Mathematics Commons^™

03: Derivative Signs, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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.

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.

08: Sine Transformations, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SineTransformations.nb allows you to use sliders to see the effects of parameters on the amplitude, period, phase shift, and vertical shift.

15: Koch Snowflakes, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

KochSnowflakes.nb contains several animations that show several steps of graphical iteration for Koch Snowflakes and several other patterns.

04: Domain And Range, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

DomainAndRange.nb allows you to graph various types of functions and shows the domain and/or range along the appropriate axis.

08: Accumulator, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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.

11: 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.

10: Slope Fields + Solns, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

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.

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 …

Life After Calculus: 20 Years Later, Darren B. Glass

Math Faculty Publications

In 1996 Math Horizons interviewed a group of students at the Joint Mathematics Meetings; now, 20 years later, one of those students, Darren Glass, interviews another group of students.

Calculus Ii (University Of North Georgia), Minsu Kim, Hashim Saber, Bikash Das, Thomas Hartfield

Mathematics Grants Collections

This Grants Collection for Calculus II was created under a Round Four ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

05: Rats Grapher, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RatsGrapher.nb graphs rational functions and labels all holes and asymptotes.

Apex Calculus Exercises (Webwork), Shaun V. Ault

Mathematics Ancillary Materials

These exercises are designed to be used in the open-source WeBWorK platform by the Mathematical Association of America. The exercises are meant to supplement the APEX Calculus 3.0 open textbook, and each folder's number corresponds to the textbook's chapters and subchapters.

Series 10, Ruth Dover

Series

Extra stuff to show more ways to work with series.

4. Dragging Along, Ruth Dover

Differential Equations

More information on air drag.

Bc 1 Rate Of Change Activity Sheet Teacher Notes, Ruth Dover

A Simple Introduction to Rates

Before beginning this section of handouts, students will be introduced to a variety of vocabulary words often associated with calculus. These words will be used in an intuitive sense only and will not have been formally defined. Vocabulary should include graphical terms such as continuous, increasing, decreasing, maximum and minimum points, concave up, concave down, and point of inflection. In addition, discussion of the concept of "rate of change" should begin. It should be mentioned that many quantities change – population, cost, and temperature, to name just a few. All that is specifically required at this point can be related …

Rate Of Change 2, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

Limits5, Ruth Dover

Limits

Limits and continuity.

Limits2, Ruth Dover

Limits

More on limits, both algebraic and graphical, including one-sided limits.

3. Derivatives Of Exponential Functions, Ruth Dover

More on Derivatives

Exploring the derivative of exponential functions.

Series 03, Ruth Dover

Series

Considers the creation of a general Maclaurin series.

Limits4, Ruth Dover

Limits

An introduction to limits as something goes to infinity.

Approximations 4, Ruth Dover

Integrals

Trapezoidal Rule.

Series 07, Ruth Dover

Series

Where did the Lagrange error bound come from?

Series 08, Ruth Dover

Series

More on error.

Rate Of Change 4, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

1. Monotonic Sequences, Ruth Dover

Series

Practice with monotonic sequences.

Approximations 3, Ruth Dover

Integrals

Understanding Riemann sum approximations, including technology.

2. Geometric Series, Ruth Dover

Series

Quick review of geometric series.

Series 01, Ruth Dover

Series

Asks students to create a polynomial function for y = ln(1 + x), extends the polynomial to a series, examines the interval of convergence and error.