Videos

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

For each topic there is a “Student Problem Solving” 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:

TopicIndividual Videos
Constant Rates of Change
  1. Student Problem Solving: Pouring Water into a Cylinder
  2. Solving the Problem of Pouring Water
  3. Formal Definition of Constant Rate of Change
Graphing Constant Rate of Change
  1. Student Problem Solving: Cannon Cow!
  2. Graphing Cannon Cow
  3. Graphing Pouring Water
Varying Rates of Change
  1. Student Problem Solving: Pouring Water into an Erlenmeyer Flask
  2. Solving the Problem of Pouring Water
  3. Frozen Yogurt in a Cone
Graphing Varying Rates of Change
  1. Student Problem Solving: Filling a Spherical Flask
  2. Making a Graph for Filling a Spherical Flask
Average Rates of Change
  1. Student Problem Solving: 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 Change
  1. Student Problem Solving: The Stationary Baseball
  2. Approximating the Speed of a Baseball
  3. Using Average Rates of Change to Approximate an Instantaneous Rate of Change
Continuity
  1. Student Problem Solving: Continuity
  2. Continuity
Differentiability and Local Linearity
  1. Student Problem Solving: Growth of a Rabbit Population
  2. Local Linearity
Limit at a Point
  1. Limit at a Point
  2. One-Sided Limits
Limit Laws
  1. Limit Laws
Limit Definition of Derivative
  1. Student Problem Solving: Rate of Absorbing Ibuprofen
  2. Defining the derivative
Using the Limit Definition of Derivative
  1. Student Problem Solving: Using Limits to Compute Derivatives
  2. Using Limits to Compute Instantaneous Rates of Change
Interpreting Derivatives
  1. Student Problem Solving: Interpreting Derivatives
  2. Interpreting the Derivative
Slopes of Secant and Tangent Lines
  1. Student Problem Solving: 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 Derivatives
  1. Student Problem Solving: Graphing the Speed of a Baseball
  2. Graphing the Derivative Function
Basic Derivative Rules
  1. Student Problem Solving: Trying to Use the Limit Definition
  2. The Power Rule
  3. Exponential and Logarithmic Functions
  4. Trigonometric Functions
The Product Rule
  1. Student Problem Solving: Products of Polynomials
  2. Procedural Description of the Product Rule
  3. Conceptual Explanation of the Product Rule
The Quotient Rule
  1. Student Problem Solving: Derivatives of Quotients
  2. The Quotient Rule
  3. Why the Quotient Rule Works
The Chain Rule
  1. Student Problem Solving: 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
l'Hopital's Rule
  1. Student Problem Solving: Evaluating Indeterminate Limits
  2. Limits of Quotients
Mean Value Theorem
  1. Student Problem Solving
  2. What the Mean Value Theorem Says
  3. Why the Mean Value Theorem Works
  4. Extended version of Why the Mean Value Theorem Works
Related Rates
  1. Student Problem Solving
  2. Defining a Related Rate Formula
  3. Solving A Related Rates Problem
Implicit Differentiation
  1. Student Problem Solving: A Complicated Tangent Line
  2. Introduction to Implicit Differentiation
  3. Tangent Lines for a Cardioid
Introduction to Optimization
  1. Student Problem Solving: Maximizing Fuel Economy
  2. Using Derivatives to Maximize Fuel Economy
  3. An Example of Optimization
Optimization: Algebraic Modeling
  1. Student Problem Solving: Maximizing an Animal Pen
  2. How to Maximize the Area of a Rectangular Pen
Introduction to Riemann Sums
  1. Student Problem Solving: 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 Notation
  1. Student Problem Solving: Writing a Riemann Sum Two Ways
  2. Writing Riemann Sums using Sigma Notation
Definite Integrals
  1. Student Problem Solving: Mars Rover Using a Formula
  2. Definite Integrals as Limits of Riemann Sums
  3. A Definite Integral for an Oil Spill
Antiderivatives
  1. Student Problem Solving: Antiderivatives
  2. Antiderivatves, Part 1: Polynomials and the Power Rule
  3. Antiderivatvies, Part 2: 1/x, Exponential, and Trig Functions
  4. Using Antiderivative Rules
The Fundamental Theorem of Calculus, Part 1
  1. Student Problem Solving: Computing Total Accumulation
  2. Computing Total Accumulation
The Fundamental Theorem of Calculus, Part 2
  1. Student Problem Solving: Cumulative Probability from a Normal Distribution
  2. Accumulation Functions
  3. Antiderivatives and Accumulation Functions
U-Substitution
  1. Student Problem Solving: Evaluating Indefinite Integrals
  2. U-Substitution
The S-I-R Model
  1. Thinking About the Spread of Disease in a Population
  2. Rate (Differential) Equations for the Spread of Disease
  3. A System of Equations for the SIR Model
An Introduction to Euler's Method
  1. Introduction to Euler's Method
  2. Using Euler's Method to Model the Spread of an Infection
  3. Spreadsheet Techniques for Euler's Method
  4. Step Size and Constant Rate Assumptions in Euler's Method
An Introduction to (Linear) Differential Equations
  1. Understanding Differential Equations
  2. Writing Differential Equations
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