Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

It was shown by Costa and Levine that the homogeneous differential equation (1-x[superscript N])y([superscript N]) + A[subscript N-1]x[superscript N-1)y([superscript N-1]) + A[subscript N-2]x[superscript N-2])y([superscript N-2]) + ... + A[subscript 1]xy[prime] + A[subscript 0]y = 0 has a finite polynomial solution if and only if [for…

Principle of duality and numerical calculation of income and substitution effects under Hicksian Compensation are often left out of intermediate microeconomics courses because they require a rigorous calculus based analysis. But these topics are critically important for understanding consumer behavior. In this paper we use excel solver--a…

Algebra and calculus students have difficulties to express themselves in a statement of mathematical symbols and to comment on written mathematical statements to end with equivalent mathematical symbols statement. In this study, the reasons behind the meaning students load to the mathematical symbols and written mathematical statements was…

A method for generating sums of series based on simple differential operators is presented, together with a number of worked examples with interesting properties.

The analysis of tautochrone problems involves the solution of integral equations. The paper shows how a reasonable assumption, based on experience with simple harmonic motion, allows one to greatly simplify such problems. Proposed solutions involve only mathematics available to students from first year calculus.

Functions with a variety of properties (sets of discontinuities, unbounded derivations, etc.) are discussed. (SD)

A discussion of differential equations is accompanied by an analysis of two situations whose solutions require differential equations. A computer program is given that will solve these equations. (MP)

Discussed is the problem of finding the volume common to two intersecting right circular cylinders. (MP)

It is advocated that introductory calculus texts should present topics in a manner that is understandable to students without necessarily sacrificing rigour. Illustrative examples are given of a conversational approach to problem solving. (Author/MN)

An experimental calculus class was instructed by inquiry-style presentation incorporating heuristic problem-solving strategies. A control class was also instructed using an inquiry style, but with no emphasis on heuristics. Based on interviews, it is suggested that heuristic-oriented instruction can be an effective mode of teaching problem…

A traveling salesman problem is used to illustrate the key idea in a general proof of a reduction technique. It is reduced to a problem in propositional calculus. (MNS)

The maximal rectangle idea is used to illustrate ways to ease students into the frame of mind required for problem solving in calculus. (MNS)