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Cover: 9783211994313 | Maple and Mathematica | A Problem Solving Approach for Mathematics
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Maple and Mathematica
A Problem Solving Approach for Mathematics
Taschenbuch von Carlos Lizárraga-Celaya (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

Side by side comparisons of practical solutions of the two computer algebra programs, Maple and Mathematica

First book to give a handy reference for these popular systems

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2009
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 504
Inhalt: xviii
484 S.
ISBN-13: 9783211994313
ISBN-10: 3211994319
Sprache: Englisch
Herstellernummer: 12689057
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lizárraga-Celaya, Carlos
Shingareva, Inna K.
Auflage: 2nd ed. 2009
Hersteller: Springer Vienna
Springer-Verlag GmbH
Maße: 235 x 155 x 28 mm
Von/Mit: Carlos Lizárraga-Celaya (u. a.)
Erscheinungsdatum: 01.09.2009
Gewicht: 0,756 kg
preigu-id: 101511792
Zusammenfassung

Side by side comparisons of practical solutions of the two computer algebra programs, Maple and Mathematica

First book to give a handy reference for these popular systems

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2009
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 504
Inhalt: xviii
484 S.
ISBN-13: 9783211994313
ISBN-10: 3211994319
Sprache: Englisch
Herstellernummer: 12689057
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lizárraga-Celaya, Carlos
Shingareva, Inna K.
Auflage: 2nd ed. 2009
Hersteller: Springer Vienna
Springer-Verlag GmbH
Maße: 235 x 155 x 28 mm
Von/Mit: Carlos Lizárraga-Celaya (u. a.)
Erscheinungsdatum: 01.09.2009
Gewicht: 0,756 kg
preigu-id: 101511792
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