Discovering Mathematics with Maple

An interactive exploration for mathematicians, engineers and econometricians
1999
ISBN: 978-3-7643-6091-7
Verlag: Springer

Buch, Englisch, 229 Seiten, Paperback, Format (B × H): 178 mm x 254 mm, Gewicht: 474 g

his book grew out of the wish to let students of econometrics get acquainted T with the powerful techniques of computer algebra at an early stage in their curriculum. As no textbook available at the time met our requirements as to content and presentation, we had no other choice than to write our own course material. The try-out on a group of 80 first year students was not without success, and after adding some necessary modifications, the same material was presented to a new group of students of similar size the year after. Some more adjustments were made, and the final result now lies before you. Working with computer algebra packages like Derive, Mathematica, and Maple over many years convinced us of the favourable prospects of computer algebra as a means of improving the student's understanding of the difficult concepts on which mathematical techniques are often based. Moreover, advanced mathematical ed­ ucation, be it for mathematics itself or for mathematical statistics, operations research and other branches of applied mathematics, can greatly profit from the large amount of non-trivial mathematical knowledge that is stored in a computer algebra system. Admittedly, the fact remains that many a tough mathematical problem, such as solving a complicated non-linear system or obtaining a finite ex­ pression for a multiple parameter integral, can not easily be handled by computer algebra either, if at all.

Zielgruppe

Research

Autoren/Hrsg.

Kaashoek, J. F.

Stroeker, R.J.

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik

Inhaltsverzeichnis

1 A Tour of Maple V.- 1.1 Introduction.- 1.2 Maple’s User Interface.- 1.3 Just a Maple Session.- 1.4 Worksheets and Assignments.- 1.5 Exercises.- 1.6 Survey of Used Maple Expressions.- 2 Functions and Sequences.- 2.1 Introduction.- 2.2 Selected Concepts from Analysis.- 2.3 A Tricky Probability Function.- 2.4 Worksheets and Assignments.- 2.5 Exercises.- 2.6 Survey of Used Maple Expressions.- 3 Matrices and Vectors.- 3.1 Introduction.- 3.2 Selected Concepts from Linear Algebra.- 3.3 A Least Squares Filter.- 3.4 Worksheets and Assignments.- 3.5 Exercises.- 3.6 Survey of Used Maple Expressions.- 4 Counting and Summation.- 4.1 Introduction.- 4.2 Selected Concepts from Discrete Mathematics.- 4.3 Binomial Coefficients.- 4.4 Worksheets and Assignments.- 4.5 Exercises.- 4.6 Survey of Used Maple Expressions.- 5 Derivative and Integral.- 5.1 Introduction.- 5.2 Further Concepts from Analysis.- 5.3 Riemann’s Non-differentiable Function.- 5.4 Worksheets and Assignments.- 5.5 Exercises.- 5.6 Survey of Used Maple Expressions.- 6 Vector Spaces and Linear Mappings.- 6.1 Introduction.- 6.2 Further Concepts from Linear Algebra.- 6.3 Diagonalization and the SVD.- 6.4 Worksheets and Assignments.- 6.5 Exercises.- 6.6 Survey of Used Maple Expressions.- A Exercises in Experimentation.- A.1 Upper Bound for a Parameterized Function.- A.2 Matrix Differentiation.- A.3 Chaotic Sequences.- B Hints and Answers.- B.1 Exercises 1.5.- B.2 Exercises 2.5.- B.3 Exercises 3.5.- B.4 Exercises 4.5.- B.5 Exercises 5.5.- B.6 Exercises 6.5.- C Quick Guide to Selected Maple Commands.- C.1 Linear Algebra.- C.1.1 Elementary Matrix Algebra.- C.1.2 Elementary Vector Algebra.- C.1.4 Eigenvalues and Eigenvectors.- C.2 Mathematical Analysis.- C.2.1 Writing Your Own Procedures.- C.2.2 Plotting the Graph of aFunction.- C.2.3 Computing Limits.- C.2.4 Differential Calculus.- C.2.5 Integration.- C.2.6 Solving Equations.- C.2.7 Solving Differential/Difference Equations.- C.3 Statistics.- C.3.1 Probabilities.- C.3.2 Generating Random Numbers.- C.3.3 Analysis of Statistical Data.- C.4 Linear Programming.- C.5 Mathematical Finance.