Maple and Mathematica

1. Front Matter

   Pages i-xvi

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2. Foundations of Maple and Mathematica

   1. Front Matter

      Pages 1-1

      PDF

3. Part I Foundations of Maple and Mathematica

   1. Maple

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 3-22

   2. Mathematica

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 23-48

4. Mathematics: Maple and Mathematica

   1. Front Matter

      Pages 49-49

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5. Part II Mathematics: Maple and Mathematica

   1. Graphics

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 51-68

   2. Algebra

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 69-132

   3. Linear Algebra

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 133-188

   4. Geometry

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 189-206

   5. Calculus and Analysis

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 207-244

   6. Complex Functions

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 245-260

   7. Special Functions and Orthogonal Polynomials

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 261-268

   8. Integral and Discrete Transforms

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 269-284

   9. Mathematical Equations

      • Inna Shingareva, Carlos Lizárraga-Celaya

      Pages 285-340

   10. Numerical Analysis and Scientific Computing

       • Inna Shingareva, Carlos Lizárraga-Celaya

       Pages 341-440

6. Back Matter

   Pages 1-44

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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.

• Algebra Software
• Analysis
• Computer Algebra Systems
• Maple
• Mathematica
• Problem Solving
• linear algebra

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