Calculus problem solutions with MATLAB:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
De Gruyter
[2020]
[Beijing] Tsinghua University Press [2020] |
| Series: | De Gruyter STEM
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XII, 300 Seiten Illustrationen 24 cm, 535 g |
| ISBN: | 9783110663624 3110663627 |
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MARC
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| 100 | 1 | |a Xue, Dingyu |e Verfasser |0 (DE-588)1098160967 |4 aut | |
| 245 | 1 | 0 | |a Calculus problem solutions with MATLAB |c Dingyü Xue |
| 264 | 1 | |a Berlin |b De Gruyter |c [2020] | |
| 264 | 1 | |a [Beijing] |b Tsinghua University Press |c [2020] | |
| 264 | 4 | |c © 2020 | |
| 300 | |a XII, 300 Seiten |b Illustrationen |c 24 cm, 535 g | ||
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-066375-4 |
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| _version_ | 1804181472221855744 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
V
1
INTRODUCTION
TO
CALCULUS
PROBLEMS
*
1
1.1
A
BRIEF
HISTORY
OF
CALCULUS
*
1
1.2
MAIN
TOPICS
IN
THE
BOOK
*
2
2
FUNCTIONS
AND
SEQUENCES
*
5
2.1
FUNCTIONS
AND
MAPPINGS
*
5
2.1.1
DEFINITIONS
OF
FUNCTIONS
*
5
2.1.2
MATLAB
COMPUTATION
OF
COMMONLY
USED
TRANSCENDENTAL
FUNCTIONS
*
6
2.1.3
MATLAB
REPRESENTATION
OF
FUNCTIONS
*
6
2.1.4
CURVES
AND
SURFACES
OF
FUNCTIONS
*
7
2.2
DESCRIPTIONS
OF
VARIOUS
FUNCTIONS
*
8
2.2.1
INVERSE
FUNCTIONS
*
8
2.2.2
COMPOSITE
FUNCTIONS
*
8
2.2.3
DESCRIBING
PIECEWISE
FUNCTIONS
*
10
2.2.4
IMPLICIT
FUNCTIONS
*
12
2.2.5
PARAMETRIC
EQUATIONS
*
14
2.2.6
POLAR
FUNCTIONS
*
16
2.3
ODD
AND
EVEN
FUNCTIONS
*
17
2.4
COMPLEX-VALUED
FUNCTIONS
AND
MAPPING
*
18
2.4.1
COMPLEX
MATRICES
AND
MANIPULATIONS
*
18
2.4.2
MAPPING
OF
COMPLEX-VALUED
FUNCTIONS
*
18
2.4.3
RIEMANN
SURFACES
*
20
2.5
NUMERIC
AND
FUNCTIONAL
SEQUENCES
*
23
2.6
EXERCISES
*
25
3
LIMITS
*
27
3.1
LIMITS
OF
UNIVARIATE
FUNCTIONS
*
28
3.1.1
THE
-5
DEFINITION
*
28
3.1.2
LIMIT
COMPUTING
WITH
MATLAB
-----30
3.1.3
LIMITS
OF
COMPOSITE
FUNCTIONS
*
32
3.1.4
LIMITS
OF
SEQUENCES
*
33
3.1.5
LIMITS
OF
PIECEWISE
FUNCTIONS
*
35
3.1.6
INFINITESIMALS
AND
INFINITY
*
35
3.2
SINGLE-SIDED
LIMITS
AND
CONTINUITY
OF
FUNCTIONS
*
36
3.2.1
LEFT
AND
RIGHT
LIMITS
*
36
3.2.2
CONTINUITY
OF
FUNCTIONS
-----
38
3.2.3
INTERVAL
LIMITS
*
40
3.2.4
APPLICATIONS
OF
CONTINUITY
-
ASSESSMENT
OF
EQUATION
SOLUTIONS
*
40
VIII
*
-
CONTENTS
3.3
3.3.1
3.3.2
3.4
3.4.1
3.4.2
3.5
SINGULARITIES,
POLES
AND
RESIDUES
OF
COMPLEX
FUNCTIONS
*
42
COMPUTATION
OF
SINGULARITIES
AND
POLES
*
42
RESIDUES
OF
COMPLEX
FUNCTIONS
-----
43
LIMITS
OF
MULTIVARIATE
FUNCTIONS
*
45
SEQUENTIAL
LIMITS
*
45
MULTIPLE
LIMITSAND
COMPUTATIONS
*
46
EXERCISES
*
49
4
4.1
4.1.1
4.1.2
4.1.3
4.1.4
4.1.5
4.2
4.3
4.3.1
4.3.2
4.3.3
4.4
4.4.1
4.4.2
4.4.3
4.5
4.5.1
4.5.2
4.5.3
4.6
4.6.1
4.6.2
4.6.3
4.7
4.7.1
4.7.2
4.7.3
4.8
DERIVATIVES
AND
DIFFERENTIALS
*
53
DERIVATIVES
AND
HIGH-ORDER
DERIVATIVES
*
54
DERIVATIVES
AND
DIFFERENTIALS
*
54
HIGHER-ORDER
DERIVATIVES
*
55
DERIVATIVES
OF
COMPOSITE
FUNCTIONS
*
58
DERIVATIVES
OF
PIECEWISE
FUNCTIONS
*
59
DERIVATIVES
OF
MATRICES
*
60
DERIVATIVES
OF
PARAMETRIC
EQUATIONS
*
61
PARTIAL DERIVATIVES
OF
MULTIVARIATE
FUNCTIONS
*
63
PARTIAL DERIVATIVES
*
63
TOTAL
DIFFERENTIAL
*
66
DERIVATIVES
OF
COMPOSITE
FUNCTIONS
*
66
INTRODUCTION
TO
FIELDS
*
67
SCALAR
AND
VECTOR
FIELDS
*
68
GRADIENT,
DIVERGENCE,
AND
CURL
*
68
POTENTIALS
OF
A
VECTOR
FIELD
-----
70
DERIVATIVE
MATRICES
*
71
JACOBIAN
MATRIX
*
71
HESSIAN
MATRIX
*
72
LAPLACIAN
OPERATORS
FOR
SCALAR
FIELDS
*
72
PARTIAL DERIVATIVES
OF
IMPLICIT
FUNCTIONS
*
73
FIRST-ORDER
DERIVATIVE
OF
AN
IMPLICIT
FUNCTION
*
73
HIGHER-ORDER
DERIVATIVES
OF
IMPLICIT
FUNCTIONS
*
74
PARTIAL DERIVATIVES
OF
SIMULTANEOUS
IMPLICIT
FUNCTIONS
*
76
APPLICATIONS
OF
DERIVATIVES
AND
DIFFERENTIALS
*
79
EXTREME
VALUE
PROBLEM
*
79
NEWTON-RAPHSON
ITERATIVE
ALGORITHM
*
82
TANGENT
PLANES
AND
NORMAL
LINES
*
83
EXERCISES
*
85
5
5.1
5.2
5.2.1
INTEGRALS
*
87
INDEFINITE
INTEGRALS
OF
UNIVARIATE
FUNCTIONS
*
87
DEFINITE
AND
IMPROPER
INTEGRALS
*
92
DEFINITE
INTEGRALS
*
92
CONTENTS
*
IX
5.2.2
5.3
5.3.1
5.3.2
5.3.3
5.3.4
5.4
5.4.1
5.4.2
5.4.3
5.4.4
5.4.5
5.5
5.5.1
5.5.2
5.6
5.6.1
5.6.2
5.7
INFINITE
AND
IMPROPER
INTEGRALS
*
95
MULTIPLE
INTEGRALS
*
98
MULTIPLE
INDEFINITE
INTEGRALS
*
98
CONSTRUCTIONS
OF
UNDETERMINED
POLYNOMIALS
*
99
COMPUTATION
OF
MULTIPLE
INTEGRALS
*
100
CONVERSIONS
OF
INTEGRATION
REGIONS
*
102
APPLICATIONS
OF
DEFINITE
INTEGRALS
*
103
COMPUTATION
OF
ARC
LENGTH
*
103
COMPUTATION
OF
VOLUME
*
105
VOLUME
AND
MASS
COMPUTATION
*
106
COMPUTATION
OF
PROBABILITY
DISTRIBUTION
*
108
AN
INTRODUCTION
TO
INTEGRAL
TRANSFORMS
*
109
PATH
INTEGRALS
*
109
TYPE
1
PATH
INTEGRAL
*
110
TYPE
II
PATH
INTEGRAL
*
112
SURFACE
INTEGRALS
*
114
TYPE
1
SURFACE
INTEGRALS
*
114
TYPE
II
SURFACE
INTEGRALS
*
116
EXERCISES
*
118
6
6.1
6.1.1
6.1.2
6.1.3
6.1.4
6.2
6.2.1
6.2.2
6.2.3
6.2.4
6.3
6.3.1
6.3.2
6.3.3
6.4
6.4.1
6.4.2
6.5
6.5.1
6.5.2
6.6
SERIES
AND
FUNCTION
FITTING
*
121
SERIES
SUMS
*
121
NUMBER
SERIES
SUMS
*
121
SUM
OF
INFINITE
SERIES
*
125
SUM
OF
FUNCTIONAL
SERIES
*
127
SPECIAL
INFINITE
TERM
PROBLEMS
*
128
CONVERGENCE
TESTS
FOR
INFINITE
SERIES
*
131
GENERAL
DESCRIPTION
OF
A
POSITIVE
SERIES
*
131
CONVERGENCE
TESTS
FOR
POSITIVE
SERIES
*
131
CONVERGENCE
TEST
FOR
ALTERNATING
SERIES
*
133
CONVERGENCE
INTERVAL
OF
A
FUNCTIONAL
SERIES
*
134
PRODUCTS
OF
SEQUENCES
*
135
PRODUCTS
OF
NUMBER
SEQUENCES
*
135
PRODUCTS
OF
FUNCTIONAL
SEQUENCES
*
136
CONVERGENCE
TEST
FOR
THE
PRODUCTS
OF
POSITIVE
SEQUENCES
*
137
TAYLOR
SERIES
*
138
TAYLOR
SERIES
EXPANSIONS
FOR
UNIVARIATE
FUNCTIONS
*
139
TAYLOR
SERIES
FOR
MULTIVARIATE
FUNCTIONS
*
142
FOURIER
SERIES
EXPANSIONS
*
144
MATHEMATICAL DESCRIPTION
OF
FOURIER
SERIES
*
144
MATLAB
IMPLEMENTATION
OF
FOURIER
SERIES
-----
145
RATIONAL
FUNCTION
APPROXIMATION
OF
UNIVARIATE
FUNCTIONS
*
148
X
CONTENTS
6.6.1
CONTINUED
FRACTION
EXPANSIONS
----
148
6.6.2
FADE
APPROXIMATIONS
-----
153
6.7
LAURENT
SERIES
------
155
6.7.1
LAURENT
SERIES
EXPANSION
------
155
6.7.2
LAURENT
SERIES
OF
RATIONAL
FUNCTIONS
------
157
6.8
EXERCISES
-----
159
7
NUMERICAL
DERIVATIVES
AND
DIFFERENTIALS
*
163
7.1
NUMERICAL
DERIVATIVE
ALGORITHMS
-----
163
7.1.1
FORWARD
AND
BACKWARD
DIFFERENCE
ALGORITHMS
-----
164
7.1.2
CENTRAL
DIFFERENCE
ALGORITHMS
WITH
O(/?
2
)
PRECISION
-----
164
7.1.3
CENTRAL
DIFFERENCE
ALGORITHM
WITH
O(/?
4
)
PRECISION
-----
165
7.1.4
CENTRAL
DIFFERENCE
ALGORITHMS
OF
HIGHER
PRECISION
-----
166
7.1.5
DERIVING
HIGH-ORDER
HIGH
PRECISION
ALGORITHMS
-----
167
7.1.6
HIGH
PRECISION
FORWARD
AND
BACKWARD
DIFFERENCE
ALGORITHMS
-----
169
7.2
MATLAB
IMPLEMENTATIONS
OF
THE
NUMERICAL
DERIVATIVE
ALGORITHMS
-----
172
7.2.1
IMPLEMENTATION
OFTHEO(/?
2
)
ALGORITHMS
-----
172
7.2.2
IMPLEMENTATION
OF
THE
SEVEN-POINT
CENTRAL
DIFFERENCE
ALGORITHMS
-----
174
7.2.3
IMPLEMENTATION
OF
FORWARD
DIFFERENCE
NUMERICAL
DERIVATIVE
ALGORITHMS
-----
176
7.3
NUMERICAL
DERIVATIVES
OF
ANY
ORDERS
-----
177
7.4
NUMERICAL
PARTIAL
DERIVATIVES
OF
2D
FUNCTIONS
-----
179
7.4.1
GRADIENT
COMPUTATION
-----
179
7.4.2
HIGH
PRECISION
ALGORITHMS
FOR
DERIVATIVES
WITH
RESPECT
TO
A
SINGLE
VARIABLE
-----
181
7.4.3
NUMERICAL
COMPUTATION
OF
MIXED
PARTIAL
DERIVATIVES
-----
183
7.4.4
NUMERICAL
COMPUTATION
OF
HIGH-ORDER
MIXED
PARTIAL
DERIVATIVES
-----
184
7.5
SPLINE
INTERPOLATION
AND
NUMERICAL
DERIVATIVES
-----
185
7.5.1
CUBIC
SPLINE
-----
186
7.5.2
B-SPLINES
-----
189
7.5.3
NUMERICAL
DERIVATIVES
WITH
SPLINES
------
190
7.5.4
UNEQUALLY
SPACED
AND
SCATTERED
SAMPLES
-----
193
7.6
EXERCISES
-----
195
8
NUMERICAL
INTEGRALS
*
197
8.1
NUMERICAL
INTEGRALS
FROM
SAMPLES
-----
197
8.1.1
DIRECT
COMPUTATION
OF
NUMERICAL
DEFINITE
INTEGRALS
-----
197
8.1.2
RECONSTRUCTION
OF
INTEGRAL
FUNCTION
-----
200
8.1.3
HIGH
PRECISION
NUMERICAL
INTEGRATION
ALGORITHM
FOR
EQUALLY
SPACED
SAMPLES
-----
201
8.2
NUMERICAL
INTEGRALS
OF
UNIVARIATE
FUNCTIONS
-----
203
8.2.1
SIMPLE
NUMERICAL
INTEGRAL
PROBLEMS
-----
204
CONTENTS
*
XI
8.2.2
MATLAB
SOLUTIONS
OF
NUMERICAL
INTEGRAL
PROBLEMS
*
205
8.2.3
NUMERICAL
COMPUTATION
OF
IMPROPER
INTEGRALS
*
210
8.2.4
NUMERICAL
INTEGRALS
FOR
INTEGRANDS
WITH
PARAMETERS
*
212
8.2.5
NUMERICAL
SOLUTIONS
OF
INTEGRAL
FUNCTIONS
*
213
8.3
NUMERICAL
COMPUTATION
OF
DOUBLE
INTEGRALS
*
214
8.3.1
COMPUTING
DOUBLE
INTEGRALS
*
215
8.3.2
COMPUTATION
OF
DOUBLE
INTEGRAL
FUNCTIONS
*
216
8.3.3
EVALUATIONS
OF
DOUBLE
INTEGRALS
IN
DIFFERENT
ORDER
*
218
8.4
NUMERICAL
COMPUTATION
OF
MULTIPLE
INTEGRALS
*
219
8.4.1
NUMERICAL
TRIPLE
INTEGRALS
*
219
8.4.2
TRIPLE
INTEGRALS
OF
INTEGRANDS
WITH
PARAMETERS
*
221
8.4.3
MULTIPLE
INTEGRALS
*
222
8.4.4
NUMERICAL
SOLUTIONS
OF
SOME
MULTIPLE
INTEGRALS
WITH
VARIABLE
BOUNDS
-----
224
8.5
OTHER
NUMERICAL
METHODS
FOR
MULTIPLE
INTEGRALS
*
225
8.5.1
NUMERICAL
INTEGRAL
APPROXIMATIONS
WITH
MONTE
CARLO
METHOD
*
226
8.5.2
SPLINE-BASED
INTEGRAL
EVALUATIONS
*
228
8.5.3
NUMERICAL
EVALUATIONS
OF
MULTIPLE
INTEGRALS
*
231
8.6
EXERCISES
*
232
9
INTEGRAL
TRANSFORMS
*
235
9.1
LAPLACE
TRANSFORMS
AND
THEIR
INVERSES
*
235
9.1.1
DEFINITION
AND
PROPERTIES
OF
LAPLACE
TRANSFORM
*
236
9.1.2
COMPUTER
SOLUTIONS
OF
LAPLACE
TRANSFORMS
*
237
9.1.3
SOLVING
DIFFERENTIAL
EQUATIONS
WITH
LAPLACE
TRANSFORM
*
240
9.2
NUMERICAL
SOLUTIONS
OF
LAPLACE
TRANSFORM
PROBLEMS
*
242
9.2.1
NUMERICAL
INVERSE
LAPLACE
TRANSFORM
*
243
9.2.2
IDEAS
OF
FEEDBACK
CONTROL
SYSTEMS
*
243
9.2.3
NUMERICAL
LAPLACE
TRANSFORMS
*
244
9.2.4
COMPUTATION
OF
IRRATIONAL
SYSTEMS
*
247
9.3
FOURIER
TRANSFORMS
AND
THEIR
INVERSES
*
248
9.3.1
DEFINITION
AND
PROPERTIES
OF
FOURIER
TRANSFORMS
*
249
9.3.2
COMPUTER
EVALUATION
OF
FOURIER
TRANSFORM
*
249
9.3.3
FOURIER
SINE
AND
COSINE
TRANSFORMS
*
251
9.3.4
DISCRETE
FOURIER
SINE
AND
COSINE
TRANSFORMS
*
252
9.3.5
FAST
FOURIER
TRANSFORM
*
253
9.4
COMPUTATION
OF
OTHER
INTEGRAL
TRANSFORMS
*
255
9.4.1
MELLIN
TRANSFORM
*
255
9.4.2
COMPUTATION
OF
HANKEL
TRANSFORMS
*
258
9.5
THE
Z
TRANSFORM
AND
ITS
INVERSE
*
259
9.5.1
DEFINITION
AND
PROPERTIES
OF
Z
TRANSFORMS
*
260
9.5.2
COMPUTER
EVALUATION
OF
Z
TRANSFORMS
*
260
XII
*
CONTENTS
9.5.3
9.5.4
9.6
BILATERAL
Z
TRANSFORM
-----
262
NUMERICAL
INVERSE
Z
TRANSFORMS
FOR
RATIONAL
FUNCTIONS
-----
263
EXERCISES
-----
264
10
10.1
10.1.1
10.1.2
10.2
INTRODUCTION
TO
FRACTIONAL
CALCULUS
*
267
DEFINITIONS
IN
FRACTIONAL
CALCULUS
-----
268
WHY
FRACTIONAL
CALCULUS?
-----
268
DEFINITIONS
-----
269
PROPERTIES
AND
RELATIONSHIPS
AMONG
DIFFERENT
FRACTIONAL
CALCULUS
DEFINITIONS
-----
270
10.3
10.3.1
10.3.2
10.3.3
10.4
10.5
10.5.1
10.5.2
10.5.3
10.6
NUMERICAL
IMPLEMENTATION
OF
GRUNWALD-LETNIKOV
DERIVATIVES
-----
272
SIMPLE
GRUNWALD-LETNIKOV
DEFINITION
EVALUATION
-----
272
HIGH
PRECISION
ALGORITHMS
AND
IMPLEMENTATION
-----
272
QUANTITATIVE
COMPARISONS
OF
DIFFERENT
ALGORITHMS
-----
277
NUMERICAL
COMPUTATION
OF
CAPUTO
DERIVATIVES
-----
279
OUSTALOUP
FILTER
ALGORITHMS
AND
APPLICATIONS
-----
282
OUSTALOUP
FILTER
APPROXIMATIONS
*
283
FILTER
FOR
CAPUTO
DERIVATIVE
FITTING
-----
285
SIMULINK-BASED
CAPUTO
DERIVATIVE
COMPUTATION
*
286
NUMERICAL
COMPUTATION
OF
EVEN
HIGHER-ORDER
DERIVATIVES
AND
INTEGRALS
-----
288
10.7
EXERCISES
-----
290
BIBLIOGRAPHY
*
291
MATLAB
FUNCTION
INDEX
*
293
INDEX
*
297
|
| adam_txt |
CONTENTS
PREFACE
*
V
1
INTRODUCTION
TO
CALCULUS
PROBLEMS
*
1
1.1
A
BRIEF
HISTORY
OF
CALCULUS
*
1
1.2
MAIN
TOPICS
IN
THE
BOOK
*
2
2
FUNCTIONS
AND
SEQUENCES
*
5
2.1
FUNCTIONS
AND
MAPPINGS
*
5
2.1.1
DEFINITIONS
OF
FUNCTIONS
*
5
2.1.2
MATLAB
COMPUTATION
OF
COMMONLY
USED
TRANSCENDENTAL
FUNCTIONS
*
6
2.1.3
MATLAB
REPRESENTATION
OF
FUNCTIONS
*
6
2.1.4
CURVES
AND
SURFACES
OF
FUNCTIONS
*
7
2.2
DESCRIPTIONS
OF
VARIOUS
FUNCTIONS
*
8
2.2.1
INVERSE
FUNCTIONS
*
8
2.2.2
COMPOSITE
FUNCTIONS
*
8
2.2.3
DESCRIBING
PIECEWISE
FUNCTIONS
*
10
2.2.4
IMPLICIT
FUNCTIONS
*
12
2.2.5
PARAMETRIC
EQUATIONS
*
14
2.2.6
POLAR
FUNCTIONS
*
16
2.3
ODD
AND
EVEN
FUNCTIONS
*
17
2.4
COMPLEX-VALUED
FUNCTIONS
AND
MAPPING
*
18
2.4.1
COMPLEX
MATRICES
AND
MANIPULATIONS
*
18
2.4.2
MAPPING
OF
COMPLEX-VALUED
FUNCTIONS
*
18
2.4.3
RIEMANN
SURFACES
*
20
2.5
NUMERIC
AND
FUNCTIONAL
SEQUENCES
*
23
2.6
EXERCISES
*
25
3
LIMITS
*
27
3.1
LIMITS
OF
UNIVARIATE
FUNCTIONS
*
28
3.1.1
THE
-5
DEFINITION
*
28
3.1.2
LIMIT
COMPUTING
WITH
MATLAB
-----30
3.1.3
LIMITS
OF
COMPOSITE
FUNCTIONS
*
32
3.1.4
LIMITS
OF
SEQUENCES
*
33
3.1.5
LIMITS
OF
PIECEWISE
FUNCTIONS
*
35
3.1.6
INFINITESIMALS
AND
INFINITY
*
35
3.2
SINGLE-SIDED
LIMITS
AND
CONTINUITY
OF
FUNCTIONS
*
36
3.2.1
LEFT
AND
RIGHT
LIMITS
*
36
3.2.2
CONTINUITY
OF
FUNCTIONS
-----
38
3.2.3
INTERVAL
LIMITS
*
40
3.2.4
APPLICATIONS
OF
CONTINUITY
-
ASSESSMENT
OF
EQUATION
SOLUTIONS
*
40
VIII
*
-
CONTENTS
3.3
3.3.1
3.3.2
3.4
3.4.1
3.4.2
3.5
SINGULARITIES,
POLES
AND
RESIDUES
OF
COMPLEX
FUNCTIONS
*
42
COMPUTATION
OF
SINGULARITIES
AND
POLES
*
42
RESIDUES
OF
COMPLEX
FUNCTIONS
-----
43
LIMITS
OF
MULTIVARIATE
FUNCTIONS
*
45
SEQUENTIAL
LIMITS
*
45
MULTIPLE
LIMITSAND
COMPUTATIONS
*
46
EXERCISES
*
49
4
4.1
4.1.1
4.1.2
4.1.3
4.1.4
4.1.5
4.2
4.3
4.3.1
4.3.2
4.3.3
4.4
4.4.1
4.4.2
4.4.3
4.5
4.5.1
4.5.2
4.5.3
4.6
4.6.1
4.6.2
4.6.3
4.7
4.7.1
4.7.2
4.7.3
4.8
DERIVATIVES
AND
DIFFERENTIALS
*
53
DERIVATIVES
AND
HIGH-ORDER
DERIVATIVES
*
54
DERIVATIVES
AND
DIFFERENTIALS
*
54
HIGHER-ORDER
DERIVATIVES
*
55
DERIVATIVES
OF
COMPOSITE
FUNCTIONS
*
58
DERIVATIVES
OF
PIECEWISE
FUNCTIONS
*
59
DERIVATIVES
OF
MATRICES
*
60
DERIVATIVES
OF
PARAMETRIC
EQUATIONS
*
61
PARTIAL DERIVATIVES
OF
MULTIVARIATE
FUNCTIONS
*
63
PARTIAL DERIVATIVES
*
63
TOTAL
DIFFERENTIAL
*
66
DERIVATIVES
OF
COMPOSITE
FUNCTIONS
*
66
INTRODUCTION
TO
FIELDS
*
67
SCALAR
AND
VECTOR
FIELDS
*
68
GRADIENT,
DIVERGENCE,
AND
CURL
*
68
POTENTIALS
OF
A
VECTOR
FIELD
-----
70
DERIVATIVE
MATRICES
*
71
JACOBIAN
MATRIX
*
71
HESSIAN
MATRIX
*
72
LAPLACIAN
OPERATORS
FOR
SCALAR
FIELDS
*
72
PARTIAL DERIVATIVES
OF
IMPLICIT
FUNCTIONS
*
73
FIRST-ORDER
DERIVATIVE
OF
AN
IMPLICIT
FUNCTION
*
73
HIGHER-ORDER
DERIVATIVES
OF
IMPLICIT
FUNCTIONS
*
74
PARTIAL DERIVATIVES
OF
SIMULTANEOUS
IMPLICIT
FUNCTIONS
*
76
APPLICATIONS
OF
DERIVATIVES
AND
DIFFERENTIALS
*
79
EXTREME
VALUE
PROBLEM
*
79
NEWTON-RAPHSON
ITERATIVE
ALGORITHM
*
82
TANGENT
PLANES
AND
NORMAL
LINES
*
83
EXERCISES
*
85
5
5.1
5.2
5.2.1
INTEGRALS
*
87
INDEFINITE
INTEGRALS
OF
UNIVARIATE
FUNCTIONS
*
87
DEFINITE
AND
IMPROPER
INTEGRALS
*
92
DEFINITE
INTEGRALS
*
92
CONTENTS
*
IX
5.2.2
5.3
5.3.1
5.3.2
5.3.3
5.3.4
5.4
5.4.1
5.4.2
5.4.3
5.4.4
5.4.5
5.5
5.5.1
5.5.2
5.6
5.6.1
5.6.2
5.7
INFINITE
AND
IMPROPER
INTEGRALS
*
95
MULTIPLE
INTEGRALS
*
98
MULTIPLE
INDEFINITE
INTEGRALS
*
98
CONSTRUCTIONS
OF
UNDETERMINED
POLYNOMIALS
*
99
COMPUTATION
OF
MULTIPLE
INTEGRALS
*
100
CONVERSIONS
OF
INTEGRATION
REGIONS
*
102
APPLICATIONS
OF
DEFINITE
INTEGRALS
*
103
COMPUTATION
OF
ARC
LENGTH
*
103
COMPUTATION
OF
VOLUME
*
105
VOLUME
AND
MASS
COMPUTATION
*
106
COMPUTATION
OF
PROBABILITY
DISTRIBUTION
*
108
AN
INTRODUCTION
TO
INTEGRAL
TRANSFORMS
*
109
PATH
INTEGRALS
*
109
TYPE
1
PATH
INTEGRAL
*
110
TYPE
II
PATH
INTEGRAL
*
112
SURFACE
INTEGRALS
*
114
TYPE
1
SURFACE
INTEGRALS
*
114
TYPE
II
SURFACE
INTEGRALS
*
116
EXERCISES
*
118
6
6.1
6.1.1
6.1.2
6.1.3
6.1.4
6.2
6.2.1
6.2.2
6.2.3
6.2.4
6.3
6.3.1
6.3.2
6.3.3
6.4
6.4.1
6.4.2
6.5
6.5.1
6.5.2
6.6
SERIES
AND
FUNCTION
FITTING
*
121
SERIES
SUMS
*
121
NUMBER
SERIES
SUMS
*
121
SUM
OF
INFINITE
SERIES
*
125
SUM
OF
FUNCTIONAL
SERIES
*
127
SPECIAL
INFINITE
TERM
PROBLEMS
*
128
CONVERGENCE
TESTS
FOR
INFINITE
SERIES
*
131
GENERAL
DESCRIPTION
OF
A
POSITIVE
SERIES
*
131
CONVERGENCE
TESTS
FOR
POSITIVE
SERIES
*
131
CONVERGENCE
TEST
FOR
ALTERNATING
SERIES
*
133
CONVERGENCE
INTERVAL
OF
A
FUNCTIONAL
SERIES
*
134
PRODUCTS
OF
SEQUENCES
*
135
PRODUCTS
OF
NUMBER
SEQUENCES
*
135
PRODUCTS
OF
FUNCTIONAL
SEQUENCES
*
136
CONVERGENCE
TEST
FOR
THE
PRODUCTS
OF
POSITIVE
SEQUENCES
*
137
TAYLOR
SERIES
*
138
TAYLOR
SERIES
EXPANSIONS
FOR
UNIVARIATE
FUNCTIONS
*
139
TAYLOR
SERIES
FOR
MULTIVARIATE
FUNCTIONS
*
142
FOURIER
SERIES
EXPANSIONS
*
144
MATHEMATICAL DESCRIPTION
OF
FOURIER
SERIES
*
144
MATLAB
IMPLEMENTATION
OF
FOURIER
SERIES
-----
145
RATIONAL
FUNCTION
APPROXIMATION
OF
UNIVARIATE
FUNCTIONS
*
148
X
CONTENTS
6.6.1
CONTINUED
FRACTION
EXPANSIONS
----
148
6.6.2
FADE
APPROXIMATIONS
-----
153
6.7
LAURENT
SERIES
------
155
6.7.1
LAURENT
SERIES
EXPANSION
------
155
6.7.2
LAURENT
SERIES
OF
RATIONAL
FUNCTIONS
------
157
6.8
EXERCISES
-----
159
7
NUMERICAL
DERIVATIVES
AND
DIFFERENTIALS
*
163
7.1
NUMERICAL
DERIVATIVE
ALGORITHMS
-----
163
7.1.1
FORWARD
AND
BACKWARD
DIFFERENCE
ALGORITHMS
-----
164
7.1.2
CENTRAL
DIFFERENCE
ALGORITHMS
WITH
O(/?
2
)
PRECISION
-----
164
7.1.3
CENTRAL
DIFFERENCE
ALGORITHM
WITH
O(/?
4
)
PRECISION
-----
165
7.1.4
CENTRAL
DIFFERENCE
ALGORITHMS
OF
HIGHER
PRECISION
-----
166
7.1.5
DERIVING
HIGH-ORDER
HIGH
PRECISION
ALGORITHMS
-----
167
7.1.6
HIGH
PRECISION
FORWARD
AND
BACKWARD
DIFFERENCE
ALGORITHMS
-----
169
7.2
MATLAB
IMPLEMENTATIONS
OF
THE
NUMERICAL
DERIVATIVE
ALGORITHMS
-----
172
7.2.1
IMPLEMENTATION
OFTHEO(/?
2
)
ALGORITHMS
-----
172
7.2.2
IMPLEMENTATION
OF
THE
SEVEN-POINT
CENTRAL
DIFFERENCE
ALGORITHMS
-----
174
7.2.3
IMPLEMENTATION
OF
FORWARD
DIFFERENCE
NUMERICAL
DERIVATIVE
ALGORITHMS
-----
176
7.3
NUMERICAL
DERIVATIVES
OF
ANY
ORDERS
-----
177
7.4
NUMERICAL
PARTIAL
DERIVATIVES
OF
2D
FUNCTIONS
-----
179
7.4.1
GRADIENT
COMPUTATION
-----
179
7.4.2
HIGH
PRECISION
ALGORITHMS
FOR
DERIVATIVES
WITH
RESPECT
TO
A
SINGLE
VARIABLE
-----
181
7.4.3
NUMERICAL
COMPUTATION
OF
MIXED
PARTIAL
DERIVATIVES
-----
183
7.4.4
NUMERICAL
COMPUTATION
OF
HIGH-ORDER
MIXED
PARTIAL
DERIVATIVES
-----
184
7.5
SPLINE
INTERPOLATION
AND
NUMERICAL
DERIVATIVES
-----
185
7.5.1
CUBIC
SPLINE
-----
186
7.5.2
B-SPLINES
-----
189
7.5.3
NUMERICAL
DERIVATIVES
WITH
SPLINES
------
190
7.5.4
UNEQUALLY
SPACED
AND
SCATTERED
SAMPLES
-----
193
7.6
EXERCISES
-----
195
8
NUMERICAL
INTEGRALS
*
197
8.1
NUMERICAL
INTEGRALS
FROM
SAMPLES
-----
197
8.1.1
DIRECT
COMPUTATION
OF
NUMERICAL
DEFINITE
INTEGRALS
-----
197
8.1.2
RECONSTRUCTION
OF
INTEGRAL
FUNCTION
-----
200
8.1.3
HIGH
PRECISION
NUMERICAL
INTEGRATION
ALGORITHM
FOR
EQUALLY
SPACED
SAMPLES
-----
201
8.2
NUMERICAL
INTEGRALS
OF
UNIVARIATE
FUNCTIONS
-----
203
8.2.1
SIMPLE
NUMERICAL
INTEGRAL
PROBLEMS
-----
204
CONTENTS
*
XI
8.2.2
MATLAB
SOLUTIONS
OF
NUMERICAL
INTEGRAL
PROBLEMS
*
205
8.2.3
NUMERICAL
COMPUTATION
OF
IMPROPER
INTEGRALS
*
210
8.2.4
NUMERICAL
INTEGRALS
FOR
INTEGRANDS
WITH
PARAMETERS
*
212
8.2.5
NUMERICAL
SOLUTIONS
OF
INTEGRAL
FUNCTIONS
*
213
8.3
NUMERICAL
COMPUTATION
OF
DOUBLE
INTEGRALS
*
214
8.3.1
COMPUTING
DOUBLE
INTEGRALS
*
215
8.3.2
COMPUTATION
OF
DOUBLE
INTEGRAL
FUNCTIONS
*
216
8.3.3
EVALUATIONS
OF
DOUBLE
INTEGRALS
IN
DIFFERENT
ORDER
*
218
8.4
NUMERICAL
COMPUTATION
OF
MULTIPLE
INTEGRALS
*
219
8.4.1
NUMERICAL
TRIPLE
INTEGRALS
*
219
8.4.2
TRIPLE
INTEGRALS
OF
INTEGRANDS
WITH
PARAMETERS
*
221
8.4.3
MULTIPLE
INTEGRALS
*
222
8.4.4
NUMERICAL
SOLUTIONS
OF
SOME
MULTIPLE
INTEGRALS
WITH
VARIABLE
BOUNDS
-----
224
8.5
OTHER
NUMERICAL
METHODS
FOR
MULTIPLE
INTEGRALS
*
225
8.5.1
NUMERICAL
INTEGRAL
APPROXIMATIONS
WITH
MONTE
CARLO
METHOD
*
226
8.5.2
SPLINE-BASED
INTEGRAL
EVALUATIONS
*
228
8.5.3
NUMERICAL
EVALUATIONS
OF
MULTIPLE
INTEGRALS
*
231
8.6
EXERCISES
*
232
9
INTEGRAL
TRANSFORMS
*
235
9.1
LAPLACE
TRANSFORMS
AND
THEIR
INVERSES
*
235
9.1.1
DEFINITION
AND
PROPERTIES
OF
LAPLACE
TRANSFORM
*
236
9.1.2
COMPUTER
SOLUTIONS
OF
LAPLACE
TRANSFORMS
*
237
9.1.3
SOLVING
DIFFERENTIAL
EQUATIONS
WITH
LAPLACE
TRANSFORM
*
240
9.2
NUMERICAL
SOLUTIONS
OF
LAPLACE
TRANSFORM
PROBLEMS
*
242
9.2.1
NUMERICAL
INVERSE
LAPLACE
TRANSFORM
*
243
9.2.2
IDEAS
OF
FEEDBACK
CONTROL
SYSTEMS
*
243
9.2.3
NUMERICAL
LAPLACE
TRANSFORMS
*
244
9.2.4
COMPUTATION
OF
IRRATIONAL
SYSTEMS
*
247
9.3
FOURIER
TRANSFORMS
AND
THEIR
INVERSES
*
248
9.3.1
DEFINITION
AND
PROPERTIES
OF
FOURIER
TRANSFORMS
*
249
9.3.2
COMPUTER
EVALUATION
OF
FOURIER
TRANSFORM
*
249
9.3.3
FOURIER
SINE
AND
COSINE
TRANSFORMS
*
251
9.3.4
DISCRETE
FOURIER
SINE
AND
COSINE
TRANSFORMS
*
252
9.3.5
FAST
FOURIER
TRANSFORM
*
253
9.4
COMPUTATION
OF
OTHER
INTEGRAL
TRANSFORMS
*
255
9.4.1
MELLIN
TRANSFORM
*
255
9.4.2
COMPUTATION
OF
HANKEL
TRANSFORMS
*
258
9.5
THE
Z
TRANSFORM
AND
ITS
INVERSE
*
259
9.5.1
DEFINITION
AND
PROPERTIES
OF
Z
TRANSFORMS
*
260
9.5.2
COMPUTER
EVALUATION
OF
Z
TRANSFORMS
*
260
XII
*
CONTENTS
9.5.3
9.5.4
9.6
BILATERAL
Z
TRANSFORM
-----
262
NUMERICAL
INVERSE
Z
TRANSFORMS
FOR
RATIONAL
FUNCTIONS
-----
263
EXERCISES
-----
264
10
10.1
10.1.1
10.1.2
10.2
INTRODUCTION
TO
FRACTIONAL
CALCULUS
*
267
DEFINITIONS
IN
FRACTIONAL
CALCULUS
-----
268
WHY
FRACTIONAL
CALCULUS?
-----
268
DEFINITIONS
-----
269
PROPERTIES
AND
RELATIONSHIPS
AMONG
DIFFERENT
FRACTIONAL
CALCULUS
DEFINITIONS
-----
270
10.3
10.3.1
10.3.2
10.3.3
10.4
10.5
10.5.1
10.5.2
10.5.3
10.6
NUMERICAL
IMPLEMENTATION
OF
GRUNWALD-LETNIKOV
DERIVATIVES
-----
272
SIMPLE
GRUNWALD-LETNIKOV
DEFINITION
EVALUATION
-----
272
HIGH
PRECISION
ALGORITHMS
AND
IMPLEMENTATION
-----
272
QUANTITATIVE
COMPARISONS
OF
DIFFERENT
ALGORITHMS
-----
277
NUMERICAL
COMPUTATION
OF
CAPUTO
DERIVATIVES
-----
279
OUSTALOUP
FILTER
ALGORITHMS
AND
APPLICATIONS
-----
282
OUSTALOUP
FILTER
APPROXIMATIONS
*
283
FILTER
FOR
CAPUTO
DERIVATIVE
FITTING
-----
285
SIMULINK-BASED
CAPUTO
DERIVATIVE
COMPUTATION
*
286
NUMERICAL
COMPUTATION
OF
EVEN
HIGHER-ORDER
DERIVATIVES
AND
INTEGRALS
-----
288
10.7
EXERCISES
-----
290
BIBLIOGRAPHY
*
291
MATLAB
FUNCTION
INDEX
*
293
INDEX
*
297 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Xue, Dingyu |
| author_GND | (DE-588)1098160967 |
| author_facet | Xue, Dingyu |
| author_role | aut |
| author_sort | Xue, Dingyu |
| author_variant | d x dx |
| building | Verbundindex |
| bvnumber | BV046727521 |
| classification_rvk | ST 601 ST 620 SK 400 SK 399 |
| ctrlnum | (OCoLC)1110051529 (DE-599)DNB1190749920 |
| dewey-full | 515.0285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.0285 |
| dewey-search | 515.0285 |
| dewey-sort | 3515.0285 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV046727521 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:35:40Z |
| indexdate | 2024-07-10T08:52:12Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110663624 3110663627 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032137632 |
| oclc_num | 1110051529 |
| open_access_boolean | |
| owner | DE-634 DE-1050 DE-83 DE-703 DE-19 DE-BY-UBM DE-706 DE-20 DE-11 |
| owner_facet | DE-634 DE-1050 DE-83 DE-703 DE-19 DE-BY-UBM DE-706 DE-20 DE-11 |
| physical | XII, 300 Seiten Illustrationen 24 cm, 535 g |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter Tsinghua University Press |
| record_format | marc |
| series2 | De Gruyter STEM |
| spelling | Xue, Dingyu Verfasser (DE-588)1098160967 aut Calculus problem solutions with MATLAB Dingyü Xue Berlin De Gruyter [2020] [Beijing] Tsinghua University Press [2020] © 2020 XII, 300 Seiten Illustrationen 24 cm, 535 g txt rdacontent n rdamedia nc rdacarrier De Gruyter STEM MATLAB (DE-588)4329066-8 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s MATLAB (DE-588)4329066-8 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-066697-7 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-066375-4 B:DE-101 application/pdf https://d-nb.info/1190749920/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032137632&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xue, Dingyu Calculus problem solutions with MATLAB MATLAB (DE-588)4329066-8 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4329066-8 (DE-588)4001865-9 |
| title | Calculus problem solutions with MATLAB |
| title_auth | Calculus problem solutions with MATLAB |
| title_exact_search | Calculus problem solutions with MATLAB |
| title_exact_search_txtP | Calculus problem solutions with MATLAB |
| title_full | Calculus problem solutions with MATLAB Dingyü Xue |
| title_fullStr | Calculus problem solutions with MATLAB Dingyü Xue |
| title_full_unstemmed | Calculus problem solutions with MATLAB Dingyü Xue |
| title_short | Calculus problem solutions with MATLAB |
| title_sort | calculus problem solutions with matlab |
| topic | MATLAB (DE-588)4329066-8 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | MATLAB Analysis |
| url | https://d-nb.info/1190749920/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032137632&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT xuedingyu calculusproblemsolutionswithmatlab AT walterdegruytergmbhcokg calculusproblemsolutionswithmatlab |
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