Maple and Mathematica

A Problem Solving Approach for Mathematics

Inna K. Shingareva, Carlos Lizarraga-Celaya

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English

Springer Verlag GmbH
01 September 2009

Numerical analysis; Applied mathematics; Maths for scientists; Mathematical & statistical software; Maths for computer scientists; Artificial intelligence

In the history of mathematics there are many situations in which cal- lations were performed incorrectly for important practical applications. Let us look at some examples, the history of computing the number ? began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated ? (e. g. , Archimedes, Ptolemy, Vi` ete, etc. ). The ?rst formula for computing decimal digits of ? was disc- ered by J. Machin (in 1706), who was the ?rst to correctly compute 100 digits of ?. Then many people used his method, e. g. , W. Shanks calculated ? with 707 digits (within 15 years), although due to mistakes only the ?rst 527 were correct. For the next examples, we can mention the history of computing the ?ne-structure constant ? (that was ?rst discovered by A. Sommerfeld), and the mathematical tables, exact - lutions, and formulas, published in many mathematical textbooks, were not veri?ed rigorously [25]. These errors could have a large e?ect on results obtained by engineers. But sometimes, the solution of such problems required such techn- ogy that was not available at that time. In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to - provetheresultsthatahumancanobtainwithoutanytechnology. With respectto our example of computing?, we can mention that recently (in 2002) Y. Kanada, Y. Ushiro, H. Kuroda, and M.

By: Inna K. Shingareva, Carlos Lizarraga-Celaya
Imprint: Springer Verlag GmbH
Country of Publication: Austria
Edition: 2nd ed. 2009
Dimensions: Height: 235mm, Width: 155mm, Spine: 25mm
Weight: 765g
ISBN: 9783211994313
ISBN 10: 3211994319
Pages: 484
Publication Date: 01 September 2009
Audience: Professional and scholarly , Undergraduate
Format: Mixed media product
Publisher's Status: Active

I Foundations of Maple and Mathematica.- Maple.- Mathematica.- II Mathematics: Maple and Mathematica.- Graphics.- Algebra.- Linear Algebra.- Geometry.- Calculus and Analysis.- Complex Functions.- Special Functions and Orthogonal Polynomials.- Integral and Discrete Transforms.- Mathematical Equations.- Numerical Analysis and Scientific Computing.