Videos

We have created videos for many topics in first-semester calculus (listed below).

The videos are currently rough drafts—there are visual, audio, and (occasionally) mathematical aspects of the videos that we are in the process of identifying and correcting.

For each topic there is a “Video 0” that features two students working on a problem that motivates the study of the topic and highlights difficulties that many students face. The subsequent videos show how to solve the problem and use this as a springboard to describe the mathematical concept.

Each collection of videos can be viewed on our Ximera platform, which allows students to try the motivating problem, watch all of the videos, and complete diagnostic questions prior to and after watching the videos.

All of the videos can also be found on the YouTube Calcvids channel:

TopicXimera Page (Video 0 Version)Individual Videos
Constant Rates of ChangeLink
  1. Video 0: Pouring Water into a Cylinder
  2. Solving the Problem of Pouring Water
  3. Formal Definition of Constant Rate of Change
Graphing Constant Rate of ChangeLink
  1. Video 0: Cannon Cow!
  2. Graphing Cannon Cow
  3. Graphing Pouring Water
Varying Rates of ChangeLink
  1. Video 0: Pouring Water into an Erlenmeyer Flask
  2. Solving the Problem of Pouring Water
  3. Frozen Yogurt in a Cone
Graphing Varying Rates of ChangeLink
  1. Video 0: Filling a Spherical Flask
  2. Making a Graph for Filling a Spherical Flask
Average Rates of ChangeLink
  1. Video 0: Two Race Cars, Constant Rates, and Average Rates
  2. Average Rates of Change as Constant Rates of Change
  3. A Precise Description of Average Rates of Change
Approximating Instantaneous Rates of ChangeLink
  1. Video 0: The Stationary Baseball
  2. Approximating the Speed of a Baseball
  3. Using Average Rates of Change to Approximate an Instantaneous Rate of Change
l'Hopital's RuleLink
  1. Video 0: Evaluating Indeterminate Limits
  2. Limits of Quotients
ContinuityLink
  1. Video 0: Continuity
  2. Video 1: Continuity
Differentiability and Local Linearity
  1. Video 0: Growth of a Rabbit Population
  2. Local Linearity
Limit Definition of DerivativeLink
  1. Video 0: Rate of Absorbing Ibuprofen
  2. Defining the derivative
Using the Limit Definition of DerivativeLink
  1. Video 0: Using Limits to Compute Derivatives
  2. Using Limits to Compute Instantaneous Rates of Change
Interpreting DerivativesLink
  1. Video 0: Interpreting Derivatives
  2. Interpreting the Derivative
Slopes of Secant and Tangent LinesLink
  1. Video 0: The Imprecision of Tangents
  2. Finding the speed of a baseball at a moment in time graphically
  3. Graphing the rate of change of metabolizing ibuprofen
Graphing DerivativesLink
  1. Video 0: Graphing the Speed of a Baseball
  2. Graphing the Derivative Function
Basic Derivative RulesLink
  1. Video 0: Trying to Use the Limit Definition
  2. The Power Rule
  3. Exponential and Logarithmic Functions
  4. Trigonometric Functions
The Product RuleLink
  1. Video 0: Products of Polynomials
  2. Procedural Description of the Product Rule
  3. Conceptual Explanation of the Product Rule
The Quotient RuleLink
  1. Video 0: Derivatives of Quotients
  2. The Quotient Rule
  3. Why the Quotient Rule Works
The Chain RuleLink
  1. Video 0: A Ripple in a Pond
  2. Computing the Average Rate of Change of a Composition of Functions
  3. How to Use the Chain Rule
  4. Why the Chain Rule Works
Mean Value TheoremLink
  1. Video 0
  2. Video 1: Mean Value Theorem
  3. Video 2: Mean Value Theorem, Why it Works
  4. Video 2 Extended: Mean Value Theorem, Why it Works
Related RatesLink
  1. Video 0
  2. Video 1: Defining a Related Rate Formula
  3. Video 2: Solving A Related Rates Problem
Implicit DifferentiationLink
  1. Video 0: A Complicated Tangent Line
  2. Introduction to Implicit Differentiation
  3. Tangent Lines for a Cardioid
Related RatesComing in 2019
    Introduction to OptimizationLink
    1. Video 0: Maximizing Fuel Economy
    2. Using Derivatives to Maximize Fuel Economy
    3. An Example of Optimization
    Optimization: Algebraic ModelingLink
    1. Video 0: Maximizing an Animal Pen
    2. How to Maximize the Area of a Rectangular Pen
    Introduction to Riemann SumsLink
    1. Video 0: Dust Accumulation on the Mars Rover
    2. Using a Riemann Sum to Approximate the Amount of Accumulated Dust
    3. A Riemann Sum for an Oil Spill
    Riemann Sum NotationLink
    1. Video 0: Writing a Riemann Sum Two Ways
    2. Writing Riemann Sums using Sigma Notation
    Definite IntegralsLink
    1. Video 0: Mars Rover Using a Formula
    2. Definite Integrals as Limits of Riemann Sums
    3. A Definite Integral for an Oil Spill
    The Fundamental Theorem of Calculus, Part 1Link
    The Fundamental Theorem of Calculus, Part 2Link
    1. Video 0: Cumulative Probability from a Normal Distribution
    2. Accumulation Functions
    3. Antiderivatives and Accumulation Functions
    AntiderivativesLink
    1. Video 0: Antiderivatives
    2. Antiderivatves
    3. Antiderivatvies, Part 2
    4. Using Antiderivative Rules
    U-SubstitutionComing in 2019
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