Mathematica Notebooks for Pre-Calculus and CalculusCopyright (c) 2021 Illinois Math and Science Academy All rights reserved.
https://digitalcommons.imsa.edu/mathematica_notebooks
Recent documents in Mathematica Notebooks for Pre-Calculus and Calculusen-usMon, 04 Oct 2021 16:44:18 PDT360017: Maclaurin Series
https://digitalcommons.imsa.edu/mathematica_notebooks/34
https://digitalcommons.imsa.edu/mathematica_notebooks/34Tue, 31 Jan 2017 11:30:59 PST
MaclaurinSeries.nb gives animations for popular Maclaurin series. It shows the series with increasing values of n both graphically and analytically.
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Ruth Dover16: Seeing Series
https://digitalcommons.imsa.edu/mathematica_notebooks/33
https://digitalcommons.imsa.edu/mathematica_notebooks/33Tue, 31 Jan 2017 11:29:47 PST
SeeingSeries.nb allows the user to enter an explicit formula for the terms of a sequence. Then it animates the pattern of the sequence of partial sums. This is particularly helpful to understand conditional convergence with alternating series, but it may be used on series with all positive terms, whether convergent or divergent.
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Ruth Dover15: Plotting S(n)
https://digitalcommons.imsa.edu/mathematica_notebooks/32
https://digitalcommons.imsa.edu/mathematica_notebooks/32Tue, 31 Jan 2017 11:28:32 PST
PlottingS(n).nb animates the second section of the preceding notebook. After inputting the formula for a sequence, this animates both the sequence itself and the sequence of partial sums together as n increases.
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Ruth Dover14: Sequences and Series
https://digitalcommons.imsa.edu/mathematica_notebooks/31
https://digitalcommons.imsa.edu/mathematica_notebooks/31Tue, 31 Jan 2017 11:26:53 PST
SequencesAndSeries.nb includes a couple of sections. The first asks the user to input a formula for a sequence. Then it generates a table of values for the sequence followed by a graph of the function. The second section does the same, though it shows the sequence as well as the sequence of partial sums.
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Ruth Dover13: Polar Path
https://digitalcommons.imsa.edu/mathematica_notebooks/30
https://digitalcommons.imsa.edu/mathematica_notebooks/30Tue, 31 Jan 2017 11:25:35 PST
PolarPath.nb allows the user to input any polar function and use a slider to see how the path is created. That is, it will allow the user to see the order in which the petals or loops are created.
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Ruth Dover12: Parametric Path
https://digitalcommons.imsa.edu/mathematica_notebooks/29
https://digitalcommons.imsa.edu/mathematica_notebooks/29Tue, 31 Jan 2017 11:19:20 PST
ParametricPath.nb allows the user to input parametrically defined curves and a domain for the parameter t. An example is given to show how the curve is traced out.
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Ruth Dover11: Eulers Method
https://digitalcommons.imsa.edu/mathematica_notebooks/28
https://digitalcommons.imsa.edu/mathematica_notebooks/28Tue, 31 Jan 2017 11:18:14 PST
EulersMethod.nb asks for a differential equation, an x-interval, a specific point, and the step size. It shows the graphical approximation given by Euler's Method. This notebook has setups that allow it to be used with one DE or with a system of two DE's.
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Ruth Dover10: Slope Fields + Solns
https://digitalcommons.imsa.edu/mathematica_notebooks/27
https://digitalcommons.imsa.edu/mathematica_notebooks/27Tue, 31 Jan 2017 11:16:28 PST
SlopeFields+Solns.nb follows similarly from the previous notebook. Here, however, there is a 2D slider that shows a specific solution function as you move the initial point.
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Ruth Dover09: Slope Field
https://digitalcommons.imsa.edu/mathematica_notebooks/26
https://digitalcommons.imsa.edu/mathematica_notebooks/26Tue, 31 Jan 2017 11:15:19 PST
SlopeField.nb does just what it says! Enter a differential equation in the form y = … and choose the window. It is also possible to choose the number of marks in each direction.
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Ruth Dover08: Accumulator
https://digitalcommons.imsa.edu/mathematica_notebooks/25
https://digitalcommons.imsa.edu/mathematica_notebooks/25Tue, 31 Jan 2017 11:13:39 PST
Accumulator.nb takes a function ƒ and other information to sketch both the graph of ƒ and the graph of F(x) = Integral of ƒ(t)from a to x. Use the slider for the x-value to see how the accumulated area under ƒ helps to create the graph of F.
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Ruth Dover07: Riemann Sums
https://digitalcommons.imsa.edu/mathematica_notebooks/24
https://digitalcommons.imsa.edu/mathematica_notebooks/24Tue, 31 Jan 2017 11:10:09 PST
RiemannSums.nb allows the user to input a function, and x-interval, and a maximum value of n, the number of rectangles. This animates Riemann and trapezoidal sums.
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Ruth Dover06: Random Riemann
https://digitalcommons.imsa.edu/mathematica_notebooks/23
https://digitalcommons.imsa.edu/mathematica_notebooks/23Tue, 31 Jan 2017 09:50:01 PST
RandomRiemann.nb takes a function, values for xmin and xmax, and a number n that represents the number of rectangles desired. This will create random subintervals with random points inside each subinterval, and then it will draw the corresponding Riemann sum. Values for the approximation and the actual value of the integral are given. This allows students to see how close (or distant) the approximation is and to visualize a wide variety of Riemann sums. Increasing values of n should help students understand the limiting process more clearly.
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Ruth Dover05: Limit Definition
https://digitalcommons.imsa.edu/mathematica_notebooks/22
https://digitalcommons.imsa.edu/mathematica_notebooks/22Fri, 27 Jan 2017 14:27:57 PST
LimitDefinition.nb asks the user to input a function. Then use the vertical slider to change the size of E. An appropriate value of 8 will be given.
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Ruth Dover04: IVT
https://digitalcommons.imsa.edu/mathematica_notebooks/21
https://digitalcommons.imsa.edu/mathematica_notebooks/21Fri, 27 Jan 2017 14:24:54 PST
IVT.nb allows the user to examine the Intermediate Value Theorem. Consider the graphs to examine whether or not the conclusions of the theorem hold.
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Ruth Dover03: Derivative Signs
https://digitalcommons.imsa.edu/mathematica_notebooks/20
https://digitalcommons.imsa.edu/mathematica_notebooks/20Fri, 27 Jan 2017 14:23:45 PST
DerivativeSigns.nb asks the user to input a function and a domain. It will color the graph to show where the derivative is positive and where it's negative. The second part colors the graph to show where the function is concave up and down.
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Ruth Dover02: Derivative Approximation
https://digitalcommons.imsa.edu/mathematica_notebooks/19
https://digitalcommons.imsa.edu/mathematica_notebooks/19Fri, 27 Jan 2017 14:22:29 PST
DerivativeApproximation.nb contains two sections. Both allow the user to input a function and an x-window and to vary the center point. Then the value of h may be changed. The first section will show a symmetric approximation while the second shows a one-sided approximation.
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Ruth Dover01: Creating Derivative
https://digitalcommons.imsa.edu/mathematica_notebooks/18
https://digitalcommons.imsa.edu/mathematica_notebooks/18Fri, 27 Jan 2017 14:21:03 PST
CreatingDerivative.nb takes any function and an x-window and animates a tangent line while plotting the value of the derivative.
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Ruth Dover17: Plotting S(n)
https://digitalcommons.imsa.edu/mathematica_notebooks/17
https://digitalcommons.imsa.edu/mathematica_notebooks/17Fri, 27 Jan 2017 14:14:59 PST
PlottingS(n).nb animates the second section of the preceding notebook. After inputting the formula for a sequence, this animates both the sequence itself and the sequence of partial sums together as n increases.
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Ruth Dover16: Sequences and Series
https://digitalcommons.imsa.edu/mathematica_notebooks/16
https://digitalcommons.imsa.edu/mathematica_notebooks/16Fri, 27 Jan 2017 14:13:32 PST
SequencesAndSeries.nb includes a couple of sections. The first asks the user to input a formula for a sequence. Then it generates a table of values for the sequence followed by a graph of the function. The second section does the same, though it shows the sequence as well as the sequence of partial sums.
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Ruth Dover15: Koch Snowflakes
https://digitalcommons.imsa.edu/mathematica_notebooks/15
https://digitalcommons.imsa.edu/mathematica_notebooks/15Fri, 27 Jan 2017 14:12:16 PST
KochSnowflakes.nb contains several animations that show several steps of graphical iteration for Koch Snowflakes and several other patterns.
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Ruth Dover