QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively…

Quantifier Elimination is a procedure that allows simplification of logical formulas that contain quantifiers. Many mathematical concepts are defined in terms of quantifiers and especially in calculus their use has been identified as an obstacle in the learning process. The automatic deduction provided by quantifier elimination thus allows…

The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…

Conventional application of these two calculus staples is stretched here, somewhat recreationally, but also to raise solid questions about the role of limit interchange in analysis--without, however, delving any deeper than first-year Calculus.

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

A program that can reduce difficult integration problems to simpler approximations using the trapezoidal rule to approximate the area under a curve is presented. (MP)

How far does the back end of a bus swing out as the driver makes a turn at an intersection?'' is the problem discussed. (MM)

A simple geometric construction giving acceptable approximations to the locations of twelve points for placing frets on a guitar is described both geometrically and analytically. (DT)

Presents a technique, using the method of variation of parameters for solving differential equations, for introducing Green's function early in an undergraduate curriculum. Presents various examples. (Author/MLH)

Elementary differential calculus is used to analyze and to discuss some complex economic situations. (JT)