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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...
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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...
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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 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...
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Volumes: Solids That are Not Solid of Revolution
Viewers learn how to calculate the volume when the cross section is not a circle by using the same principle as if it was a circle. The video goes through an example of finding the volume of a figure where the cross sections are squares...
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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...
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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...
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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...
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Optimization: Maximum Area
Viewers discover how to apply derivatives to determine dimensions that maximize area with a video that presents a problem that asks for the maximum area of a rectangle inscribed in a circle with radius (r). The instructor demonstrates...
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Related Rates
A video tutorial examines the application of related rates to determine the rate of change of an angle at a line of sight. The instructor shows the process of solving the problem using a known rate to find the desired rate and analyzes...
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Possible and Relative Error
Here's a video that demonstrate the meaning of possible and relative error using differentials. As the instructor works through the problem, he gives formulas for determining the different types of errors. He shows two approaches to the...
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Implicit Differentiation
Model for class members how to find both a first and second derivative of a trigonometric function with a video tutorial that works through a problem that uses the Quotient Rule to evaluate the derivative. The instructor shows the steps...
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Chain Rule
Class members learn how to evaluate derivatives of functions using the Chain Rule through a video that shows the steps of finding a derivative with the Chain Rule. The two examples include both a trigonometric and polynomial function.
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The Product, Power, and Quotient Rules
Teach the rules of finding derivatives using the video lesson. The instructor explains in detail the Product, Power, and Quotient Rules. He describes each rule and then illustrates several examples.
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Derivatives Example: f(x)=√x
Introduce your classes to the derivative formula using a video lesson. The instructor works through an example using the parent square root function. He then shows how to write the equation of the tangent line at a given x value.
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Calculating Limits as x Goes to Infinity
Build on your class' understanding of limits by exploring limits as x approaches infinity. The instructor explains how to find the limit by considering specific values. He then makes a connection to the graphical representation.
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Limit of a Function
Explore the meaning of the limit of a function as it approaches a given value with a video that explains limits in reference to a derivative. The narrator then shows how to evaluate the limit of a function at a given integer value.
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Desmos Tutorial
Demonstrate the functionality of the Desmos software for your pupils. with a video that discusses different aspects of the software from graphing piecewise function to finding roots and changing axis. The overview is sufficient to...
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Slopes of Curves Examples
Provide a homework resource to your classes as they work to complete challenging problem-solving questions. The video tutorial works through several homework questions addressing the slopes of curves. It shows each problem in its...
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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.
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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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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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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...
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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.