Numerical tables of mathematical functions are in continual demand by scientists and engineers for preliminary surveys of problems before programming for computing machines. This handbook was designed to provide scientific investigators with a comprehensive and self-contained summary of the mathematical functions that arise in physical and…

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)

Demonstrates the number theory property that the number of divisors of an integer n times the number of positive integers k, less than or equal to and relatively prime to n, equals the sum of the divisors of n using theory developed about multiplicative functions, the units of a convolution ring, and the Mobius Function. (MDH)

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)

Considers the reflections of the graphs of a function through an arbitrary line. Determines whether the result is a function and which functions are reflected on to themselves through a given line. (YP)

Offers an approach to the understanding and to the teaching of the fundamental theorem of calculus. Stresses teaching the relation between a function and its derivative and the functions themselves. (YP)

Describes a five-step graphing method for various trigonometric periodic functions. Emphases is on teaching constants and functions. (YP)

Plotting a polynomial over the range of real numbers when its derivative contains complex roots is discussed. The polynomials are graphed by calculating the minimums, maximums, and zeros of the function. (MNS)

Discusses when to use the computer, paper-and-pencil, or mental-computation procedures. Provides examples of solving problems dealing with roots of polynomial using computer graphing and other strategies. Suggests implications for curricular planning. (YP)

Analyzes two transcripts of children's mathematical behavior to observe the nature of recursive levels and interrelationships among them. Describes several levels of the recursions. (YP)

Describes Newton's method to locate roots of an equation using the Newton-Raphson iteration formula. Develops an adaptive method overcoming limitations of the iteration method. Provides the algorithm and computer program of the adaptive Newton-Raphson method. (YP)

Examines aspects of the images and definitions that college students and junior high school teachers have for the concept of function. Provides a seven-item questionnaire. Describes and categorizes the various images and definitions of the concept. (YP)

Discusses the application of probabilistic ideas, especially Monte Carlo simulation, to calculus. Describes some applications using the Monte Carlo method: Riemann sums; maximizing and minimizing a function; mean value theorems; and testing conjectures. (YP)

Provides some significant figure rules used in chemistry including the general theoretical basis; logarithms and antilogarithms; exponentiation (with exactly known exponents); sines and cosines; and the extreme value rule. (YP)

Discussed is a project promoting "thinking about what students did" in an Israeli high school. Five examples of the project are described with LOGO commands. Several educational ideas are provided. (YP)