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Connect2Calculus Video Series
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The Meaning of the Limit of a Function

Limits and Continuity

The Intermediate Value Theorem

A Precise Definition of the Limit

Tangents and Rates of Change

Interpreting the Derivative Function

When the Derivative Does Not Exist

Derivatives and Motion: Distance, Velocity, and Acceleration

Basic Differentiation Formulas

The Derivative of a Product of Functions: Damped Oscillations

Derivatives of Trigonometric Functions

Derivatives of Exponential and Logarithmic Functions

Modeling with Exponential Functions

Implicit Differentiation

Rolles Theorem

The Mean Value Theorem

Linear Approximation

L'Hopital's Rule

The Extreme Value Theorem

Increasing and Decreasing Functionsn

Second Derivatives: Concavity

Reviewing Tools for Graphing

Using Calculus to Describe a Graph

Using Graphs and Calculus to Describe Functions

Finding Maximum and Minimum Values

Rates of Change: Chemical Reactions

Related Rates in Two Dimensions

Related Rates in Three Dimensions

Rates of Change and Optimization

Modeling with Exponential Functions

Integration: Foundations and Notation

Integration as a Limit of Sums

The Area Problem

From Riemann Sums to the Definite Integral

Fundamental Theorem of Calculus I: Using Antiderivatives

Fundamental Theorem of Calculus II: Unifying Calculus

Area for an Irregular Planar Region

Volume of an Irregular Space

Arc Length and Surface Area

A One-Dimensional Model for Center of Mass and Moments

Modeling the Spread of an Infection

Direction Fields and Approximate Solutions to Differential Equations

Numerical Solutions to Differential Equations

Partial Sums and Infinite Series

Series Convergence

Modeling: x and y as Functions of t

Arc Length

Surface Area

Constructing Circular Shapes with Polar Coordinates

Polar Coordinates and Calculus

Limit Cycles: Heart Dynamics

Vector Components and Operations

Projection and Dot Products

Surfaces and Vectors, Cross Products

Vector-Valued Functions: Velocity and Direction

Curvature

Tangent Planes

The Chain Rule for Multivariable Functions

The Gradient Vector and Directional Derivatives

Extreme Values for Multivariable Functions: Critical Points

Classifying Critical Points

Lagrange Multipliers

Multiple Integrals: Moments and Centers of Mass

Change of Variables for Multiple Integration

Vector Fields and Gradients

Computing Work Using Vector Fields

Conservative Vector Fields

Greens Theorem

Curl: Turbulence and Rotation

Divergence and Flow

Surface Integrals: Fluid Dynamics and Flux Integrals

The Divergence Theorem

Stokes Theorem
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