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 “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:

TopicXimera Page (Student Problem Solving Version, when available)Individual Videos
Constant Rates of ChangeLink
  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 ChangeLink
  1. Student Problem Solving: Cannon Cow!
  2. Graphing Cannon Cow
  3. Graphing Pouring Water
Varying Rates of ChangeLink
  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 ChangeLink
  1. Student Problem Solving: Filling a Spherical Flask
  2. Making a Graph for Filling a Spherical Flask
Average Rates of ChangeLink
  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 ChangeLink
  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
ContinuityLink
  1. Student Problem Solving: Continuity
  2. Continuity
Differentiability and Local LinearityLink
  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 (Coming Soon)
Limits at Infinity
  1. Limits at Infinity Laws (Coming Soon)
Limit Definition of DerivativeLink
  1. Student Problem Solving: Rate of Absorbing Ibuprofen
  2. Defining the derivative
Using the Limit Definition of DerivativeLink
  1. Student Problem Solving: Using Limits to Compute Derivatives
  2. Using Limits to Compute Instantaneous Rates of Change
Interpreting DerivativesLink
  1. Student Problem Solving: Interpreting Derivatives
  2. Interpreting the Derivative
Slopes of Secant and Tangent LinesLink
  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 DerivativesLink
  1. Student Problem Solving: Graphing the Speed of a Baseball
  2. Graphing the Derivative Function
Basic Derivative RulesLink
  1. Student Problem Solving: Trying to Use the Limit Definition
  2. The Power Rule
  3. Exponential and Logarithmic Functions
  4. Trigonometric Functions
The Product RuleLink
  1. Student Problem Solving: Products of Polynomials
  2. Procedural Description of the Product Rule
  3. Conceptual Explanation of the Product Rule
The Quotient RuleLink
  1. Student Problem Solving: Derivatives of Quotients
  2. The Quotient Rule
  3. Why the Quotient Rule Works
The Chain RuleLink
  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 RuleLink
  1. Student Problem Solving: Evaluating Indeterminate Limits
  2. Limits of Quotients
Mean Value TheoremLink
  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 RatesLink
  1. Student Problem Solving
  2. Defining a Related Rate Formula
  3. Solving A Related Rates Problem
Implicit DifferentiationLink
  1. Student Problem Solving: A Complicated Tangent Line
  2. Introduction to Implicit Differentiation
  3. Tangent Lines for a Cardioid
Introduction to OptimizationLink
  1. Student Problem Solving: Maximizing Fuel Economy
  2. Using Derivatives to Maximize Fuel Economy
  3. An Example of Optimization
Optimization: Algebraic ModelingLink
  1. Student Problem Solving: Maximizing an Animal Pen
  2. How to Maximize the Area of a Rectangular Pen
Introduction to Riemann SumsLink
  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 NotationLink
  1. Student Problem Solving: Writing a Riemann Sum Two Ways
  2. Writing Riemann Sums using Sigma Notation
Definite IntegralsLink
  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
AntiderivativesLink
  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 1Link
  1. Student Problem Solving:
  2. Computing Total Accumulation
The Fundamental Theorem of Calculus, Part 2Link
  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