Topic  Ximera Page (Student Problem Solving Version, when available)  Individual Videos 

Constant Rates of Change  Link   Student Problem Solving: Pouring Water into a Cylinder
 Solving the Problem of Pouring Water
 Formal Definition of Constant Rate of Change

Graphing Constant Rate of Change  Link   Student Problem Solving: Cannon Cow!
 Graphing Cannon Cow
 Graphing Pouring Water

Varying Rates of Change  Link   Student Problem Solving: Pouring Water into an Erlenmeyer Flask
 Solving the Problem of Pouring Water
 Frozen Yogurt in a Cone

Graphing Varying Rates of Change  Link   Student Problem Solving: Filling a Spherical Flask
 Making a Graph for Filling a Spherical Flask

Average Rates of Change  Link   Student Problem Solving: Two Race Cars, Constant Rates, and Average Rates
 Average Rates of Change as Constant Rates of Change
 A Precise Description of Average Rates of Change

Approximating Instantaneous Rates of Change  Link   Student Problem Solving: The Stationary Baseball
 Approximating the Speed of a Baseball
 Using Average Rates of Change to Approximate an Instantaneous Rate of Change

Continuity  Link   Student Problem Solving: Continuity
 Continuity

Differentiability and Local Linearity  Link   Student Problem Solving: Growth of a Rabbit Population
 Local Linearity

Limit at a Point    Limit at a Point
 OneSided Limits

Limit Laws    Limit Laws

Limits at Infinity    Limits at Infinity Laws (Coming Soon)

Limit Definition of Derivative  Link   Student Problem Solving: Rate of Absorbing Ibuprofen
 Defining the derivative

Using the Limit Definition of Derivative  Link   Student Problem Solving: Using Limits to Compute Derivatives
 Using Limits to Compute Instantaneous Rates of Change

Interpreting Derivatives  Link   Student Problem Solving: Interpreting Derivatives
 Interpreting the Derivative

Slopes of Secant and Tangent Lines  Link   Student Problem Solving: The Imprecision of Tangents
 Finding the speed of a baseball at a moment in time graphically
 Graphing the rate of change of metabolizing ibuprofen

Graphing Derivatives  Link   Student Problem Solving: Graphing the Speed of a Baseball
 Graphing the Derivative Function

Basic Derivative Rules  Link   Student Problem Solving: Trying to Use the Limit Definition
 The Power Rule
 Exponential and Logarithmic Functions
 Trigonometric Functions

The Product Rule  Link   Student Problem Solving: Products of Polynomials
 Procedural Description of the Product Rule
 Conceptual Explanation of the Product Rule

The Quotient Rule  Link   Student Problem Solving: Derivatives of Quotients
 The Quotient Rule
 Why the Quotient Rule Works

The Chain Rule  Link   Student Problem Solving: A Ripple in a Pond
 Computing the Average Rate of Change of a Composition of Functions
 How to Use the Chain Rule
 Why the Chain Rule Works

l'Hopital's Rule  Link   Student Problem Solving: Evaluating Indeterminate Limits
 Limits of Quotients

Mean Value Theorem  Link   Student Problem Solving
 What the Mean Value Theorem Says
 Why the Mean Value Theorem Works
 Extended version of Why the Mean Value Theorem Works

Related Rates  Link   Student Problem Solving
 Defining a Related Rate Formula
 Solving A Related Rates Problem

Implicit Differentiation  Link   Student Problem Solving: A Complicated Tangent Line
 Introduction to Implicit Differentiation
 Tangent Lines for a Cardioid

Introduction to Optimization  Link   Student Problem Solving: Maximizing Fuel Economy
 Using Derivatives to Maximize Fuel Economy
 An Example of Optimization

Optimization: Algebraic Modeling  Link   Student Problem Solving: Maximizing an Animal Pen
 How to Maximize the Area of a Rectangular Pen

Introduction to Riemann Sums  Link   Student Problem Solving: Dust Accumulation on the Mars Rover
 Using a Riemann Sum to Approximate the Amount of Accumulated Dust
 A Riemann Sum for an Oil Spill

Riemann Sum Notation  Link   Student Problem Solving: Writing a Riemann Sum Two Ways
 Writing Riemann Sums using Sigma Notation

Definite Integrals  Link   Student Problem Solving: Mars Rover Using a Formula
 Definite Integrals as Limits of Riemann Sums
 A Definite Integral for an Oil Spill

Antiderivatives  Link   Student Problem Solving: Antiderivatives
 Antiderivatves, Part 1: Polynomials and the Power Rule
 Antiderivatvies, Part 2: 1/x, Exponential, and Trig Functions
 Using Antiderivative Rules

The Fundamental Theorem of Calculus, Part 1  Link   Student Problem Solving: Computing Total Accumulation
 Computing Total Accumulation

The Fundamental Theorem of Calculus, Part 2  Link   Student Problem Solving: Cumulative Probability from a Normal Distribution
 Accumulation Functions
 Antiderivatives and Accumulation Functions

USubstitution    Student Problem Solving: Evaluating Indefinite Integrals
 USubstitution
