Calculus - Single Variable

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Calculus - Part 1: Limits and Derivatives

Limits 1a - Definitions and Concepts

Limits 1b - Delta-Epsilon Formulation

Limits 1c - Limit Failure

Limits 1d - Polynomials and Rational Functions

Limits 1e - Compositions and the Squeeze Theorem

Limits 1f - Trigonometric Functions

Examples of Limits

Continuity 1a - Definition and Basic Concepts

Continuity 1b - Polynomial/Rational Functions and The Extreme Value Theorem

Examples of Continuity

Fast Solution of Inequality Using Continuity

Bisection Method 1

Bisection Method 2

Vertical Asymptotes 1a

Vertical Asymptotes 1b

Definition of Tangent Line

Example of Tangent Line

Definition of Derivative

Power Rule for Derivatives

Derivatives of Polynomials

Tangent Line to x^2 - 4x

Horizontal Tangent Lines to a Polynomial

Derivative of sin(x) and cos(x)

Tangent Lines to sin(x)

Motion in a Line

The Product Rule

General Product Rule

Power Rule for Rational Exponents

The Quotient Rule

Trig Derivatives

Examples of Trig Derivatives

Tangent Lines to sec(x)

Tangent Lines to cot(x)

The Chain Rule

Example of Chain Rule 1 - Basic examples

Example of Chain Rule 2 - Approximation with Tangent Line

Example of Chain Rule 3 - Trig Functions

Example of Chain Rule 4 - Triple Chain Rule

Higher Order Derivatives

Graphs and Higher Order Derivatives

Motion of a Spring

Implicit Differentiation 1 - Definition and Basic Concepts

Implicit Differentiation 2 - Basic Example

Implicit Differentiation 3 - Approximation with Tangent Line

Implicit Differentiation 4 - Example with Trig Functions

Implicit Differentiation 5 - Higher Derivatives

Related Rates

Example of Related Rates 1

Example of Related Rates 2

Extreme Value Theorem

Example of Extreme Value Theorem 1

Example of Extreme Value Theorem 2

Example of Extreme Value Theorem 3

Rolle's Theorem

Mean Value Theorem

Increasing/Decreasing and Derivatives 1

Increasing/Decreasing and Derivatives 2

Example of Increasing/Decreasing 1

Example of Increasing/Decreasing 2

Example of Increasing/Decreasing 3

First/Second Derivative Test for f(x) = x^4 - 12x^3

First/Second Derivative Test for f(x) = sin(x)

First/Second Derivative Test for f(x) = x^2 - 6x^{4/3}

Concavity and the Second Derivative

Concavity for f(x) = sin(x)

Concavity for f(x) = (x^2 - 36)/(x-2)

Concavity for f(x) = |x^2 - 4x - 12|

Example of Limit at Infinity 1

Example of Limit at Infinity 2

Example of Limit at Infinity 3

Checklist for Sketching Functions

Graph of f(x) = x^4 - 8x^3

Graph of f(x) = (x-2)/(x-1)

Graph of f(x) = sin(x) + cos(x)

Graph of f(x) = sin(x)/(1+cos(x))

Graph of f(x) = x^{4/3} - 8x^{2/3}

Optimization 1

Optimization 2

Optimization 3

Optimization - Maximizing Profit

Newton's Method 1

Newton's Method 2

Differentials 1

Differentials 2

Calculus - Part 2: Basic Integration

Definition of Antiderivative

Antiderivative of a Polynomial

Antiderivative of (x-1)(x-2)/sqrt(x^3)

Basic Trig Antiderivatives

Antiderivative of tan^2(x)

Antiderivative of sin(x)/[1-sin^2(x)]

Visualizing an Antiderivative

Solving Differential Equations

Equations of Motion

Graphing f(x) from f'(x)

Antiderivative of a Piecewise-Defined Function

Overview of Rectangular Approximation of Area

Rectangular Approximation of Area

Overview of Summation Formulas

General Method for Integer Sum Formula

Riemann Sum with Signed Area

Limit Summation Formula

Limit Process for Area

Definition of Definite Integral

Definite Integral as Area 1 - Using the Graph

Definite Integral as Area 2 - Breaking Up the Region

Definite Integral as Area 3 - Area Below the x-axis

The First Fundamental Theorem of Calculus

Area Under a Curve 1

Area Under a Curve 2

The Mean Value Theorem for Integrals

Example of Mean Value Theorem for Integrals

The Second Fundamental Theorem of Calculus

Example of 2nd Fundamental Theorem of Calculus 1

Example of 2nd Fundamental Theorem of Calculus 2

Integration By Substitution: Antiderivatives

Integration by Substitution: Definite Integrals

Integration by Substitution 1

Integration by Substitution 2

Integration by Substitution 3

Integration by Substitution 4

Integration by Substitution 5

Trapezoid Rule

Simpson's Rule