Numerical methods for engineers and scientists: a students' course book
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Wiley
1977
|
| Schriftenreihe: | A series of programmes on mathematics for scientists and technologists
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 380 S. graph. Darst. |
| ISBN: | 0471995428 |
Internformat
MARC
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| 100 | 1 | |a Bajpai, Avinash C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical methods for engineers and scientists |b a students' course book |
| 264 | 1 | |a London [u.a.] |b Wiley |c 1977 | |
| 300 | |a XII, 380 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a A series of programmes on mathematics for scientists and technologists | |
| 650 | 7 | |a Matematica Aplicada |2 larpcal | |
| 650 | 4 | |a Naturwissenschaft | |
| 650 | 4 | |a Engineering mathematics |v Programmed instruction | |
| 650 | 4 | |a Numerical analysis |v Programmed instruction | |
| 650 | 4 | |a Science |x Methodology |v Programmed instruction | |
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Datensatz im Suchindex
| _version_ | 1804135904585973760 |
|---|---|
| adam_text | CONTENTS
UNIT 1 Equations and Matrices
FRAMES PAGE
BASIC IDEAS, ERRORS AND EVALUATION OF FORMULAE
1 6 Why Numerical Methods 2
7 10 Aids to Calculation 4
Accuracy and Errors
11 15 Types of Error 5
16 18 Round Off 7
19 32 Effects of Errors on Calculations 9
33 38 Evaluation of Formulae 17
39 42 Synthetic Division 21
43 — 44 Miscellaneous Examples and Answers 24
SOLUTION OF NON LINEAR EQUATIONS
1 3 Introduction 28
4 10 Iteration 29
11 18 Solution of Non Linear Equations by means of the
Iteration Formula x , = F(x ) 33
n+1 n
19 31 The Newton Raphson Iteration Formula 37
32 34 The Newton Raphson Formula applied to Examples
with more than One Real Root 46
35 37 The Choice of x0 for the Newton Raphson Process 47
38 Errors in the Calculation 48
39 Equal or Nearly Equal Roots 49
40 41 The Accuracy of the Result 49
42 Complex Roots 50
43 48 The Secant Method and the Method of False Position 50
49 Simultaneous Non Linear Equations 55
50 51 Miscellaneous Examples and Answers 55
APPENDIX A Equal or Nearly Equal Roots 58
APPENDIX B The Accuracy of the Result 61
APPENDIX C Solution of Polynomial Equations with no Real Root
Cl C5 Extension of Newton s Method to Complex Roots 63
C6 C17 Bairstow s Method 66
APPENDIX D Solution of Simultaneous Non Linear Equations
Dl D9 Extension of Direct Iteration Method 73
D10 D16 Extension of Newton Raphson Method 78
SIMULTANEOUS LINEAR EQUATIONS
1 8 Introduction 82
9 19 Solution of Linear Algebraic Equations
Gaussian Elimination 86
20 23 Gaussian Elimination with Partial Pivoting 93
24 28 Gauss Jordan Elimination 99
29 The Effect of Inaccurate Data 102
(ix)
30 40 The Gauss Seidel Iteration Method 102
41 Choleski s Method 109
42 Which Method is Best? 109
43 44 Miscellaneous Examples and Answers 111
APPENDIX The Effect of Inaccurate Data 114
MATRIX ALGEBRA, EIGENVALUES AND EIGENVECTORS
1 Arithmetical Operations 117
2 17 Inversion by the Gauss Jordan Process 117
18 The Effect of Inaccurate Data 128
19 31 Choleski s Factorisation Process 128
32 34 Application to Simultaneous Linear Equations 134
35 42 Application to Matrix Inversion 136
Eigenvalues and Eigenvectors
43 48 The Numerically Greatest Eigenvalue 138
49 57 The Numerically Least Eigenvalue 141
58 71 The Remaining Eigenvalues and Eigenvectors 145
72 73 Miscellaneous Examples and Answers 151
APPENDIX Justification of Process for Numerically
Largest Eigenvalue 155
UNIT 1 Revision Examples and Answers 159
UNIT 2 Finite Differences and their Applications
LEAST SQUARES
1 3 Introduction 162
4 14 Fitting the Best Straight Line to a Set of Points 163
15 19 Extension to Laws reducible to a Linear Form 168
20 28 Extension to Polynomial Laws 170
29 30 Use of a False Origin or Coding 173
31 The Best Straight Line when Both Variables are
subject to Error 175
32 33 Miscellaneous Examples and Answers 175
FINITE DIFFERENCES
1 2 Introduction 179
3 4 Finite Differences 179
5 6 The Link between Differencing and Differentiation 181
7 8 Decimals in a Difference Table 183
9 19 The Build up of Errors in a Difference Table due
to Errors in the Functional Values 184
20 21 Finite Difference Notations 190
22 26 The Forward Difference Operator A 191
27 29 The Shift Operator E 195
30 32 The Backward Difference Operator V 195
33 38 The Central Difference Operator 6 197
39 41 The Averaging Operator u 199
42 44 Other Operational Formulae 200
45 Summary 201
46 47 Miscellaneous Examples and Answers 202
INTERPOLATION
1 5 Introduction and Linear Interpolation 205
6 15 The Newton Gregory Forward Difference
Interpolation Formula 207
16 17 The Newton Gregory Backward Difference Formula 211
18 24 Other Finite Difference Interpolation Formulae 212
25 Unequal Intervals of Tabulation 216
26 35 Divided Differences 21 6
36 45 Lagrange s Interpolation Formula 221
46 47 A Word of Warning 226
48 56 Inverse Interpolation 227
57 Summary of Interpolation Formulae 230
58 59 Miscellaneous Examples and Answers 231
NUMERICAL DIFFERENTIATION
1 3 Introduction 235
4 9 A Basic Process 236
10 22 Differentiation Based on Equal Interval
Interpolation Formulae 238
23 25 Differentiation Based on Lagrange s
Interpolation Polynomial 243
26 34 Higher Order Derivatives 244
35 36 Miscellaneous Examples and Answers 247
NUMERICAL INTEGRATION
1 6 Introduction 250
7 8 Counting Squares 252
9 15 The Rectangular Rule 253
16 19 The Trapezium Rule 255
20 23 Integration Formulae via Interpolation Formulae 257
24 31 Simpson s Rule 258
32 34 The Three Eighths Rule 261
35 37 Other Integration Formulae 263
38 42 Errors 265
43 Summary of Integration Formulae 267
44 59 Romberg Integration 267
60 Unequally Spaced Data Use of Lagrange s
Interpolation Formula 275
61 62 Miscellaneous Examples and Answers 275
UNIT 2 Revision Examples and Answers 281
UNIT 3 Differential Equations
FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
1 7 Introduction 284
8 16 Euler s Method 287
17 21 The Improved Euler Method 289
22 23 Predictor Corrector Methods 291
24 28 The Modified Euler Method 292
(xi)
29 36 Milne s Method 294
37 40 Taylor s Series Method for starting the
Milne Process 298
41 43 Modification of the Milne Method 300
44 The Accuracy of the Various Methods 302
45 47 Stability of Milne s Method Hamming s Method 302
48 Modified Hamming s Method 303
49 55 Runge Kutta Method 304
56 Comparison of Methods 305
57 Summary of Formulae for solving ^ = f (x, y) 307
58 59 Miscellaneous Examples and Answers 308
SIMULTANEOUS AND SECOND ORDER DIFFERENTIAL EQUATIONS
1 3 Simultaneous Differential Equations Introduction 315
4 6 Euler s Method 316
7 8 The Improved Euler Method 317
9 12 The Modified Euler Method 318
13 16 Runge Kutta Method 319
17 19 Milne s Method 321
20 21 Modified Milne Method 322
22 Hamming s Method 323
23 24 Modified Hamming Method 323
25 26 Comparison of the Results 324
27 More Complicated Systems of Equations 325
28 29 Examples and Answers 325
30 36 Second Order Differential Equations Initial
Value Problems 326
37 44 The Special Case when the First Derivative
is missing 328
45 Boundary Value Problems 331
46 51 The Trial and Error or Shooting Method 331
52 63 The Simultaneous Algebraic Equations Method 334
64 65 Miscellaneous Examples and Answers 338
PARTIAL DIFFERENTIAL EQUATIONS
1 3 Introduction 343
g2g jn2q
4 20 Laplace s Equation s y + yj = 0 344
21 38 The Equation |^ = c2 |^| 350
39 53 The Equation |H. = c •— 357
54 57 Errors in the Methods 364
58 59 Miscellaneous Examples I including Poisson s
Equation r y + ¦*—j = f (x, y) j and Answers 366
UNIT 3 Revision Examples and Answers 372
REFERENCES 377
INDEX 378
(xii)
|
| adam_txt |
CONTENTS
UNIT 1 Equations and Matrices
FRAMES PAGE
BASIC IDEAS, ERRORS AND EVALUATION OF FORMULAE
1 6 Why Numerical Methods 2
7 10 Aids to Calculation 4
Accuracy and Errors
11 15 Types of Error 5
16 18 Round Off 7
19 32 Effects of Errors on Calculations 9
33 38 Evaluation of Formulae 17
39 42 Synthetic Division 21
43 — 44 Miscellaneous Examples and Answers 24
SOLUTION OF NON LINEAR EQUATIONS
1 3 Introduction 28
4 10 Iteration 29
11 18 Solution of Non Linear Equations by means of the
Iteration Formula x , = F(x ) 33
n+1 n
19 31 The Newton Raphson Iteration Formula 37
32 34 The Newton Raphson Formula applied to Examples
with more than One Real Root 46
35 37 The Choice of x0 for the Newton Raphson Process 47
38 Errors in the Calculation 48
39 Equal or Nearly Equal Roots 49
40 41 The Accuracy of the Result 49
42 Complex Roots 50
43 48 The Secant Method and the Method of False Position 50
49 Simultaneous Non Linear Equations 55
50 51 Miscellaneous Examples and Answers 55
APPENDIX A Equal or Nearly Equal Roots 58
APPENDIX B The Accuracy of the Result 61
APPENDIX C Solution of Polynomial Equations with no Real Root
Cl C5 Extension of Newton's Method to Complex Roots 63
C6 C17 Bairstow's Method 66
APPENDIX D Solution of Simultaneous Non Linear Equations
Dl D9 Extension of Direct Iteration Method 73
D10 D16 Extension of Newton Raphson Method 78
SIMULTANEOUS LINEAR EQUATIONS
1 8 Introduction 82
9 19 Solution of Linear Algebraic Equations
Gaussian Elimination 86
20 23 Gaussian Elimination with Partial Pivoting 93
24 28 Gauss Jordan Elimination 99
29 The Effect of Inaccurate Data 102
(ix)
30 40 The Gauss Seidel Iteration Method 102
41 Choleski's Method 109
42 Which Method is Best? 109
43 44 Miscellaneous Examples and Answers 111
APPENDIX The Effect of Inaccurate Data 114
MATRIX ALGEBRA, EIGENVALUES AND EIGENVECTORS
1 Arithmetical Operations 117
2 17 Inversion by the Gauss Jordan Process 117
18 The Effect of Inaccurate Data 128
19 31 Choleski's Factorisation Process 128
32 34 Application to Simultaneous Linear Equations 134
35 42 Application to Matrix Inversion 136
Eigenvalues and Eigenvectors
43 48 The Numerically Greatest Eigenvalue 138
49 57 The Numerically Least Eigenvalue 141
58 71 The Remaining Eigenvalues and Eigenvectors 145
72 73 Miscellaneous Examples and Answers 151
APPENDIX Justification of Process for Numerically
Largest Eigenvalue 155
UNIT 1 Revision Examples and Answers 159
UNIT 2 Finite Differences and their Applications
LEAST SQUARES
1 3 Introduction 162
4 14 Fitting the 'Best' Straight Line to a Set of Points 163
15 19 Extension to Laws reducible to a Linear Form 168
20 28 Extension to Polynomial Laws 170
29 30 Use of a False Origin or Coding 173
31 The Best Straight Line when Both Variables are
subject to Error 175
32 33 Miscellaneous Examples and Answers 175
FINITE DIFFERENCES
1 2 Introduction 179
3 4 Finite Differences 179
5 6 The Link between Differencing and Differentiation 181
7 8 Decimals in a Difference Table 183
9 19 The Build up of Errors in a Difference Table due
to Errors in the Functional Values 184
20 21 Finite Difference Notations 190
22 26 The Forward Difference Operator A 191
27 29 The Shift Operator E 195
30 32 The Backward Difference Operator V 195
33 38 The Central Difference Operator 6 197
39 41 The Averaging Operator u 199
42 44 Other Operational Formulae 200
45 Summary 201
46 47 Miscellaneous Examples and Answers 202
INTERPOLATION
1 5 Introduction and Linear Interpolation 205
6 15 The Newton Gregory Forward Difference
Interpolation Formula 207
16 17 The Newton Gregory Backward Difference Formula 211
18 24 Other Finite Difference Interpolation Formulae 212
25 Unequal Intervals of Tabulation 216
26 35 Divided Differences 21 6
36 45 Lagrange's Interpolation Formula 221
46 47 A Word of Warning 226
48 56 Inverse Interpolation 227
57 Summary of Interpolation Formulae 230
58 59 Miscellaneous Examples and Answers 231
NUMERICAL DIFFERENTIATION
1 3 Introduction 235
4 9 A Basic Process 236
10 22 Differentiation Based on Equal Interval
Interpolation Formulae 238
23 25 Differentiation Based on Lagrange's
Interpolation Polynomial 243
26 34 Higher Order Derivatives 244
35 36 Miscellaneous Examples and Answers 247
NUMERICAL INTEGRATION
1 6 Introduction 250
7 8 Counting Squares 252
9 15 The Rectangular Rule 253
16 19 The Trapezium Rule 255
20 23 Integration Formulae via Interpolation Formulae 257
24 31 Simpson's Rule 258
32 34 The Three Eighths Rule 261
35 37 Other Integration Formulae 263
38 42 Errors 265
43 Summary of Integration Formulae 267
44 59 Romberg Integration 267
60 Unequally Spaced Data Use of Lagrange's
Interpolation Formula 275
61 62 Miscellaneous Examples and Answers 275
UNIT 2 Revision Examples and Answers 281
UNIT 3 Differential Equations
FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
1 7 Introduction 284
8 16 Euler's Method 287
17 21 The Improved Euler Method 289
22 23 Predictor Corrector Methods 291
24 28 The Modified Euler Method 292
(xi)
29 36 Milne's Method 294
37 40 Taylor's Series Method for starting the
Milne Process 298
41 43 Modification of the Milne Method 300
44 The Accuracy of the Various Methods 302
45 47 Stability of Milne's Method Hamming's Method 302
48 Modified Hamming's Method 303
49 55 Runge Kutta Method 304
56 Comparison of Methods 305
57 Summary of Formulae for solving ^ = f (x, y) 307
58 59 Miscellaneous Examples and Answers 308
SIMULTANEOUS AND SECOND ORDER DIFFERENTIAL EQUATIONS
1 3 Simultaneous Differential Equations Introduction 315
4 6 Euler's Method 316
7 8 The Improved Euler Method 317
9 12 The Modified Euler Method 318
13 16 Runge Kutta Method 319
17 19 Milne's Method 321
20 21 Modified Milne Method 322
22 Hamming's Method 323
23 24 Modified Hamming Method 323
25 26 Comparison of the Results 324
27 More Complicated Systems of Equations 325
28 29 Examples and Answers 325
30 36 Second Order Differential Equations Initial
Value Problems 326
37 44 The Special Case when the First Derivative
is missing 328
45 Boundary Value Problems 331
46 51 The Trial and Error or Shooting Method 331
52 63 The Simultaneous Algebraic Equations Method 334
64 65 Miscellaneous Examples and Answers 338
PARTIAL DIFFERENTIAL EQUATIONS
1 3 Introduction 343
g2g jn2q
4 20 Laplace's Equation s y + yj = 0 344
21 38 The Equation |^ = c2 |^| 350
39 53 The Equation |H. = c •— 357
54 57 Errors in the Methods 364
58 59 Miscellaneous Examples I including Poisson's
Equation r y + ¦*—j = f (x, y) j and Answers 366
UNIT 3 Revision Examples and Answers 372
REFERENCES 377
INDEX 378
(xii) |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-search | 511/.07/7 519.4 |
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| id | DE-604.BV021943118 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:07:08Z |
| indexdate | 2024-07-09T20:47:55Z |
| institution | BVB |
| isbn | 0471995428 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015158268 |
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| physical | XII, 380 S. graph. Darst. |
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| publisher | Wiley |
| record_format | marc |
| series2 | A series of programmes on mathematics for scientists and technologists |
| spelling | Bajpai, Avinash C. Verfasser aut Numerical methods for engineers and scientists a students' course book London [u.a.] Wiley 1977 XII, 380 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A series of programmes on mathematics for scientists and technologists Matematica Aplicada larpcal Naturwissenschaft Engineering mathematics Programmed instruction Numerical analysis Programmed instruction Science Methodology Programmed instruction Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Calus, Irene M. Verfasser aut Fairley, James A. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015158268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bajpai, Avinash C. Calus, Irene M. Fairley, James A. Numerical methods for engineers and scientists a students' course book Matematica Aplicada larpcal Naturwissenschaft Engineering mathematics Programmed instruction Numerical analysis Programmed instruction Science Methodology Programmed instruction Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4042805-9 |
| title | Numerical methods for engineers and scientists a students' course book |
| title_auth | Numerical methods for engineers and scientists a students' course book |
| title_exact_search | Numerical methods for engineers and scientists a students' course book |
| title_exact_search_txtP | Numerical methods for engineers and scientists a students' course book |
| title_full | Numerical methods for engineers and scientists a students' course book |
| title_fullStr | Numerical methods for engineers and scientists a students' course book |
| title_full_unstemmed | Numerical methods for engineers and scientists a students' course book |
| title_short | Numerical methods for engineers and scientists |
| title_sort | numerical methods for engineers and scientists a students course book |
| title_sub | a students' course book |
| topic | Matematica Aplicada larpcal Naturwissenschaft Engineering mathematics Programmed instruction Numerical analysis Programmed instruction Science Methodology Programmed instruction Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Matematica Aplicada Naturwissenschaft Engineering mathematics Programmed instruction Numerical analysis Programmed instruction Science Methodology Programmed instruction Numerisches Verfahren Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015158268&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bajpaiavinashc numericalmethodsforengineersandscientistsastudentscoursebook AT calusirenem numericalmethodsforengineersandscientistsastudentscoursebook AT fairleyjamesa numericalmethodsforengineersandscientistsastudentscoursebook |