Videos
We have created videos for many topics in firstsemester 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:
Topic  Ximera Page (Video 0 Version)  Individual Videos 

Constant Rates of Change  Link  
Graphing Constant Rate of Change  Link  
Varying Rates of Change  Link  
Graphing Varying Rates of Change  Link  
Average Rates of Change  Link  
Approximating Instantaneous Rates of Change  Link  
l'Hopital's Rule  Link  
Continuity  Link  
Differentiability and Local Linearity  
Limit Definition of Derivative  Link  
Using the Limit Definition of Derivative  Link  
Interpreting Derivatives  Link  
Slopes of Secant and Tangent Lines  Link  
Graphing Derivatives  Link  
Basic Derivative Rules  Link  
The Product Rule  Link  
The Quotient Rule  Link  
The Chain Rule  Link  
Mean Value Theorem  Coming in 2019  
Extreme Value Theorem  Coming in 2020  
Implicit Differentiation  Link  
Related Rates  Coming in 2019  
Introduction to Optimization  Link  
Optimization: Algebraic Modeling  Link  
Introduction to Riemann Sums  Link  
Riemann Sum Notation  Link  
Definite Integrals  Link  
The Fundamental Theorem of Calculus, Part 1  Link  
The Fundamental Theorem of Calculus, Part 2  Link  
Antiderivatives  Link  
USubstitution  Coming in 2019  
An Introduction to (Linear) Differential Equations  Link 

An Introduction to Euler's Method  Link 
