# MTN Issue 10, Fall 1993

## Extended Functionality (Maple V Release 2)

Tips for Maple Users
M.B. Monagan
This is the first article of a column that will be regularly included in the MTN. It contains discussions of plotting, data structure transformations using `seq`, `map`, `zip`, and `select`, and an overview of simplifications in Maple.
Recipes for Solving Broad Classes of Definite Integrals and Applications
T.C. Scott, Y.B. Band, K.O. Geddes,
This is brief survey of some of Maple's capabilities for providing exact analytical solutions to definite integrals. This includes a few examples of how and where such integrals appear in science and engineering.
A Package for Numerical Approximation
K.O. Geddes
Written as a Maple worksheet, this article presents examples involving the `numapprox` package which contains various procedures for developing numerical approximations of functions.

## Applications

Binomial Sums and Identities
V. Strehl
This is an expository article on binomial sums and their identities. The article includes some new results about Apery numbers and an application of the `gfun` package.
Thermodynamics with Maple: I, Equations of State
R.Taylor, M.B. Monagan
This is an educational article in the area of thermodynamics aimed at the undergraduate curriculum.
Construction of Stochastic Numerical Schemes through Maple
P.E. Kloeden, W.D. Scott
For those interested in stochastic processes, this article shows how Maple can play a role in the construction of useful numerical schemes.
Computing one million digits of sqrt(2)
X. Gourdon, B. Salvy
This article considers the problem of how to compute the square root of an integer to very high precision. The Maple implementation uses a different Newton iteration than the "usual" one and uses Karatsuba's algorithm for fast integer multiplication.
A Model for an HIV Infection
J.V. Herod
Although, the MTN had biology-related articles in previous issues, this would certainly qualify as the Maple Technical Newsletter's first article in the area of Medicine. In this case, the article is focussed on the HIV infection.
Application of Maple in Optimal Control Systems Design and Analysis
G.P. Porciello, T. Lee
Partially written as an educationally-oriented Maple worksheet, this article presents another application of Maple to engineering, namely on the topic of optimal control systems design and analysis.
Formula Manipulation using Maple
D. Gruntz
The last article of this issue presents some useful tools in the "art" of formula manipulation.

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Copyright 1996, Massachusetts Institute of Technology