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Visual Mathematics, Illustrated by the Ti-92 and the Ti-89 - Jean-Michel Ferrard

Visual Mathematics, Illustrated by the Ti-92 and the Ti-89

By: Jean-Michel Ferrard (Editor), Henri Lemberg (Editor)

Paperback Published: 1st March 2000
ISBN: 9782287596858
Number Of Pages: 451

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The aim of this book is to present basic and advanced mathematical concepts using the graphical and traditional calculator, the TI 92 and the TI 89. These mathematical concepts are commonly taught at some stage of the first three years of college curricula; Analysis (approximations, convergence, differential equations, etc.) Linear Algebra (orthogonality, reduction, etc.). The idea behind this book is totally original and will teach the reader not only all the necessary theorems and examples, but illustrations of the calculator screens and the programs (short versions) will allow the reader to visualize these new concepts directly from the book, or on the calculator, leading to a better understanding through "seeing" and "touching" the mathematical lesson being taught.

Discrete Dynamical Systemsp. 1
Dynamical systems in Rp. 1
Newton's method in Rp. 21
Equivalence between different systemsp. 25
Dynamical systems of the planep. 26
Differential Equationsp. 41
Definition of the problemp. 41
Linear equations of first orderp. 42
Non linear first order equationsp. 48
Systems of differential equations of first orderp. 59
Linear differential equations of order np. 76
Autonomous systems of the planep. 82
Numeric solutionsp. 98
The Laplace transformationp. 106
Fourier analysisp. 111
Fourier seriesp. 111
Acceleration of convergence of Fourier seriesp. 126
Hilbert analysisp. 131
Discrete Fourier Transformp. 135
Fast Fourier Transformp. 138
An introduction to waveletsp. 144
Interpolation and approximationp. 159
Interpolating polynomialsp. 159
The Runge phenomenonp. 171
Interpolating by equally spaces x-valuesp. 172
Hermite interpolationp. 178
Bezier curvesp. 187
Spline functionsp. 192
Interpolating by rational fractionsp. 204
Trigonometric interpolationp. 213
Orthogonalityp. 221
PreHilbert or Inner Product Spacesp. 221
Problems of least squaresp. 230
Orthogonal polynomialsp. 244
Gaussian quadraturep. 267
Orthogonal operatorsp. 274
QR factorizationp. 288
Eigenvalues and eigenvectorsp. 305
Review of theoryp. 305
Reduction of operatorsp. 319
Localization of eigenvaluesp. 351
Power methods of finding eigenvaluesp. 360
Other iterative methodsp. 378
Symetric operatorsp. 388
Positive symetric matricesp. 409
Calculator guidep. 421
Expansion, factorizationp. 421
Equations and systemsp. 424
Differentiation and integrationp. 430
Matrices and listsp. 433
Sums, products, limitsp. 439
Expressions, sub-expressionsp. 440
Bibliographyp. 441
List of the programsp. 443
Symbols used in the bookp. 447
Indexp. 449
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9782287596858
ISBN-10: 2287596852
Audience: General
Format: Paperback
Language: English
Number Of Pages: 451
Published: 1st March 2000
Publisher: Springer Editions
Country of Publication: FR
Dimensions (cm): 23.22 x 15.44  x 2.01
Weight (kg): 0.79

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