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Calculus

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Articles 61 - 90 of 193

Full-Text Articles in Mathematics

Discovering Calculus With The Ti-Nspire Cas Calculator, Meghan A. Nielsen Jul 2017

Discovering Calculus With The Ti-Nspire Cas Calculator, Meghan A. Nielsen

Masters Essays

No abstract provided.

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Active Calculus Multivariable, Steven Schlicker, David Austin, Matthew Boelkins Jul 2017

Active Calculus Multivariable, Steven Schlicker, David Austin, Matthew Boelkins

Open Textbooks

Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with …

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The Derivatives Of The Sine And Cosine Functions: A Mini_Primary Source Project For Calculus I Students, Dominic Klyve Jun 2017

The Derivatives Of The Sine And Cosine Functions: A Mini_Primary Source Project For Calculus I Students, Dominic Klyve

Mathematics Faculty Scholarship

This curricular modular guides students through a method of calculating the derivative of the sine and cosine functions using differentials. It is based on one primary source: Leonhard Euler's Institutiones calculi differentialis (Foundations of Differential Calculus) [2], published in 1755.

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Complementary Coffee Cups, Brandon Sams May 2017

Complementary Coffee Cups, Brandon Sams

Mathematics Undergraduate Theses

In a 2006 paper [1], mathematician Thomas Banchoff posed a new calculus problem, when he filled two cups with coffee. One was convex, while the other was concave, but in such a way so as to fit together perfectly. These cups were thus, complementary. The next natural question he asked was "Which cup has more volume?", so that he could be gracious enough to give the larger of the two to his wife. Banchoff decided to explore this topic, but he left some unanswered questions along the way. Under what conditions would two Complementary Coffee Cups have the same volume? …

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13: Polar Reciprocal, Ruth Dover Jan 2017

13: Polar Reciprocal, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarReciprocal.nb first shows a transformation of the circle r = 3 into the circle r = 3sin (theta). Second, it shows the original and reciprocal graphs through the animation. Interesting stuff!

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09: Solving Trig Equations, Ruth Dover Jan 2017

09: Solving Trig Equations, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SolvingTrigEquations.nb develops the idea of solving trigonometric equations with special angles by looking at a sequence of problems. The student is asked to think about solutions and to do more problems along the way.

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09: Slope Field, Ruth Dover Jan 2017

09: Slope Field, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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07: Tan Animation, Ruth Dover Jan 2017

07: Tan Animation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

TanAnimation.nb is a nice little animation to illustrate similar triangles to show why the graph of y = tan(x) looks the way it does.

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12: Polar Path, Ruth Dover Jan 2017

12: Polar Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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02: Poly Basics 1, Ruth Dover Jan 2017

02: Poly Basics 1, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolyBasics1.nb deals with the graphs of polynomial functions of higher degrees. In this notebook, each factor is linear.

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05: Limit Definition, Ruth Dover Jan 2017

05: Limit Definition, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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14: Polar Vs Rectangular Animation, Ruth Dover Jan 2017

14: Polar Vs Rectangular Animation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolarVsRectangularAnimation.nb allows the user to input a polar function and then relates the graphs of r = ƒ(theta) and y = ƒ(x).

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16: Sequences And Series, Ruth Dover Jan 2017

16: Sequences And Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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15: Plotting S(N), Ruth Dover Jan 2017

15: Plotting S(N), Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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12: Parametric Path, Ruth Dover Jan 2017

12: Parametric Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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16: Seeing Series, Ruth Dover Jan 2017

16: Seeing Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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06: Reciprocal Functions, Ruth Dover Jan 2017

06: Reciprocal Functions, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

ReciprocalFunctions.nb asks the user to input a function. The notebook will graph the original function and its reciprocal.

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06: Random Riemann, Ruth Dover Jan 2017

06: Random Riemann, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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17: Maclaurin Series, Ruth Dover Jan 2017

17: Maclaurin Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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02: Derivative Approximation, Ruth Dover Jan 2017

02: Derivative Approximation, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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An Early Semester Mastery Activity And Intervention In First-Year Calculus, Allan P. Donsig, Nathan Wakefield Jan 2017

An Early Semester Mastery Activity And Intervention In First-Year Calculus, Allan P. Donsig, Nathan Wakefield

Department of Mathematics: Faculty Publications

Success in first-year mathematics courses is essential for students to pursue STEM careers, including teaching careers. We investigate a mastery activity given during the first two weeks of a first-year calculus course at the research site. Previous work showed a model using this activity in College Algebra, together with ACT and high school rank, was predictive of student success in precalculus. Here we do a similar analysis for such an activity in calculus, including an intervention for students who do not complete the activity. We also investigate the intervention’s effectiveness. These results show that the early mastery activity, especially when …

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01: Quadratic Functions, Ruth Dover Jan 2017

01: Quadratic Functions, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

QuadraticFunctions.nb examines the path of the vertex of quadratic polynomial graphs as each parameter a, b, and c changes.

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03: Poly Basics 2, Ruth Dover Jan 2017

03: Poly Basics 2, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolyBasics2.nb looks for patterns in polynomial graphs with three different factors when each factor is raised to various powers.

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17: Plotting S(N), Ruth Dover Jan 2017

17: Plotting S(N), Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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01: Creating Derivative, Ruth Dover Jan 2017

01: Creating Derivative, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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04: Ivt, Ruth Dover Jan 2017

04: Ivt, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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07: Riemann Sums, Ruth Dover Jan 2017

07: Riemann Sums, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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14: Sequences And Series, Ruth Dover Jan 2017

14: Sequences And Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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13: Polar Path, Ruth Dover Jan 2017

13: Polar Path, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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11: Eulers Method, Ruth Dover Jan 2017

11: Eulers Method, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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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