In this note several cubic polynomials and their roots are examined, in particular, how these roots move as some of the coefficients are modified. The results obtained are applied to eigenvalues of matrices. (Contains 8 figures and 1 footnote.)

The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…

This note generalizes the well-known Leibnitz rule of successive differentiation for the product of two functions to a similar result for the product of three functions.

An article by Skemp (1976) on mathematical understanding describes two different types of "understanding", "relational" understanding which he initially describes simply as "knowing both what to do and why", and "instrumental" understanding which he describes in the first instance as "rules without reasons". In this article, the author highlights…

Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…

In this paper, the author gives a further simple generalization of a power series evaluation of an integral using Taylor series to derive the result. The author encourages readers to consider numerical methods to evaluate the integrals and sums. Such methods are suitable for use in courses in advanced calculus and numerical analysis.

We sometimes teach our students a method of finding all integral triples that satisfy the Pythagorean Theorem x[squared]+y[squared]=z[squared]. These are called Pythagorean triples. In this paper, we show how to solve the equation x[squared]+ky[squared]=z[squared], where again, all variables are integers.

Authors use combinatorical analysis to prove some interesting facts about the Fibonacci sequence.

This article investigates a specific instance when the textbook answer for finding a root of a complex number differed with the answer given by the TI-83. After explaining the reason for the difference the article then expands the definition of the integral root of a complex number to an arbitrary complex power of a complex number.

This article describes activities that introduce basic trigonometric functions in a smooth and natural way. The only requirements are basic algebra, the Pythagorean theorem, and the concept of area.

This article discusses divisibility tests for any prime number.

This article describes a way to use color to help students develop formulas for functions that describe growing patterns. (Contains 4 figures.)

The paper details a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers…

This article discusses the art of storytelling as a means of introducing new mathematics topics. Telling a mathematically based story can be a break from the routine and can serve as literary mnemonics full of mental imagery that helps students recall in problem-solving steps. The authors provide a certain story that has been tried by several…

This study presents the results of a multi-year mixed-methods study of students' performance (n = 94) and experiences (n = 28) with electromagnetics in an elective Electrical and Computer Engineering Technology RF communications course. Data sources used in this study include academic transcripts, course exams, interviews, a learning styles…