractions Problem
• Using a Rationalizing Substitution
  

Improper Integrals

• Basic Improper Integral Examples
• Improper Integral/L'Hospitals Rule
• Infinity in the Upper and Lower Limit
• Infinite Discontinuity at an Endpoint
• Infinite Discontinuity in the Middle

Double & Triple Integrals, Line Integrals, and Differential Equations

• Double Integrals - Rectangular Regions
• Double Integrals - General Regions
• Double Integral - Polar Coordinates - #1
• Double Integral - Polar Coordinates - #2
• Double Integral - Polar Coordinates - #3
• Evaluating a Triple Integral
• Triple Integral in Spherical Coordinates

Line Integrals

• Evaluating a Line Integral

Volume by Slicing

• Volumes of a Sphere by Slicing

Volume with Disks and Washers

• Solids of Revolution - Circular Cross Sections
• Solids of Revolution - The Washer Method
• Volumes Using Disks/Washers
• Disk/Washer- Rotate about Horizontal Line
• Disk/Washer - Rotate about Vertical Line
• Using the Disk/Washer Method

Volume with Cylindrical Shells

• Volumes of Revolution Using Cylindrical Shells
• Volumes with Cylindrical Shells

Arc Length/Surface Area

• Length of a Plane Curves Part 1
• Length of a Plane Curves Part 2
• Arc Length
• Finding Surface Area - Part 1 of 2
• Finding Surface Area - Part 2 of 2

Work Problems

• Leaky Bag of Sand
• Pumping a Half-Full Tank
• Empty a Tank Full of Water

Fluid Forces

• Fluid Force on a Vertical Plate

Heat Transfer

• Heat Transfer: Newton's Law of Cooling

Centroids & Centers of Mass

• Moments and Centers of Mass - Part 1
• Moments and Centers of Mass - Part 2
• Centroids/Centers of Mass - Part 1
• Centroids/Centers of Mass - Part 2
  

Differential Equations

• First Order Separable Differential Eqns.
• First Order Linear Differential Equations

Polar Coordinates

• Polar Coordinates - The Basics
• Polar Coordinates - Basic Graphing
• Graphing a Polar Curve - Part 1
• Graphing a Polar Curve - Part 2
  

Parametric Curves

• Parametric Curves - Basic Graphing
• Parametric Functions - First Derivatives
• Parametric Functions - Second Derivs.
• Parametric Curves - Calculating Areas

Sample Questions #1-14

• AP / AB Sample Questions 1 & 2
• AP / AB Sample Questions 3 & 4
• AP / AB Sample Questions 5 & 6
• AP / AB Sample Questions 7 & 8
• AP / AB Sample Questions 9 & 10
• AP / AB Sample Questions 11 & 12
• AP / AB Sample Questions 13 & 14

Sample Questions #15-28

• AP / AB Sample Questions 15 & 16
• AP / AB Sample Questions 17 & 18
• AP / AB Sample Questions 19 & 20
• AP / AB Sample Questions 21 & 22
• AP / AB Sample Questions 23 & 24
• AP / AB Sample Questions 25 & 26
• AP / AB Sample Questions 27 & 28