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Math 131 Calculus 1 Resources

Tag: desmos

7.1 Sequences on Desmos

Posted on March 23, 2020

At this demos link, you can experiment with how the formula for the sequence determines the terms, as well as tell whether the function is bounded, increasing, eventually increasing, etc.

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Desmos – Riemann Sums and Definite Integrals (4.2, 4.3)

Posted on January 24, 2020January 24, 2020

At this link, you will learn how to use desmos to calculate Riemann Sums and definite integrals very quickly, check your work, and also see what is going on with the graph.

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Interlude 4 – Newton’s Law of Cooling

Posted on December 1, 2019

In this interlude, we will investigate a famous and simple way to model temperature using differential equations, known as “Newton’s Law of Cooling”. Although the situation is much more complicated in reality (see Heat Equation), we can already understand the calculus behind Newton’s Law of Cooling, which is a very useful approximation in many situations….

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Interlude 3 – Slope Fields

Posted on November 3, 2019November 5, 2019

For any differential equation of the form dy/dx = f(x,y), we can construct a “slope field” for the differential equation, which allows us to understand the qualitative behavior of the solutions without needing to know a formula for the solutions. The following set of notes introduces the main ideas, and has some exercises for you…

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The Definition of ‘e’ (0.4, 2.5)

Posted on October 21, 2019October 23, 2019

In this handout, we investigate an alternative way of defining the number e, as the base of the exponential function which is its own derivative. This Desmos graph lets you experiment with different bases of an exponential function, and observe the connection between the exponential function and its derivative.

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Implicit Differentiation (2.4)

Posted on October 21, 2019October 23, 2019

These notes contain a summary of the important ideas behind implicit differentiation, its connection to the Chain Rule, and how it may be used to find tangent lines to general equations. You can use this Desmos graph to look at the graphs produced by various equations, as well as to check that your answers to…

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Interlude 1 – Newton’s Method

Posted on October 7, 2019July 21, 2022

The handout below contains a summary of the important points about Newton’s Method, as well as introduces the Bisection Method for comparison. There are some exercises at the end for you to test your understanding of some of the important ideas. This Desmos graph gives a visual representation of what is going on during each…

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Linear approximations and their derivatives (2.2)

Posted on October 6, 2019October 23, 2019

This graph shows how we can make an approximation to the graph of a function using a piecewise function where each piece is a secant line. For this piecewise function — since lines are easy to deal with — we can compute the piecewise derivative and see how this compares with the graph of the…

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Definition of the derivative (2.2)

Posted on October 4, 2019October 23, 2019

This Desmos graph shows how the derivative represents the slope of the tangent line to the graph, and can be calculated as the limit of the slopes of secant lines. In the same way that the slope of a secant line represents an “average rate of change”, the slope of the tangent line represents an…

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Epsilon-Delta Definition of Limit (1.2)

Posted on September 11, 2019October 23, 2019

This Desmos graph allows you graphically investigate the relationship between epsilon and delta when considering the formal definition of limit. There are two accompanying videos on the YouTube page: Video 1.2a explains the interpretation of epsilon, delta, and how you can make sense of the formal definition of limit. Video 1.2b shows how to solve…

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Ch 0 (5) Ch 1 (2) Ch 2 (6) Ch 4 (1) Ch 7 (1) desmos (15) handout (8) interlude (4) review problems (1)
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