# 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:

Topic | Ximera Page (Video 0 Version) | Individual Videos |
---|---|---|

Constant Rates of Change | Link | |

Graphing Constant Rate of Change | Link | |

Increasing Rates of Change | Link | |

Graphing Varying Rates of Change | Link | |

Average Rates of Change | Link | |

Approximating Instantaneous Rates of Change | Link | |

Limits | Coming in 2019 | |

l'Hopital's Rule | Coming in 2019 | |

Continuity | Coming in 2019 | |

Differentiability and Local Linearity | Coming in 2019 | |

Limit Definition of Derivative | Link | |

Slopes of Secant and Tangent Lines | Link | |

Graphing Derivatives | Link | |

Basic Derivative Rules | Link | |

The Product Rule | Link | |

The Quotient Rule | Coming in 2019 | |

The Chain Rule | Link | |

Derivative Theorems | Coming in 2019 | |

Linear Approximation | Coming in 2019 | |

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 | Coming in 2019 | |

U-Substitution | Coming in 2019 | |

An Introduction to (Linear) Differential Equations | Link | |

An Introduction to Euler's Method | Link |