Mathematics Commons^™

Calculus: An Integrated Approach, Matthew E. Cathey, Joseph A. Spivey

Faculty Books

This is a self-published digital textbook “Calculus: An Integrated Approach” by Matt Cathey and Joseph Spivey. The textbook covers a two-semester calculus sequence for Wofford College. The text is freely available for use under the terms of the creative commons copyright, found in the textbook file. The free software application Wolfram Player is required to read the textbook; it can be downloaded here: https://www.wolfram.com/player/.

The complete, up-to-date version of the text can be found here: http://digitalcommons.wofford.edu/facultybooks/1/.

The authors welcome questions, comments, or suggestions. Our email addresses are spiveyja@wofford.edu and catheyme@wofford.edu.

The version of the book associated with …

On The Construction Of Simply Connected Solvable Lie Groups, Mark E. Fels

Research Vignettes

This worksheet contains the implementation of Theorems 4.2, 5.4 and 5.7 in the paper On the Construction of Solvable Lie Groups. All the examples in the paper are demonstrated here, along with one in Section 6 that was too long to include in the article.

Differentialgeometry In Brno, Ian M. Anderson

Presentations

This page will provide files supporting Ian Anderson's presentations in Brno, December 2015. The files can be found and downloaded from "Additional Files", below.

The files include:

(1) DifferentialGeometryUSU.mla: This is the Maple Library Archive file which provides all the DifferentialGeometry functionality. Here are Installation Instructions.

(2) DifferentialGeometry.help : this is the latest version of the DifferentialGeometry documentation. Copy this file to the same directory used for DifferentialGeometryUSU.mla (from step (1)).

Alg Calculus Ii (Lecture Slides), Lake Ritter, Shangrong Deng

Mathematics Ancillary Materials

Authors' Description:

Upon completing this course students should be able to:

1. Find derivatives and integrals of transcendental functions.
2. Apply techniques to evaluate integrals.
3. Use tests to determine series convergence.
4. Determine Taylor series for common functions.
5. Describe curves in parametric form and polar coordinates.

Important Note:

All are welcome to use and modify these slides for nonprofit educational activities. They are intended to be used with smart board/smart podium or touch screen technology and cannot serve as a primary text. They were produced with LaTeX and converted to .ppt.

The original Beamer slides are superior quality but require several additional figure …

Non-Isomorphic Real Simple Lie Algebras Of The Same Complex Type And Character, Ian M. Anderson

Tutorials on... in 1 hour or less

Complex simple Lie algebras are classified by their root types. The type of a real simple Lie algebra is the root type of the associated complex algebra. The character of a real simple Lie algebra is the signature of its Killing form.

For many root types, the character is sufficient to uniquely classify the corresponding real Lie algebras. However, one should not take this statement to be literally true – there are a few cases where the character does not suffice to distinguish all possible real forms.

In this worksheet we will show that the 2 real non-isomorphic Lie algebras …

K-Theory And Pseudospectra For Topological Insulators [Dataset], Terry A. Loring

Math and Statistics Datasets

We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to perturbing approximately compatible observables into compatible observables. We derive formulas in all symmetry classes up to dimension two, and in one symmetry class in dimension three, that can be computed with sparse matrix algorithms. We present algorithms in two symmetry classes in 2D and one in 3D and provide illustrative studies regarding how these algorithms can detect the scaling properties of phase transitions.

Cartan Involutions And Cartan Decompositions Of A Semi-Simple Lie Algebra, Ian M. Anderson

Tutorials on... in 1 hour or less

In this worksheet we shall review the basic definitions and properties of Cartan involutions and Cartan decompositions and illustrate these using the DifferentialGeometry software package for Lie algebras.

A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson

Tutorials on... in 1 hour or less

Let I be a differential system on a manifold M. The infinitesimal symmetry algebra of I is the set of all vectors fields X on M such that preserve I. In this worksheet we present an example, due to E. Cartan of a rank 7 Pfaffian system on a 15-dimensional manifold whose infinitesimal symmetry algebra is the split real form of the exceptional Lie algebra f4 .

Polynomials Occuring In Generating Function Identities For B-Ary Partitions, David Dakota Blair

Graduate Student Publications and Research

Let p_b(n) be the number of integer partitions of n whose parts are powers of b. For each m there is a generating function identity:

f_m(b,q)\sum_{n} p_b(n) q^n = (1-q)^m \sum_{n} p_b(b^m n q)q^n

where n ranges over all integer values. The proof of this identity appears in the doctoral thesis of the author. For more information see http://dakota.tensen.net/2015/rp/.

This dataset is a JSON object with keys m from 1 to 23 whose values are f_m(b,q).