Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Discusses a numerical technique called the method of adjoints, turning a linear two-point boundary value problem into an initial value problem. Described are steps for using the method in linear or nonlinear systems. Applies the technique to solve a simple pendulum problem. Lists 15 references. (YP)

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

Four algebra problems and their solutions are presented to illustrate the use of a mathematical theorem. (CW)

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

Investigates the problem of finding the expected number of questions necessary to identify 1 out of a set of 30 attribute blocks. Solutions include the use of a tree diagram or a computer simulation. Generalizes the problem for increased numbers of attributes. (MDH)

The dynamics of some common sports, such as race walking, running, cycling, jumping, and throwing, are presented. Rough estimates of the relevant physical quantities required for these individual sports are discussed. General mathematical formulas are derived which can be used for judging the performance of any athlete. (Author/KR)

Developed are simple recursion formulas for generating the exact distribution of the longest run of heads, both for a fair coin and for a biased coin. Discusses the applications of runs-related phenomena such as molecular biology, Markov chains, geometric variables, and random variables. (YP)

Discusses the use of the recursive method to permutations of n objects and a problem making c cents in change using pennies and nickels when order is important. Presents a LOGO program for the examples. (YP)

Discusses an alternative form of the quadratic formula to solve quadratic equations. Presents an application to chemistry to illustrate the need for quadratic formulas better suited to approximations obtained using hand-held calculators. Addresses the problems of rounding errors, accuracy of solutions, and factoring as a method of solution. (MDH)

Presents a short study of proper values of two-by-two matrices with real entries. Gives examples of symmetric matrices and applications to systems of linear equations of perpendicular lines intersecting at the origin and central conics rotated about the origin to eliminate the xy term from its equation. (MDH)

Presents a public-key cryptosystem application to introduce students to several topics in discrete mathematics. A computer algorithms using recursive methods is presented to solve a problem in which one person wants to send a coded message to a second person while keeping the message secret from a third person. (MDH)

A pair of experiments, appropriate for the lower division fourth semester calculus or differential equations course, are presented. The second order differential equation representing the equation of motion of a simple pendulum is derived. The period of oscillation for a particular pendulum can be predicted from the solution to this equation. As a…

Many drugs are used up by the body at rates described in terms of exponential decay. Two simple exponential formulas are discussed. (MNS)