Visual mathematics, illustrated by the TI-92 and the TI-89:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Paris ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ;
Springer
2000
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 440 S. Illustrationen |
| ISBN: | 2287596852 |
Staff View
MARC
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| 100 | 1 | |a Dorner, George C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Visual mathematics, illustrated by the TI-92 and the TI-89 |c George C. Dorner ; Jean Michel Ferrard ; Henri Lemberg |
| 264 | 1 | |a Paris ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; |b Springer |c 2000 | |
| 300 | |a 440 S. |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Algebra |x Graphic methods | |
| 650 | 4 | |a Graphic calculators | |
| 650 | 4 | |a TI-89 (Calculator) | |
| 650 | 4 | |a TI-92 (Calculator) | |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a TI 89 |0 (DE-588)4517814-8 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Ferrard, Jean Michel |e Verfasser |4 aut | |
| 700 | 1 | |a Lemberg, Henri |e Verfasser |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008954750 | |
Record in the Search Index
| _version_ | 1807504669412425728 |
|---|---|
| adam_text |
CONTENTS
1.
DISCRETE
DYNAMICAL
SYSTEMS
1
1.
DYNAMICAL
SYSTEMS
IN
R
1
THE
LOGISTIC
MODEL
OF
VERHULST
1
THE
CASE
OF
CONVERGENCE
5
CYCLES
7
THE
BIFURCATION
DIAGRAM
10
THE
FEIGENBAUM
CONSTANT
11
STUDY
OF
CYCLES
16
2.
NEWTON
'
S
METHOD
IN
R
21
3.
EQUIVALENCE
BETWEEN
DIFFERENT
SYSTEMS
25
4.
DYNAMICAL
SYSTEMS
OF
THE
PLANE
26
JULIA
SETS
26
THE
MANDELBROT
SET
29
REVISITING
NEWTON
'
S
METHOD
31
THE
HENON
ATTRACTOR
35
2.
DIFFERENTIAL
EQUATIONS
41
1.
DEFINITION
OF
THE
PROBLEM
41
2.
LINEAR
EQUATIONS
OF
FIRST
ORDER
42
NON
NORMALIZED
EQUATIONS
45
3.
NON
LINEAR
FIRST
ORDER
EQUATIONS
48
EXAMPLES
OF
THE
CAUCHY-LIPSCHITZ
THEOREM
53
4.
SYSTEMS
OF
DIFFERENTIAL
EQUATIONS
OF
FIRST
ORDER
59
LINEAR
DIFFERENTIAL
SYSTEMS
OF
FIRST
ORDER
60
DIFFERENTIAL
SYSTEMS
WITH
CONSTANT
COEFFICIENTS
65
5.
LINEAR
DIFFERENTIAL
EQUATIONS
OF
ORDER
N
76
LINEAR
EQUATIONS
OF
ORDER
2
WITH
CONSTANT
COEFFICIENTS
76
LINEAR
EQUATIONS
OF
ORDER
N
WITH
CONSTANT
COEFFICIENTS
80
6.
AUTONOMOUS
SYSTEMS
OF
THE
PLANE
82
LINEAR
SYSTEMS
82
NON
LINEAR
SYSTEMS
89
7.
NUMERIC
SOLUTIONS
98
EULER
'
S
METHOD
98
RUNGE-KUTTA
METHOD
102
8.
THE
LAPLACE
TRANSFORMATION
106
3.
FOURIER
ANALYSIS
111
1.
FOURIER
SERIES
111
CONVERGENCE
OF
FOURIER
SERIES
114
THE
GIBBS
PHENOMENON
119
CESARO
SUMMABILITY
121
2.
ACCELERATION
OF
CONVERGENCE
OF
FOURIER
SERIES
126
3.
Z
HILBERT
ANALYSIS
131
4.
DISCRETE
FOURIER
TFANSFORM
135
5.
FAST
FOURIER
TRANSFORM
138
PRINCIPLE
OF
THE
FFT
138
PROGRAMMING
THE
FFT
140
APPLICATIONS
OF
THE
FFT
141
6.
AN
INTRODUCTION
TO
WAVELETS
144
GABOR
WINDOWS
146
THE
MORLET
WAVELETS
149
THE
MULTI-RESOLUTION
ANALYSIS
151
4.
INTERPOLATION
AND
APPROXIMATION
159
1.
INTERPOLATING
POLYNOMIALS
159
THE
LAGRANGE
FORM
OF
THE
INTERPOLATING
POLYNOMIAL
159
THE
VANDERMONDE
FORM
161
NEWTON
'
S
INTERPOLATING
POLYNOMIAL
163
NEVILLE
'
S
ALGORITHM
168
2.
THE
RUNGE
PHENOMENON
171
3.
INTERPOLATING
BY
EQUALLY
SPACES
A?-VALUES
172
CALCULATION
OF
THE
INTERPOLATION
ERROR
174
4.
HERMITE
INTERPOLATION
178
FROM
LAGRANGE
TO
HERMITE
178
CHEBYSHEV
TO
THE
RESCUE
OF
HERMITE
180
RETURN
TO
DIVIDED
DIFFERENCES
183
POLYNOMIAL
INTERPOLATION
"
A
LA
CARTE
"
185
5.
BEZIER
CURVES
187
THE
CASTELJAU
ALGORITHM
191
6.
SPLINE
FUNCTIONS
192
A
FIRST
EXAMPLE
192
DEFINITIONS
AND
FORST
PROPERTIES
FOR
SPLINES
194
INTERPOLATION
USING
SPLINE
FUNCTIONS
196
CONVERGENCE
199
ALGORITHM
FOR
CALCULATION
OF
CUBIC
SPLINES
200
7.
INTERPOLATING
BY
RATIONAL
FRACTIONS
204
A
"
VANDERMONDE
STYLE
"
METHOD
205
RECIPROCAL
DIVIDED
DIFFERENCES
209
USE
OF
RECIPROCAL
DIVIDED
DIFFERENCES
211
8.
TRIGONOMETRIC
INTERPOLATION
213
RETURN
TO
POLYNOMIAL
INTERPOLATION
214
USING
UNDERTERMINED
COEFFICIENTS
216
EQUIDISTANTS
ABSCISSAS
216
5.
ORTHOGONALITY
221
1.
PREHILBERT
OR
INNER
PRODUCT
SPACES
221
INNER
PRODUCT
221
CLASSICAL
EXAMPLES
222
ORTHONORMAL
FAMILIES
224
ORTHOGONAL
COMPLEMENT
OF
A
SUBSPACE
226
GRAM-SCHMIDT
ORTHOGONALIZATION
227
2.
PROBLEMS
OF
LEAST
SQUARES
230
DISTANCE
TO
A
SUBSPACE
231
"
CONTINUOUS
"
OR
"
DISCRETE
"
LEAST
SQUARES:
A
COMPARISON
233
"
DISCRETE
"
LEAST
SQUARES.
A
GENERALIZATION
239
3.
ORTHOGONAL
POLYNOMIALS
244
FIRST
PROPERTIES
244
CHEBYSHEV
POLYNOMIALS
248
CHEBYSHEV
POLYNOMIALS
AND
DISCRETE
LEAST
SQUARES
254
LEGENDRE
POLYNOMIALS
259
LAGUERRE
AND
HERMITE
POLYNOMIALS
265
4.
GAUSSIAN
QUADRATURE
267
INTRODUCTION
TO
THE
METHOD
267
THE
USE
OF
ORTHOGONAL
POLYNOMIALS
268
PRECISION
OF
THE
METHOD
269
THE
CLASSIC
CASES
OF
GAUSSIAN
QUADRATURE
271
5.
ORTHOGONAL
OPERATORS
274
GENERAL
INFORMATION
ABOUT
ORTHOGONAL
OPERATORS
275
ISOMETRIES
OF
THE
PLANE
278
ISOMETRIES
OF
SPACE
279
ISOMETRIES
IN
DIMENSION
N
286
UNITARY
MATRICES
287
6.
QR
FACTORIZATION
288
USE
OF
THE
GRAM-SCHMIDT
ALGORITHM
290
TOWARD
OTHER
METHODS
291
GIVENS
'
METHOD
292
HOUSEHOLDER
'
S
METHOD
295
QUESTIONS
OF
PRECISION
300
6.
EIGENVALUES
AND
EIGENVECTORS
305
1.
REVIEW
OF
THEORY
305
FIRST
DEFINITIONS
305
POLYNOMIALS
OF
OPERATORS
309
POLYNOMIALS
OF
MATRICES
311
POLYNOMIALS
ANNIHILATORS
312
THE
CHARACTERISTIC
POLYNOMIAL
314
2.
REDUCTION
OF
OPERATORS
319
EIGENVALUES
AND
MULTIPLICITIES
320
FINDING
EIGENSPACES
321
DIAGONALIZATION
327
TRIANGULARIZATION
331
JORDAN
MATRICES
332
JORDAN
REDUCTION
335
CHARACTERISTIC
SUBSPACES
343
THE
DUNFORD
DECOMPOSITION
AND
APPLICATIONS
344
3.
LOCALIZATION
OF
EIGENVALUES
351
THE
INSTRUCTIONS
EIGVL
AND
EIGVC
352
MATRIX
NORMS
AND
THE
SPECTRAL
RADIUS
354
GERSHGORIN
DISKS
358
4.
POWER
METHODS
OF
FINDING
EIGENVALUES
360
DIRECT
ITERATIONS
(FAVORABLE
CASE)
360
DIRECT
ITERATIONS
(UNFAVORABLE
CASE)
367
ITERATED
INVERSE
POWERS
374
ITERATIONS
TO
AN
ARBITRARY
EIGENVALUE
375
IMPROVEMENT
OF
THE
METHOD
377
5.
OTHER
ITERATIVE
METHODS
378
USE
OF
THE
LU
DECOMPOSITION
378
USE
OF
THE
QR
DECOMPOSITION
380
THE
JACOBI
METHOD
FOR
REAL
SYMETRIC
MATRICES
381
6.
SYMETRIC
OPERATORS
388
REVIEW
OF
THEORY
389
SYMETRIC
OR
HERMITIAN
MATRICES
390
DIAGONALIZATION
IN
AN
ORTHONORMAL
BASIS
392
ORTHOGONAL
POLYNOMIALS:
A
RETURN
VISIT
399
TRIDIAGONALIZATION
OF
SYMETRIC
MATRICES
401
7.
POSITIVE
SYMETRIC
MATRICES
409
PRELIMINARY
THEORY
409
SQUARE
ROOT
OF
A
POSITIVE
SYMETRIC
MATRIX
411
POLAR
DECOMPOSITION
414
THE
CHOLEVSKY
DECOMPOSITION
415
CALCULATOR
GUIDE
421
EXPANSION,
FACTORIZATION
421
EXPANSION
421
FACTORIZATION
423
EQUATIONS
AND
SYSTEMS
424
THE
EQUATION
F(X)
=
0
424
THE
NUMERICAL
SOLVER
426
SYSTEMS
OF
EQUATIONS
427
DIFFERENTIAL
EQUATIONS
428
DIFFERENTIATION
AND
INTEGRATION
430
SYMBOLIC
DIFFERENTIATION
430
NUMERIC
DIFFERENTIATION
431
TAYLOR
FORMULA
431
INTEGRATION
432
MATRICES
AND
LISTS
433
MATRICES
433
LISTS
437
SUMS,
PRODUCTS,
LIMITS
439
EXPRESSIONS,
SUB-EXPRESSIONS
440
BIBLIOGRAPHY
441
LIST
OF
THE
PROGRAMS
443
SYMBOLS
USED
IN
THE
BOOK
447
INDEX
449 |
| any_adam_object | 1 |
| author | Dorner, George C. Ferrard, Jean Michel Lemberg, Henri |
| author_facet | Dorner, George C. Ferrard, Jean Michel Lemberg, Henri |
| author_role | aut aut aut |
| author_sort | Dorner, George C. |
| author_variant | g c d gc gcd j m f jm jmf h l hl |
| building | Verbundindex |
| bvnumber | BV013144347 |
| callnumber-first | Q - Science |
| callnumber-label | QA155 |
| callnumber-raw | QA155.7.G73 |
| callnumber-search | QA155.7.G73 |
| callnumber-sort | QA 3155.7 G73 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 900 |
| classification_tum | DAT 758f |
| ctrlnum | (OCoLC)43495143 (DE-599)BVBBV013144347 |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV013144347 |
| illustrated | Illustrated |
| indexdate | 2024-08-16T01:12:59Z |
| institution | BVB |
| isbn | 2287596852 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008954750 |
| oclc_num | 43495143 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-188 |
| physical | 440 S. Illustrationen |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| spelling | Dorner, George C. Verfasser aut Visual mathematics, illustrated by the TI-92 and the TI-89 George C. Dorner ; Jean Michel Ferrard ; Henri Lemberg Paris ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; Springer 2000 440 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Algebra Graphic methods Graphic calculators TI-89 (Calculator) TI-92 (Calculator) Lineare Algebra (DE-588)4035811-2 gnd rswk-swf TI 89 (DE-588)4517814-8 gnd rswk-swf TI 92 (DE-588)4401164-7 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s TI 92 (DE-588)4401164-7 s DE-604 Lineare Algebra (DE-588)4035811-2 s TI 89 (DE-588)4517814-8 s Ferrard, Jean Michel Verfasser aut Lemberg, Henri Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008954750&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dorner, George C. Ferrard, Jean Michel Lemberg, Henri Visual mathematics, illustrated by the TI-92 and the TI-89 Algebra Graphic methods Graphic calculators TI-89 (Calculator) TI-92 (Calculator) Lineare Algebra (DE-588)4035811-2 gnd TI 89 (DE-588)4517814-8 gnd TI 92 (DE-588)4401164-7 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4517814-8 (DE-588)4401164-7 (DE-588)4001865-9 |
| title | Visual mathematics, illustrated by the TI-92 and the TI-89 |
| title_auth | Visual mathematics, illustrated by the TI-92 and the TI-89 |
| title_exact_search | Visual mathematics, illustrated by the TI-92 and the TI-89 |
| title_full | Visual mathematics, illustrated by the TI-92 and the TI-89 George C. Dorner ; Jean Michel Ferrard ; Henri Lemberg |
| title_fullStr | Visual mathematics, illustrated by the TI-92 and the TI-89 George C. Dorner ; Jean Michel Ferrard ; Henri Lemberg |
| title_full_unstemmed | Visual mathematics, illustrated by the TI-92 and the TI-89 George C. Dorner ; Jean Michel Ferrard ; Henri Lemberg |
| title_short | Visual mathematics, illustrated by the TI-92 and the TI-89 |
| title_sort | visual mathematics illustrated by the ti 92 and the ti 89 |
| topic | Algebra Graphic methods Graphic calculators TI-89 (Calculator) TI-92 (Calculator) Lineare Algebra (DE-588)4035811-2 gnd TI 89 (DE-588)4517814-8 gnd TI 92 (DE-588)4401164-7 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Algebra Graphic methods Graphic calculators TI-89 (Calculator) TI-92 (Calculator) Lineare Algebra TI 89 TI 92 Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008954750&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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