Scientific computing: for scientists and engineers
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2023]
|
| Ausgabe: | 2nd edition |
| Schriftenreihe: | De Gruyter textbook
|
| Schlagworte: | |
| Online-Zugang: | https://www.degruyter.com/isbn/9783110999617 Inhaltsverzeichnis Klappentext |
| Beschreibung: | XIII, 170 Seiten Diagramme 24 cm x 17 cm |
| ISBN: | 9783110999617 |
Internformat
MARC
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| 100 | 1 | |a Heister, Timo |d 1983- |e Verfasser |0 (DE-588)1183011571 |4 aut | |
| 245 | 1 | 0 | |a Scientific computing |b for scientists and engineers |c Timo Heister, Leo G. Rebholz |
| 250 | |a 2nd edition | ||
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2023] | |
| 300 | |a XIII, 170 Seiten |b Diagramme |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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| 653 | |a Numerical Analysis | ||
| 653 | |a Scientific Computing | ||
| 653 | |a TB: Textbook | ||
| 653 | |a Fachhochschul-/Hochschulausbildung | ||
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-098875-8 |
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| 883 | 1 | |8 1\p |a vlb |d 20221222 |q DE-101 |u https://d-nb.info/provenance/plan#vlb | |
Datensatz im Suchindex
| _version_ | 1805076669907599360 |
|---|---|
| adam_text |
CONTENTS
PREFACE
-
VII
ACKNOWLEDGMENTS
-
IX
1
INTRODUCTION
-
1
1.1
WHY
STUDY
NUMERICAL
METHODS?
-
1
1.2
TERMINOLOGY
-
2
1.3
CONVERGENCE
TERMINOLOGY
-
3
1.4
EXERCISES
-
5
2
COMPUTER
REPRESENTATION
OF
NUMBERS
AND
ROUNDOFF
ERROR
-
7
2.1
EXAMPLES
OF
THE
EFFECTS
OF
ROUNDOFF
ERROR
-
7
2.2
BINARY
NUMBERS
-
10
2.3
64-BIT
FLOATING-POINT
NUMBERS
-
12
2.4
FLOATING-POINT
ARITHMETIC
-
14
2.4.1
AVOID
ADDING
LARGE
AND
SMALL
NUMBERS
-
14
2.4.2
SUBTRACTING
TWO
NEARLY
EQUAL
NUMBERS
IS
BAD
-
14
2.5
VISUALIZING
A
FLOATING-POINT
NUMBER
SYSTEM
-
16
2.6
EXERCISES
-
17
3
SOLVING
LINEAR
SYSTEMS
OF
EQUATIONS
-
20
3.1
LINEAR
SYSTEMS
OF
EQUATIONS
AND
SOLVABILITY
-
20
3.2
SOLVING
TRIANGULAR
SYSTEMS
-
22
3.3
GAUSSIAN
ELIMINATION
-
24
3.4
THE
BACKSLASH
OPERATOR
-
28
3.5
LU
DECOMPOSITION
-
28
3.6
EXERCISES
-
30
4
FINITE
DIFFERENCE
METHODS
-
33
4.1
APPROXIMATING
THE
FIRST
DERIVATIVE
-
34
4.1.1
FORWARD
AND
BACKWARD
DIFFERENCES
-
34
4.1.2
CENTERED
DIFFERENCE
-
37
4.1.3
THREE-POINT
DIFFERENCE
FORMULAS
-
40
4.1.4
FURTHER
NOTES
-
41
4.2
APPROXIMATING
THE
SECOND
DERIVATIVE
-
41
4.3
APPLICATION:
INITIAL
VALUE
ODE
'
S
USING
THE
FORWARD
EULER
METHOD
-
42
4.4
APPLICATION:
BOUNDARY
VALUE
ODE
'
S
-
45
4.5
EXERCISES
-
50
XII
-
CONTENTS
5
SOLVING
NONLINEAR
EQUATIONS
-
53
5.1
THE
BISECTION
METHOD
-
54
5.2
NEWTON
'
S
METHOD
-
58
5.3
SECANT
METHOD
-
60
5.4
COMPARING
BISECTION,
NEWTON,
AND
SECANT
METHODS
-
61
5.5
COMBINING
METHODS,
INVERSE
INTERPOLATION,
AND
THE
FZERO
COMMAND
-
62
5.6
NEWTON
'
S
METHOD
IN
HIGHER
DIMENSIONS
-
64
5.7
FIXED
POINT
THEORY
AND
ALGORITHMS
-
67
5.7.1
NONLINEAR
HELMHOLTZ
-
70
5.7.2
NAVIER-STOKES
-
71
5.7.3
ANDERSON
ACCELERATION
-
74
5.8
EXERCISES
-
77
6
ACCURACY
IN
SOLVING
LINEAR
SYSTEMS
-
80
6.1
GAUSS-JORDAN
ELIMINATION
AND
FINDING
MATRIX
INVERSES
-
80
6.2
MATRIX
AND
VECTOR
NORMS
AND
CONDITION
NUMBER
-
83
6.3
SENSITIVITY
IN
LINEAR
SYSTEM
SOLVING
-
85
6.4
EXERCISES
-
87
7
EIGENVALUES
AND
EIGENVECTORS
-
90
7.1
MATHEMATICAL
DEFINITION
-
90
7.2
POWER
METHOD
-
92
7.3
APPLICATION:
POPULATION
DYNAMICS
-
95
7.4
EXERCISES
-
96
8
FITTING
CURVES
TO
DATA
-
98
8.1
INTERPOLATION
-
98
8.1.1
INTERPOLATION
BY
A
SINGLE
POLYNOMIAL
-
99
8.1.2
PIECEWISE
POLYNOMIAL
INTERPOLATION
-
101
8.2
CURVE
FITTING
-
104
8.2.1
LINE
OF
BEST
FIT
-
104
8.2.2
CURVE
OF
BEST
FIT
-
107
8.3
EXERCISES
-
110
9
NUMERICAL
INTEGRATION
-
113
9.1
NEWTON-COTES
METHODS
-
113
9.2
COMPOSITE
RULES
-
117
9.3
MATLAB
'
S
INTEGRAL
FUNCTION
-
122
9.4
GAUSS
QUADRATURE
-
122
9.5
EXERCISES
-
125
CONTENTS
-
XIII
10
10.1
10.2
10.2.1
10.2.2
10.2.3
10.3
10.4
10.4.1
10.4.2
10.4.3
10.4.4
10.5
10.5.1
10.5.2
10.5.3
10.5.4
10.6
10.7
10.8
INITIAL
VALUE
ODES
-
128
REDUCTION
OF
HIGHER-ORDER
ODES
TO
FIRST-ORDER
ODES
-
128
COMMON
METHODS
AND
DERIVATION
FROM
INTEGRATION
RULES
-
130
BACKWARD
EULER
-
131
CRANK-NICOLSON
-
132
RUNGE-KUTTA
4
-
133
COMPARISON
OF
SPEED
OF
IMPLICIT
VERSUS
EXPLICIT
SOLVERS
-
134
STABILITY
OF
ODE
SOLVERS
-
135
STABILITY
OF
FORWARD
EULER
-
136
STABILITY
OF
BACKWARD
EULER
-
137
STABILITY
OF
CRANK-NICOLSON
-
138
STABILITY
OF
RUNGE-KUTTA
4
-
139
ACCURACY
OF
ODE
SOLVERS
-
139
FORWARD
EULER
-
140
BACKWARD
EULER
-
140
CRANK-NICOLSON
-
141
RUNGE-KUTTA
4
-
142
SUMMARY,
GENERAL
STRATEGY,
AND
MATLAB
ODE
SOLVERS
-
143
THE
1
D
HEAT
EQUATION
-
145
EXERCISES
-
152
A
A.1
A.2
A.3
A.4
A.5
A.5.1
A.5.2
A.6
A.7
A.8
A.9
GETTING
STARTED
WITH
OCTAVE
AND
MATLAB
-
155
BASIC
OPERATIONS
-
155
ARRAYS
-
158
OPERATING
ON
ARRAYS
-
160
SCRIPT
FILES
-
161
FUNCTION
FILES
-
162
INLINE
FUNCTIONS
-
162
PASSING
FUNCTIONS
TO
OTHER
FUNCTIONS
-
163
OUTPUTTING
INFORMATION
-
163
PROGRAMMING
IN
MATLAB
-
164
PLOTTING
-
165
EXERCISES
-
166
INDEX
-
169
The book is designed to teach undergraduate students relevant numerical methods and required fundamentals in scientific computing. Most problems in science and engineering require the solution of mathematical problems, most of which can only be done on a computer. Accurately approximating those problems requires solving differential equations and linear systems with millions of unknowns, and smart algorithms can be used on computers to reduce calculation times from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations? The book covers: ► An introduction to a wide range of numerical methods for linear systems, eigenvalue problems, differential equations, numerical integration, and nonlinear problems; ► Scientific computing fundamentals like floating point representation of numbers and convergence; ► Analysis of accuracy and efficiency; ► Simple programming examples in MATLAB to illustrate the algorithms and to solve real life problems; ► Exercises to reinforce all topics. |
| adam_txt |
CONTENTS
PREFACE
-
VII
ACKNOWLEDGMENTS
-
IX
1
INTRODUCTION
-
1
1.1
WHY
STUDY
NUMERICAL
METHODS?
-
1
1.2
TERMINOLOGY
-
2
1.3
CONVERGENCE
TERMINOLOGY
-
3
1.4
EXERCISES
-
5
2
COMPUTER
REPRESENTATION
OF
NUMBERS
AND
ROUNDOFF
ERROR
-
7
2.1
EXAMPLES
OF
THE
EFFECTS
OF
ROUNDOFF
ERROR
-
7
2.2
BINARY
NUMBERS
-
10
2.3
64-BIT
FLOATING-POINT
NUMBERS
-
12
2.4
FLOATING-POINT
ARITHMETIC
-
14
2.4.1
AVOID
ADDING
LARGE
AND
SMALL
NUMBERS
-
14
2.4.2
SUBTRACTING
TWO
NEARLY
EQUAL
NUMBERS
IS
BAD
-
14
2.5
VISUALIZING
A
FLOATING-POINT
NUMBER
SYSTEM
-
16
2.6
EXERCISES
-
17
3
SOLVING
LINEAR
SYSTEMS
OF
EQUATIONS
-
20
3.1
LINEAR
SYSTEMS
OF
EQUATIONS
AND
SOLVABILITY
-
20
3.2
SOLVING
TRIANGULAR
SYSTEMS
-
22
3.3
GAUSSIAN
ELIMINATION
-
24
3.4
THE
BACKSLASH
OPERATOR
-
28
3.5
LU
DECOMPOSITION
-
28
3.6
EXERCISES
-
30
4
FINITE
DIFFERENCE
METHODS
-
33
4.1
APPROXIMATING
THE
FIRST
DERIVATIVE
-
34
4.1.1
FORWARD
AND
BACKWARD
DIFFERENCES
-
34
4.1.2
CENTERED
DIFFERENCE
-
37
4.1.3
THREE-POINT
DIFFERENCE
FORMULAS
-
40
4.1.4
FURTHER
NOTES
-
41
4.2
APPROXIMATING
THE
SECOND
DERIVATIVE
-
41
4.3
APPLICATION:
INITIAL
VALUE
ODE
'
S
USING
THE
FORWARD
EULER
METHOD
-
42
4.4
APPLICATION:
BOUNDARY
VALUE
ODE
'
S
-
45
4.5
EXERCISES
-
50
XII
-
CONTENTS
5
SOLVING
NONLINEAR
EQUATIONS
-
53
5.1
THE
BISECTION
METHOD
-
54
5.2
NEWTON
'
S
METHOD
-
58
5.3
SECANT
METHOD
-
60
5.4
COMPARING
BISECTION,
NEWTON,
AND
SECANT
METHODS
-
61
5.5
COMBINING
METHODS,
INVERSE
INTERPOLATION,
AND
THE
FZERO
COMMAND
-
62
5.6
NEWTON
'
S
METHOD
IN
HIGHER
DIMENSIONS
-
64
5.7
FIXED
POINT
THEORY
AND
ALGORITHMS
-
67
5.7.1
NONLINEAR
HELMHOLTZ
-
70
5.7.2
NAVIER-STOKES
-
71
5.7.3
ANDERSON
ACCELERATION
-
74
5.8
EXERCISES
-
77
6
ACCURACY
IN
SOLVING
LINEAR
SYSTEMS
-
80
6.1
GAUSS-JORDAN
ELIMINATION
AND
FINDING
MATRIX
INVERSES
-
80
6.2
MATRIX
AND
VECTOR
NORMS
AND
CONDITION
NUMBER
-
83
6.3
SENSITIVITY
IN
LINEAR
SYSTEM
SOLVING
-
85
6.4
EXERCISES
-
87
7
EIGENVALUES
AND
EIGENVECTORS
-
90
7.1
MATHEMATICAL
DEFINITION
-
90
7.2
POWER
METHOD
-
92
7.3
APPLICATION:
POPULATION
DYNAMICS
-
95
7.4
EXERCISES
-
96
8
FITTING
CURVES
TO
DATA
-
98
8.1
INTERPOLATION
-
98
8.1.1
INTERPOLATION
BY
A
SINGLE
POLYNOMIAL
-
99
8.1.2
PIECEWISE
POLYNOMIAL
INTERPOLATION
-
101
8.2
CURVE
FITTING
-
104
8.2.1
LINE
OF
BEST
FIT
-
104
8.2.2
CURVE
OF
BEST
FIT
-
107
8.3
EXERCISES
-
110
9
NUMERICAL
INTEGRATION
-
113
9.1
NEWTON-COTES
METHODS
-
113
9.2
COMPOSITE
RULES
-
117
9.3
MATLAB
'
S
INTEGRAL
FUNCTION
-
122
9.4
GAUSS
QUADRATURE
-
122
9.5
EXERCISES
-
125
CONTENTS
-
XIII
10
10.1
10.2
10.2.1
10.2.2
10.2.3
10.3
10.4
10.4.1
10.4.2
10.4.3
10.4.4
10.5
10.5.1
10.5.2
10.5.3
10.5.4
10.6
10.7
10.8
INITIAL
VALUE
ODES
-
128
REDUCTION
OF
HIGHER-ORDER
ODES
TO
FIRST-ORDER
ODES
-
128
COMMON
METHODS
AND
DERIVATION
FROM
INTEGRATION
RULES
-
130
BACKWARD
EULER
-
131
CRANK-NICOLSON
-
132
RUNGE-KUTTA
4
-
133
COMPARISON
OF
SPEED
OF
IMPLICIT
VERSUS
EXPLICIT
SOLVERS
-
134
STABILITY
OF
ODE
SOLVERS
-
135
STABILITY
OF
FORWARD
EULER
-
136
STABILITY
OF
BACKWARD
EULER
-
137
STABILITY
OF
CRANK-NICOLSON
-
138
STABILITY
OF
RUNGE-KUTTA
4
-
139
ACCURACY
OF
ODE
SOLVERS
-
139
FORWARD
EULER
-
140
BACKWARD
EULER
-
140
CRANK-NICOLSON
-
141
RUNGE-KUTTA
4
-
142
SUMMARY,
GENERAL
STRATEGY,
AND
MATLAB
ODE
SOLVERS
-
143
THE
1
D
HEAT
EQUATION
-
145
EXERCISES
-
152
A
A.1
A.2
A.3
A.4
A.5
A.5.1
A.5.2
A.6
A.7
A.8
A.9
GETTING
STARTED
WITH
OCTAVE
AND
MATLAB
-
155
BASIC
OPERATIONS
-
155
ARRAYS
-
158
OPERATING
ON
ARRAYS
-
160
SCRIPT
FILES
-
161
FUNCTION
FILES
-
162
INLINE
FUNCTIONS
-
162
PASSING
FUNCTIONS
TO
OTHER
FUNCTIONS
-
163
OUTPUTTING
INFORMATION
-
163
PROGRAMMING
IN
MATLAB
-
164
PLOTTING
-
165
EXERCISES
-
166
INDEX
-
169
The book is designed to teach undergraduate students relevant numerical methods and required fundamentals in scientific computing. Most problems in science and engineering require the solution of mathematical problems, most of which can only be done on a computer. Accurately approximating those problems requires solving differential equations and linear systems with millions of unknowns, and smart algorithms can be used on computers to reduce calculation times from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations? The book covers: ► An introduction to a wide range of numerical methods for linear systems, eigenvalue problems, differential equations, numerical integration, and nonlinear problems; ► Scientific computing fundamentals like floating point representation of numbers and convergence; ► Analysis of accuracy and efficiency; ► Simple programming examples in MATLAB to illustrate the algorithms and to solve real life problems; ► Exercises to reinforce all topics. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Heister, Timo 1983- Rebholz, Leo G. |
| author_GND | (DE-588)1183011571 (DE-588)1020166274 |
| author_facet | Heister, Timo 1983- Rebholz, Leo G. |
| author_role | aut aut |
| author_sort | Heister, Timo 1983- |
| author_variant | t h th l g r lg lgr |
| building | Verbundindex |
| bvnumber | BV048935866 |
| classification_rvk | ST 601 SK 900 SK 970 |
| ctrlnum | (OCoLC)1385302118 (DE-599)DNB1276364105 |
| dewey-full | 518.0285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.0285 |
| dewey-search | 518.0285 |
| dewey-sort | 3518.0285 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik |
| edition | 2nd edition |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV048935866 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:58:14Z |
| indexdate | 2024-07-20T06:00:58Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110999617 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034199724 |
| oclc_num | 1385302118 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-1028 DE-1051 DE-384 DE-20 |
| owner_facet | DE-29T DE-703 DE-1028 DE-1051 DE-384 DE-20 |
| physical | XIII, 170 Seiten Diagramme 24 cm x 17 cm |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter textbook |
| spelling | Heister, Timo 1983- Verfasser (DE-588)1183011571 aut Scientific computing for scientists and engineers Timo Heister, Leo G. Rebholz 2nd edition Berlin ; Boston De Gruyter [2023] XIII, 170 Seiten Diagramme 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter textbook Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Wissenschaftliches Rechnen (DE-588)4338507-2 gnd rswk-swf Numerical Analysis Scientific Computing TB: Textbook Fachhochschul-/Hochschulausbildung (DE-588)4123623-3 Lehrbuch gnd-content Numerische Mathematik (DE-588)4042805-9 s MATLAB (DE-588)4329066-8 s Wissenschaftliches Rechnen (DE-588)4338507-2 s DE-604 Rebholz, Leo G. Verfasser (DE-588)1020166274 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-098845-1 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-098875-8 X:MVB https://www.degruyter.com/isbn/9783110999617 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034199724&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034199724&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p vlb 20221222 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Heister, Timo 1983- Rebholz, Leo G. Scientific computing for scientists and engineers Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd Wissenschaftliches Rechnen (DE-588)4338507-2 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4329066-8 (DE-588)4338507-2 (DE-588)4123623-3 |
| title | Scientific computing for scientists and engineers |
| title_auth | Scientific computing for scientists and engineers |
| title_exact_search | Scientific computing for scientists and engineers |
| title_exact_search_txtP | Scientific computing for scientists and engineers |
| title_full | Scientific computing for scientists and engineers Timo Heister, Leo G. Rebholz |
| title_fullStr | Scientific computing for scientists and engineers Timo Heister, Leo G. Rebholz |
| title_full_unstemmed | Scientific computing for scientists and engineers Timo Heister, Leo G. Rebholz |
| title_short | Scientific computing |
| title_sort | scientific computing for scientists and engineers |
| title_sub | for scientists and engineers |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd Wissenschaftliches Rechnen (DE-588)4338507-2 gnd |
| topic_facet | Numerische Mathematik MATLAB Wissenschaftliches Rechnen Lehrbuch |
| url | https://www.degruyter.com/isbn/9783110999617 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034199724&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034199724&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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