An introduction to scientific, symbolic, and graphical computation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wellesley, Mass.
Peters
1995
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 306 S. graph. Darst. |
| ISBN: | 1568810512 |
Staff View
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Record in the Search Index
| _version_ | 1804124616531116032 |
|---|---|
| adam_text | Contents
Preface xi
0. Mathematical Computation 1
0.1. Scientific, Symbolic, and Graphical Computation 1
0.2. Themes of this Book 4
0.3. Symbolic Computation 5
0.3.1. An Example 6
0.3.2. A More Complex Example 13
1. The Representation of Functions 19
1.1. Sets and Number Systems 19
1.2. Vectors 21
1.3. Functions 22
1.4. Representation of Functions 24
1.4.1. Explicit and Implicit Representations 24
1.4.2. Parametric Representations 26
1.4.3. Polynomial Representations 36
1.4.4. Procedural Representations 42
1.5. Discretisation and Computation of Functions 48
1.5.1. Line Segments and Circles 49
Appendix A. Raster Graphics Fundamentals 61
Appendix B. Simple Maple Examples 64
Appendix C. Matrix Representations 66
Supplementary Exercises 69
viii Contents
2. Interpolation 73 i
2.1. A Motivating Problem 73
2.2. Properties of Polynomials 74
2.3. Lagrange Interpolation 76
2.4. Piecewise Polynomial Interpolation 82
2.4.1. Piecewise Linear Interpolation 83
2.4.2. Representations for Polynomial Curves 85
2.4.3. Putting the Pieces Together 101
2.4.4. General Space Curves 102
2.5. Computational Methods for Polynomial Evaluation 106
2.5.1. Matrix computation 106
2.5.2. Direct Polynomial Evaluation 108 t
2.5.3. Horner s Rule 108 |
2.5.4. Table Look Up 109
2.5.5. Forward Differencing Techniques 109
2.6. Transforming Curves 111
2.6.1. Motivation 111
2.6.2. Formulation 112
2.7. An Introduction to Polynomial Surfaces 114
Appendix A. Computing the Change of Basis Matrix 116
Supplementary Exercises 122
3. Approximation and Sampling 123
3.1. Problems with Interpolation 124
3.1.1. Ringing 124
3.1.2. Noise 127
3.1.3. Undersampling 127
3.1.4. Divergence 129
3.1.5. Summary 130
3.2. Types of Approximation 130
3.3. Approximation Using Uniform Cubic B Splines 133
3.4. Signals and Filters 137 i
3.4.1. Sample Filters and Their Effect 143
3.5. Sampling, Filtering, and Reconstruction 158
3.5.1. The Sampling Theorem: An Intuitive View 160 j
3.5.2. Reconstruction 166 ,
3.5.3. Filtering 168
Supplementary Exercises 171 J
I
4. Computational Integration 173
4.1. Introduction 174 1
4.2. Basic Numerical Quadrature 178 !
4.2.1. Riemann Sums 179
4.2.2. Integration Based on Piecewise Polynomial Interpolation 184 !
i
Contents ix
4.2.3. Formulae for Compound Integration 199
4.2.4. Adaptive Numerical Integration 202
4.3. Comparison of Results 203
4.4. Monte Carlo Methods 205
4.5. Summary 213
Appendix A. Maple Code to Model Quadrature Rules 215
5. Series Approximations 219
5.1. Representations for the Real Numbers 219
5.1.1. The Representation of Integers and Fixed Point Numbers 222
5.1.2. The Representation of Floating Point Numbers 227
5.2. Polynomial Series 232
5.2.1. Taylor Polynomials 232
5.2.2. Error Analysis of Quadrature Algorithms 237
5.3. Non Polynomial Series: Trigonometric Fourier Series 243
5.3.1. Definition 243
5.3.2. Examples 246
5.4. Generalised Fourier Series and the Fourier Transform 256
5.4.1. Changing the Domain of a Fourier Series 257
5.4.2. The Fourier Transform 258
5.4.3. Convolution and Frequency Domain Representations 262
5.4.4. Frequency Domain Filtering 264
5.5. The Sampling Theorem Revisited 269
Appendix A. Maple Code to Compute Quadrature Rules 274
6. Finding the Zeros of a Function 277
6.1. Motivation: Intersection Problems 277
6.2. Symbolic Computation of the Roots of Polynomials 284
6.3. Numerical Methods for Computing Zeros 288
6.3.1. Piecewise Approximation 289
6.3.2. Bisection 290
6.3.3. The Newton Raphson Method 292
6.3.4. The Secant Method 297
Index 299
|
| any_adam_object | 1 |
| author | Fiume, Eugene L. |
| author_facet | Fiume, Eugene L. |
| author_role | aut |
| author_sort | Fiume, Eugene L. |
| author_variant | e l f el elf |
| building | Verbundindex |
| bvnumber | BV010209684 |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76 |
| callnumber-search | QA76 |
| callnumber-sort | QA 276 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)31707972 (DE-599)BVBBV010209684 |
| dewey-full | 510/.285/51 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510/.285/51 |
| dewey-search | 510/.285/51 |
| dewey-sort | 3510 3285 251 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:48:30Z |
| institution | BVB |
| isbn | 1568810512 |
| language | English |
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| publisher | Peters |
| record_format | marc |
| spelling | Fiume, Eugene L. Verfasser aut An introduction to scientific, symbolic, and graphical computation Eugene Fiume Wellesley, Mass. Peters 1995 XV, 306 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computermethoden gtt Dataprocessing gtt Datenverarbeitung Electronic data processing Informatik (DE-588)4026894-9 gnd rswk-swf Maple Programm (DE-588)4209397-1 gnd rswk-swf Nullstelle (DE-588)4140515-8 gnd rswk-swf Wissenschaftliches Rechnen (DE-588)4338507-2 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Computergrafik (DE-588)4010450-3 gnd rswk-swf Maple V (DE-588)4276266-2 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Programm (DE-588)4047394-6 gnd rswk-swf Computergrafik (DE-588)4010450-3 s DE-604 Numerische Mathematik (DE-588)4042805-9 s Maple V (DE-588)4276266-2 s Programm (DE-588)4047394-6 s 1\p DE-604 Computeralgebra (DE-588)4010449-7 s 2\p DE-604 Wissenschaftliches Rechnen (DE-588)4338507-2 s 3\p DE-604 Nullstelle (DE-588)4140515-8 s 4\p DE-604 Informatik (DE-588)4026894-9 s 5\p DE-604 Interpolation (DE-588)4162121-9 s 6\p DE-604 Maple Programm (DE-588)4209397-1 s 7\p DE-604 Funktion Mathematik (DE-588)4071510-3 s 8\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006784396&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 8\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fiume, Eugene L. An introduction to scientific, symbolic, and graphical computation Computermethoden gtt Dataprocessing gtt Datenverarbeitung Electronic data processing Informatik (DE-588)4026894-9 gnd Maple Programm (DE-588)4209397-1 gnd Nullstelle (DE-588)4140515-8 gnd Wissenschaftliches Rechnen (DE-588)4338507-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd Funktion Mathematik (DE-588)4071510-3 gnd Interpolation (DE-588)4162121-9 gnd Computergrafik (DE-588)4010450-3 gnd Maple V (DE-588)4276266-2 gnd Computeralgebra (DE-588)4010449-7 gnd Programm (DE-588)4047394-6 gnd |
| subject_GND | (DE-588)4026894-9 (DE-588)4209397-1 (DE-588)4140515-8 (DE-588)4338507-2 (DE-588)4042805-9 (DE-588)4071510-3 (DE-588)4162121-9 (DE-588)4010450-3 (DE-588)4276266-2 (DE-588)4010449-7 (DE-588)4047394-6 |
| title | An introduction to scientific, symbolic, and graphical computation |
| title_auth | An introduction to scientific, symbolic, and graphical computation |
| title_exact_search | An introduction to scientific, symbolic, and graphical computation |
| title_full | An introduction to scientific, symbolic, and graphical computation Eugene Fiume |
| title_fullStr | An introduction to scientific, symbolic, and graphical computation Eugene Fiume |
| title_full_unstemmed | An introduction to scientific, symbolic, and graphical computation Eugene Fiume |
| title_short | An introduction to scientific, symbolic, and graphical computation |
| title_sort | an introduction to scientific symbolic and graphical computation |
| topic | Computermethoden gtt Dataprocessing gtt Datenverarbeitung Electronic data processing Informatik (DE-588)4026894-9 gnd Maple Programm (DE-588)4209397-1 gnd Nullstelle (DE-588)4140515-8 gnd Wissenschaftliches Rechnen (DE-588)4338507-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd Funktion Mathematik (DE-588)4071510-3 gnd Interpolation (DE-588)4162121-9 gnd Computergrafik (DE-588)4010450-3 gnd Maple V (DE-588)4276266-2 gnd Computeralgebra (DE-588)4010449-7 gnd Programm (DE-588)4047394-6 gnd |
| topic_facet | Computermethoden Dataprocessing Datenverarbeitung Electronic data processing Informatik Maple Programm Nullstelle Wissenschaftliches Rechnen Numerische Mathematik Funktion Mathematik Interpolation Computergrafik Maple V Computeralgebra Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006784396&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT fiumeeugenel anintroductiontoscientificsymbolicandgraphicalcomputation |