Mathematics Commons^™

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.

Series 04, Ruth Dover

Series

A closer examination of y = cosx and y = sinx, including error estimation.

2. Population, Ruth Dover

Differential Equations

Introduction to logistic population growth.

More Limits, Ruth Dover

Limits

No abstract provided.

Limits1, Ruth Dover

Limits

A basic idea to limits and notation.

2. Intro To Concavity, Ruth Dover

More on Derivatives

Looking at changes in ƒ’ to understand concavity.

3. Upper Bounds, Ruth Dover

Series

Understanding upper bounds and a proof of the divergence of the harmonic series.

Series 02, Ruth Dover

Series

Repeats Series01 with the function y = arctanx.

Approximating Alternating Series, Ruth Dover

Series

Error bounds with alternating series.

3: Drugs And De's, Ruth Dover

Differential Equations

Making a connection between discrete recursion and differential equations.

Alternating Series 1, Ruth Dover

Series

Partial sums of alternating series.

Taylor Review, Ruth Dover

Series

Assorted problems.

Series 09, Ruth Dover

Series

Practice using series to evaluate limits and definite integrals.

Limits3, Ruth Dover

Limits

Algebraic techniques for functions with holes.

Approximations 1, Ruth Dover

Integrals

Measuring distance and accumulation.

Approximations 2, Ruth Dover

Integrals

Drawing rectangles and calculating Riemann sums.

Rate Of Change 1, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

Rate Of Change 3, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

4. Integral Test For Series, Ruth Dover

Series

Relating Riemann sums and series – requiring a lot of teacher help!

Calculus I (University Of North Georgia), Michael Goodroe, Berhanu Kidane, Julian Allagan, John Williams

Mathematics Grants Collections

This Grants Collection for Calculus I was created under a Round Two 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

Analytic Geometry And Calculus I, Shaun V. Ault, Sudhir Goel

Mathematics Grants Collections

This Grants Collection for Analytic Geometry and Calculus I was created under a Round Two 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

Some Problems In Differential And Subdifferential Calculus Of Matrices., Priyanka Grover Dr.

Doctoral Theses

A central problem in many subjects like matrix analysis, perturbation theory, numerical analysis and physics is to study the effect of small changes in a matrix A on a function f(A). Among much studied functions on the space of matrices are trace, determinant, permanent, eigenvalues, norms. These are real or complex valued functions. In addition, there are some interesting functions that are matrix valued. For example, the (matrix) absolute value, tensor power, antisymmetric tensor power, symmetric tensor power.When a function is differentiable, one of the ways to study the above problem is by using the derivative of f at A, …

Student Understanding Of Function And Success In Calculus, Daniel I. Drlik

Boise State University Theses and Dissertations

The purpose of this study was to determine if there is a relationship between student success in calculus and student understanding of function. Student understanding of function was measured using two questionnaires, one of which is a modification of an existing measure based on APOS theory. The other I developed with items from the concept image literature. The participants of this study were 116 high school students who were enrolled in a first-year calculus course. The results of the questionnaires were aligned to course exam scores to determine connections between function understanding and rate of success in calculus.

A major …

Armstrong Calculus, Michael Tiemeyer, Jared Schlieper

Mathematics Open Textbooks

Authors' Description:

An open-source textbook for calculus.

The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen of the Virginia Military Institute and Mount Saint Mary's University. Both of these texts can be found at http://aimath.org/textbooks/approved-textbooks/.

The authors of this text have combined sections, examples, and exercises from the above two texts along with some of their own content to generate this text. The impetus for the creation of this text …

Neutrosophic Precalculus And Neutrosophic Calculus, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis.

Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change.

The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy.

In this book, the author presents a few examples of indeterminacies and several methods to deal with these specific indeterminacies, but many other indeterminacies there exist in our everyday life, and they have to be studied …

Calculus For Everyone, Sandra Kingan, Brooklyn College Library And Academic It

Open Educational Resources

Professor Kingan’s motivation for writing her free Calculus I textbook was to help address the departments high failure rates in Calculus. Along with another CUNY initiative to offer Calculus workshops in advance of taking the course, Kingan’s concise textbook in Calculus I offers students inside and outside of CUNY an opportunity to prepare for Calculus I at their own pace. She also believes that by providing free access to this material she could help to overcome some of the inequity students experience when Calculus is not offered in their high school. The textbook was written specifically for this pilot project. …

Students' Perceived Utility Of Precision Taught Calculus, Rebecca-Anne Dibbs, David Glassmeyer, Wafa Yacoub

Faculty Articles

The last decade of calculus research has showed students learn best when lecture is supplemented with thoughtful use of technology and group work; however, educators are given little direction of how they are to balance the already full first semester calculus class. Precision teaching is an instructional model that employs formative assessment to provide information on what topics are understood by students as well as indicate troublesome concepts. With this information, the instructor can adjust class time accordingly by incorporating supplemental activities most beneficial to students. The purpose of this interview study was to explore the perceived utility of precision …

Generalized Local Test For Local Extrema In Single-Variable Functions, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

We give a detailed derivation of a generalization of the second derivative test of single-variable calculus which can classify critical points as local minima or local maxima (or neither), whenever the traditional second derivative test fails, by considering the values of higher-order derivatives evaluated at the critical points. The enhanced test is local, in the sense that it is only necessary to evaluate all relevant derivatives at the critical point itself, and it is reasonably robust. We illustrate an application of the generalized test on a trigonometric function where the second derivative test fails to classify some of the critical …