
02108370
b
2011f.00853
Impedovo, Michele
General mathematics with the calculator. (Matematica generale con il calcolatore.)
Unitext 16. La Matematica per il 3 + 2. Milano: Springer (ISBN 8847002583/pbk; 9788847003453/ebook). ix, 527~p. (2005).
2005
Milano: Springer
IT
U25
I25
H65
K15
N15
R25
R65
R75
textbook
symbolic calculus
discrete models
sums and series
continuous models
derivatives and integrals
discrete models in several dimensions
continuous models in several dimensions
dynamical models
Mathcad and Excel software
numerical results
graphical representations
textbook for nonmathematicians
textbook for economists
Zbl 0566.10007
doi:10.1007/b138109
This book is an unconventional introduction into some important basic fields of mathematics and their applications: calculus of one and several variables, linear algebra, dynamical models (discrete, continuous, stochastic), optimization, elementary probability, and some other matters. The author introduces concepts through their constructive and numerical aspects and by discussion of relevant approximation methods, exhibited in their working (with displays of many small routines for Mathcad and Excel software, of numerical results and graphical representations), thereby presenting to the reader many well chosen examples of applications. He expresses his viewpoint in his introduction as follows (translation by the reviewer): ``In this book mathematics is interpreted as a service discipline: the treatment is rich in examples, applications, models, drawn from the contexts of economics, statistics, physics, biology, and even of mathematics itself. The analysis of these models constitutes in a certain sense the true scope of the mathematical theory developed." So, the book can be recommended as a useful introduction into mathematics and its use for modelling and computing purposes. Students of mathematics can gain from it insights and acquaintance with viewpoints they may not encounter in their purely mathematical studies and as such get preparation for fruitful joint work in industry or research institutes where mathematics is a service discipline. The mathematical instructor can find many inspirations for better considering the aspects of applicability in his teaching. The reviewer really enjoyed studying the book. Pure mathematicians might critisize it for not going deep into mathematical subtleties, also for occasional lack rigour in the presentation. Clearly, students of mathematics must study their science (also) in more abstract context. Citatation of the chapter headings in form of a list may give the prospective reader an impression of the contents: Numerical and symbolic calculus, Discrete Models, Sums and series, Continuous models, Derivatives and Integrals, Discrete models in several dimensions, Continuous models in several dimensions, Dynamical models. The reviewer really enjoyed studying this book. However, he finds it appropriate to point out an error the author could have avoided just by using ``Advanced Search" in the GOOGLE system, simply asking for Lothar Collatz. In Section 8.3.6 of his book the author gives a nice description of the wellknown Collatz $3n+1$ problem (``il gioco di Collatz") which was posed around 1930 by Lothar Collatz (19101990). He seems to know from L. Collatz nothing but this problem and calls him ``uno studente americano", However, Collatz in his student time (19281933) never was in America, he was a student in Germany. In 1986 he published (in Chinese) an article ``On the origin of the $(3n+1)$ problem", Journal of Qufu Normal University, Natural Sciences Edition 3, 911 (1986). The reviewer gratefully acknowledges to have got this article with a translation into German from G. Opfer (Hamburg). For history and theory see also {\it J. C. Lagarias}: ``The $3x+1$ problem and its generalizations", Am. Math. Mon. 92, 323 (1985; Zbl 0566.10007).
Rudolf Gorenflo (Berlin)
Riassunto della casa editrice: Lo scopo \`e quello di illustrare i modelli pi\`u importanti di un corso di matematica generale (modelli discreti, continui, a una o pi\`u dimensioni, statici o dinamici). Il ``target" \`e lo studente di un corso di laurea in economia.