Introduction to scientific computing: for scientists and engineers
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
De Gruyter
2015
|
| Series: | De Gruyter Textbook
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XI, 138 S. graph. Darst. |
| ISBN: | 3110359405 9783110359404 |
Staff View
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| 245 | 1 | 0 | |a Introduction to scientific computing |b for scientists and engineers |c Timo Heister ; Leo G. Rebholz |
| 246 | 1 | 3 | |a Scientific computing |
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Record in the Search Index
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CONTENTS
PREFACE VII
1 INTRODUCTION 1
1.1 WHY STUDY NUMERICAL METHODS? 1
1.2 TERMINOLOGY 2
1.3 CONVERGENCE TERMINOLOGY 4
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
2.3.1 AVOID ADDING LARGE AND SMALL NUMBERS 14
2.3.2 SUBTRACTING TWO NEARLY EQUAL NUMBERS IS BAD 14
2.4 EXERCISES 16
3 SOLVING
LINEAR SYSTEMS OF EQUATIONS 17
3.1 LINEAR SYSTEMS OF EQUATIONS AND SOLVABILITY 17
3.2 SOLVING TRIANGULAR SYSTEMS 19
3.3 GAUSSIAN ELIMINATION 21
3.4 THE BACKSLASH OPERATOR 25
3.5 LU DECOMPOSITION 25
3.6 EXERCISES 26
4 FINITE DIFFERENCE METHODS 28
4.1 APPROXIMATING THE FIRST DERIVATIVE 29
4.1.1 FORWARD AND BACKWARD DIFFERENCES 29
4.1.2 CENTERED DIFFERENCE 32
4.1.3 THREE POINT DIFFERENCE FORMULAS 35
4.1.4 FURTHER NOTES 36
4.2 APPROXIMATING THE SECOND DERIVATIVE 36
4.3 APPLICATION: INITIAL VALUE ODE'S USING
THE FORWARD EULER METHOD
4.4 APPLICATION: BOUNDARY VALUE ODE'S 40
4.5 EXERCISES 45
5 SOLVING NONLINEAR
EQUATIONS 46
5.1 THE BISECTION METHOD 47
5.2 NEWTON'S METHOD 51
5.3 SECANT METHOD 54
HTTP://D-NB.INFO/106519157X
X * CONTENTS
5.4 COMPARING BISECTION, NEWTON, SECANT METHOD 54
5.5 COMBINING SECANT AND BISECTION AND THE FZERO COMMAND 55
5.6 EQUATION SOLVING IN HIGHER DIMENSIONS 57
5.7 EXERCISES 59
6 ACCURACY IN SOLVING
LINEAR SYSTEMS 61
6.1 GAUSS-JORDAN ELIMINATION AND FINDING MATRIX INVERSES 61
6.2 MATRIX AND VECTOR NORMS AND CONDITION NUMBER 64
6.3 SENSITIVITY IN LINEAR SYSTEM SOLVING 66
6.4 EXERCISES 68
7 EIGENVALUES AND EIGENVECTORS 69
7.1 MATHEMATICAL DEFINITION 69
7.2 POWER METHOD 71
7.3 APPLICATION: POPULATION DYNAMICS 74
7.4 EXERCISES 75
8 FITTING
CURVES TO DATA 77
8.1 INTERPOLATION 77
8.1.1 INTERPOLATION BY A SINGLE POLYNOMIAL
8.1.2 PIECEWISE POLYNOMIAL INTERPOLATION -
8.2 CURVE FITTING 83
8.2.1 LINE OF BEST FIT 83
8.2.2 CURVE OF BEST FIT 86
8.3 EXERCISES 89
9 NUMERICAL
INTEGRATION 91
9.1 NEWTON-COTES METHODS 91
9.2 COMPOSITE RULES 95
9.3 MATLAB'S INTEGRAL FUNCTION 99
9.4 GAUSS QUADRATURE 99
9.5 EXERCISES 102
10 INITIAL VALUE ODES 104
10.1 REDUCTION OF HIGHER ORDER ODES TO FIRST ORDER 104
10.2 COMMON METHODS AND DERIVATION FROM INTEGRATION RULES 106
10.2.1 BACKWARD EULER 107
10.2.2 CRANK-NICOLSON 108
10.2.3 RUNGE-KUTTA4 108
10.3 COMPARISON OF SPEED OF IMPLICIT VERSUS EXPLICIT SOLVERS 109
10.4 STABILITY OF ODE SOLVERS 111
10.4.1 STABILITY OF FORWARD EULER 111
CONTENTS
* XI
10.4.2 STABILITY OF BACKWARD EULER 112
10.4.3 STABILITY OF CRANK-NICOLSON 114
10.4.4 STABILITY OF RUNGE-KUTTA 4 115
10.5 ACCURACY OF ODE SOLVERS 115
10.5.1 FORWARD EULER 115
10.5.2 BACKWARD EULER 116
10.5.3 CRANK-NICOLSON 117
10.5.4 RUNGE-KUTTA 4 118
10.6 SUMMARY, GENERAL STRATEGY, AND MATLAB ODE SOLVERS 119
10.7 EXERCISES 121
A GETTING STARTED
WITH OCTAVE AND
MATLAB 123
A.L BASIC OPERATIONS 123
A. 2 ARRAYS 126
A.3 OPERATING ON ARRAYS 129
A.4 SCRIPT FILES 131
A.5 FUNCTION FILES 132
A.5.1 INLINE FUNCTIONS 132
A.5.2 PASSING FUNCTIONS TO OTHER FUNCTIONS 133
A.6 OUTPUTTING INFORMATION 133
A.7 PROGRAMMING IN MATLAB 134
A.8 PLOTTING 135
A.9 EXERCISES 136 |
| any_adam_object | 1 |
| author | Heister, Timo Rebholz, Leo G. |
| author_GND | (DE-588)1020166274 |
| author_facet | Heister, Timo Rebholz, Leo G. |
| author_role | aut aut |
| author_sort | Heister, Timo |
| author_variant | t h th l g r lg lgr |
| building | Verbundindex |
| bvnumber | BV042387779 |
| classification_rvk | SK 900 ST 600 ST 601 |
| ctrlnum | (OCoLC)901518831 (DE-599)DNB106519157X |
| dewey-full | 510 518.0285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 518 - Numerical analysis |
| dewey-raw | 510 518.0285 |
| dewey-search | 510 518.0285 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| spelling | Heister, Timo Verfasser aut Introduction to scientific computing for scientists and engineers Timo Heister ; Leo G. Rebholz Scientific computing Berlin [u.a.] De Gruyter 2015 XI, 138 S. graph. Darst. 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 (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 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-038680-6 Erscheint auch als Online-Ausgabe, PDF 978-3-11-035942-8 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5130763&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027823734&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Heister, Timo Rebholz, Leo G. Introduction to 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 | Introduction to scientific computing for scientists and engineers |
| title_alt | Scientific computing |
| title_auth | Introduction to scientific computing for scientists and engineers |
| title_exact_search | Introduction to scientific computing for scientists and engineers |
| title_full | Introduction to scientific computing for scientists and engineers Timo Heister ; Leo G. Rebholz |
| title_fullStr | Introduction to scientific computing for scientists and engineers Timo Heister ; Leo G. Rebholz |
| title_full_unstemmed | Introduction to scientific computing for scientists and engineers Timo Heister ; Leo G. Rebholz |
| title_short | Introduction to scientific computing |
| title_sort | introduction to 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 |
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