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
Increasing 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
LimitsComing in 2019
    l'Hopital's RuleComing in 2019
      ContinuityComing in 2019
        Differentiability and Local LinearityComing in 2019
        Limit Definition of DerivativeLink
        1. Video 0: Rate of Absorbing Ibuprofen
        2. Defining 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 RuleComing in 2019
          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
          Derivative TheoremsComing in 2019
          Linear ApproximationComing in 2019
          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
            AntiderivativesComing in 2019
              U-SubstitutionComing in 2019
                An Introduction to (Linear) Differential EquationsLink
                An Introduction to Euler's MethodLink
                1. Video 0: Computing the Spread of an Infection
                2. Using Euler's Method to Model the Spread of an Infection