Flipped Math
Calculus AB/BC - Can Change Occur at an Instant?
Be instantly transfixed by the idea of instantaneous rates of change. Scholars watch an informative video that introduces the fathers of calculus, Newton and Leibniz. They then learn about instantaneous rates of change by first...
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The Second Fundamental Theorem of Calculus
How many fundamental theorems are there? The Second Fundamental Theorem of Calculus is also known as the second part of the Fundamental Theorem of Calculus. Here's a video that introduces the theorem as the method to evaluate a definite...
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Separation of Variables and Initial Value Problem
Ap Calculus classes learn how to solve a differential equation by getting like variables together with a video that presents an example of how to solve a differential equation by using the method of separation of variables. The example...
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Calculus AB/BC - Selecting Procedures for Derivatives
Don't get lost trying to memorize all those derivative rules. Scholars review the different methods at their disposal to determine derivatives from Units 2 and 3. They fill out a graphic organizer and then complete a set of practice...
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Calculus AB/BC - Solving Related Rates Problems
A solution to a lack of resources on related rates awaits. Viewers of an educational video learn how to solve related rates problems. They build on their prior experience of related rates to write equations for contextual situations,...
Curated OER
Newton Leibniz and Usain Bolt
What do Usain Bolt and calculus have in common? Using Usain Bolt as an example of distance traveled over a period of time, Sal shows why you need differential calculus to answer the question of how fast something is traveling at a...
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Properties of the Definite Integral
What are the properties that can be associated with the definite integral? The AP Calculus video lists nine properties of the definite integral and provides explanations of why the properties hold for integrals in language that is simple...
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Calculus AB/BC - Removing Discontinuities
It's called a removable discontinuity for a reason. After reviewing the conditions for a removable discontinuity to exist, scholars watch an informative video to learn how to remove the discontinuity. They look at several examples...
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Calculus AB/BC - Defining Continuity at a Point
Learning about continuity is a continuous process. An educational video first shows individuals the definition of continuity at a point. They see several examples on the topic and then investigate how to identify the types of...
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Calculus AB/BC - Selecting Techniques for Antidifferentiation
Here's the antidote to ignorance on antiderivatives. Pupils try a set of problems that require finding the antiderivative. They choose from different techniques they already know to determine the indefinite integral or the definite...
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Volumes by Washers
Here's an AP Calculus resource that works an example problem of finding the volume where the cross sections of a solid are washer shaped. In the example the axis of rotation is vertical, creating horizontal washers.
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Introduction to Limits (HD)
Sal begins his explanation of limits with a few basic examples and takes a more intuitive point of view before looking at a formal mathematical definition in later videos. He starts by introducing the notation for limits and describes...
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Finding The Area Under a Curve Using Rectangles
Here's an AP Calculus video that provides a discussion on determining an approximate for the area under a curve by calculating the sum of areas of rectangles that is smaller than the area and by finding the sum of areas of rectangles...
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Solving Integrals Using Substitution
The concept of solving integrals by substitution with trigonometric functions is modeled by a video designed for AP Calculus classes. The narrator works an example problem using substitution and shows that careful substitution makes...
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Integration by Parts
Class members view how to derive the formula to integrate by parts with a video that uses the Product Rule from the beginning of AP Calculus to derive the rule to integrate products. The resource shows the formula in two different forms,...
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Areas Between Curves
There are times that it is necessary to add areas to find the area between the curves. The video for AP Calculus presents how to find the area between curves by subtracting the area under the lower curve from the area under the upper...
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Volumes by Cylindrical Shells
Shells sometimes work better than washers. The AP Calculus video presents an example of finding the volume of a rotational solid by using the shell method. The method uses the integral of the lateral surface area of a cylinder as opposed...
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Average Value of a Function
Viewers learn how to find the average of a variable density with a video made for AP Calculus. The presenter applies the formula to find the average value of a function with an example that provides a density function for a rod. The...
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Trigonometric Integrals
Present examples of trigonometric integrals with a video that shows an example of determining a trigonometric integral. The AP Calculus example shows that many of the trigonometric integrals require manipulation and using trigonometric...
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Integration by Partial Fractions
Demonstrate a complex integration by using partial fractions with an AP Calculus resource that works an example of integrating a rational function. The function's denominator has linear factors with one of them repeated.
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Differential Equations and Initial Value Problems
Demonstrate working an initial value problem with an AP Calculus video that verifies that a family of functions is a solution to a differential equation by substitution. The presentation goes on to find a particular solution that belongs...
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Antiderivatives: Finding Position and Velocity
This AP Calculus resource works through an example that shows how to find the velocity function and the position function given acceleration. It concludes by covering how to use them to solve problems.
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Volumes by Slicing
Find the volume of a rotational solid by integrating the area of a slice. The AP Calculus resource works through an example of finding the volume of a solid created by rotating a function about the x-axis. The presentation breaks the...
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Relative Rates of Growth
It's all relative! A video introduces the concept that the relative rate of growth is the rate of growth relative to the dependent variable, and then compares the equation of the standard model and the relative growth version.