Linear operator methods in chemical engineering: with applications to transport and chemical reaction systems
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Englewood Cliffs, NJ
Prentice-Hall
1985
|
| Schriftenreihe: | Prentice-Hall international series in the physical and chemical engineering sciences
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 471 S. graph. Darst. |
| ISBN: | 0135373417 |
Internformat
MARC
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| 100 | 1 | |a Ramkrishna, Doraiswami |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear operator methods in chemical engineering |b with applications to transport and chemical reaction systems |c Doraiswami Ramkrishna ; Neal R. Amundson |
| 264 | 1 | |a Englewood Cliffs, NJ |b Prentice-Hall |c 1985 | |
| 300 | |a XV, 471 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Prentice-Hall international series in the physical and chemical engineering sciences | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Chemical engineering |x Mathematics | |
| 650 | 4 | |a Linear operators | |
| 650 | 0 | 7 | |a Verfahrenstechnik |0 (DE-588)4062781-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Linearer Operator |0 (DE-588)4167721-3 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Verfahrenstechnik |0 (DE-588)4062781-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Amundson, Neal Russell |d 1916- |e Verfasser |0 (DE-588)118502689 |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001337256&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001337256 | ||
Datensatz im Suchindex
| _version_ | 1804116495109718016 |
|---|---|
| adam_text | Contents
Preface xiii
0. Sets, Mappings, and Other Preliminaries 7
0.0 Foreword 1
0.1 Introduction 7
0.2 Sets, Elements, and Operation in Sets 2
0.3 Mappings 6
0.4 Concluding Remarks 8
1. The Number System. Real Numbers 9
1.0 Foreword 9
1.1 Introduction 9
1.2 Fields 70
1.3 Ordered Fields 72
1.4 The Axiom of Continuity 13
1.5 Real Numbers 74
1.6 Mathematical Induction 76
1.7 Denumerability 17
1.8 Bounded Sets 79
1.9 Concluding Remarks 22
vii
viii Contents
2. Linear Spaces 24
2.0 Foreword 24
2.1 Introduction 25
2.2 Linear Dependence 30
2.3 Bases, Components, and Dimension 33
2.4 Linear Subspaces 36
2.5 Linear Manifolds. Hyperplanes 38
2.6 Linear and Bilinear Functionals. Quadratic Forms 40
2.7 Linear Transformations or Operators 42
2.8 Null and Range Spaces of a Linear Transformation 44
2.9 Operations on Linear Transformations. Linear Space of Operators 48
2.10 The Inverse Operator 51
2.11 Isomorphisms. Isomorphic Spaces 56
2.12 Direct Sums and Tensor Products of Linear Spaces 58
2.13 Concluding Remarks 67
3. Metric Spaces 70
3.0 Foreword 70
3.1 Introduction 70
3.2 Convergence of Sequences 73
3.3 Continuity of Functions 74
3.4 Pseudometric Spaces 77
3.5 Subsets of Metric Spaces 80
3.5.1 Compact Sets 84
3.6 Completeness of Metric Spaces 89
3.6.1 Equivalence of Metric Spaces 93
3.7 A Fixed Point Theorem 95
3.8 Concluding Remarks 102
4. Introduction to Integration Theory.
The Riemann and Lebesgue Integrals 704
4.0 Foreword 104
4.1 Introduction 104
4.2 The Riemann Integral 105
4.3 The Lebesque Integral 108
4.3.1 The Concept of Measure 110
4.3.2 Measurable Functions 114
4.3.3 Lebesgue Spaces 119
4.3.4 Differentiation 120
4.3.5 Dense Subspaces of £2[a, b] 120
4.4 Concluding Remarks 122
Contents JX
5. Normed Linear Spaces 124
5.0 Foreword 124
5.1 Introduction 125
5.1.1 Direct Sums of Normed Linear Spaces 128
5.2 Bases 129
5.3 Bounded Linear Transformations 132
5.3.1 Domains of Bounded Linear Transformations 136
5.3.2 Space of Bounded Linear Transformations 136
5.3.3 Compact Operators 143
5.4 Bounded Linear Functional 147
5.5 Unbounded Operators 148
5.6 Concluding Remarks 150
6. Inner Product Spaces 753
6.0 Foreword 153
6.1 Introduction 154
6.1.1 Orthogonality 159
6.1.2 Gram Schmidt Orthogonalization 161
6.2 Orthonormal Bases 162
6.3 Direct Sums and Tensor Products of Inner Product Spaces 167
6.4 Subspaces in Hilbert Spaces 171
6.5 Bounded Linear Functionals 176
6.6 Bounded Linear Operators 178
6.7 Unbounded Operators 183
6.7.1 Adjoint of an Unbounded Operator 184
6.8 Concluding Remarks 188
7. Spectral Theory of Self Adjoint Operators 192
7.0 Foreword 192
7.1 Introduction 193
7.2 Bounded Self Adjoint Operators. Some Properties 193
7.3 Eigenvalues, Eigenvectors, and Eigenspaces 200
7.4 Spectral Theorems 202
7.4.1 Functions of a Self Adjoint Operator 213
7.5 Some Common Equations 217
7.6 The Spectra of Bounded and Unbounded Self Adjoint Operators 221
7.7 Another View of Spectral Representation 229
7.8 Concluding Remarks 230
8. Applications in Finite Dimensional Space 233
8.0 Foreword 233
8.1 Introduction 234
X Contents
8.2 First Order Reaction Systems 235
8.3 Multicomponent Rectification 243
8.4 Jacobi Matrices and Stagewise Operations 247
8.5 Multicomponent Diffusion 251
8.5.1 Multicomponent Diffusion with Chemical Reaction 255
8.5.2 The First Order Reaction System in a Tubular Reactor 259
8.6 Concluding Remarks 265
9. Ordinary Linear Differential Operators 266
9.0 Foreword 266
9.1 Introduction 267
9.2 Self Adjoint Differential Operators. Continuous Coefficients 276
9.2.1 Existence of a Compact Inverse 281
9.2.2 Evaluation of Spectra 298
9.2.3 Boundary Value Problems 308
9.2.4 Convergence of Eigenfunction Expansions in £z{[a, b]:r(x)} 320
9.3 Self Adjoint Differential Operators. Discontinuous Coefficients 323
9.3.1 Existence of a Compact Inverse 329
9.3.2 Evaluation of Spectra 336
9.3.3 Boundary Value Problems 341
9.4 Self Adjoint Differential Operators. Weighted Boundaries and
Discontinuities 345
9.4.1 Existence of a Compact Inverse 355
9.4.2 Evaluation of Spectra 357
9.4.3 Boundary Value Problems 360
9.5 General Even Order Differential Operators 361
9.5.1 Self Adjoint Operators 364
9.6 Concluding Remarks 370
10. Partial Differential Operators 374
10.0 Foreword 374
10.1 Introduction 374
10.2 Partial Differential Expressions of Second Order 375
10.2.1 Boundary Conditions 378
10.2.2 Discontinuous Coefficients 383
10.3 Higher Order Partial Expressions 390
10.4 Separable Partial Differential Operators 392
10.5 Solution of Some Elliptic Problems by Decomposition into
First Order Systems 407
10.5.1 Boundary and Interface Conditions 408
10.5.2 The Method of Decomposition into First Order Systems 413
10.5.3 Spectral Analysis of Self Adjoint First Order Systems 421
10.5.4 Solution of the Boundary Value Problems 425
10.6 Concluding Remarks 427
Contents XI
11. Non Self Adjoint Orerators 429
11.0 Foreword 429
11.1 Introduction 429
11.2 Eigenvalues, Eigenvectors, and Root Vectors.
Biorthogonal Expansions 431
11.3 Concluding Remarks 445
Appendix 447
Index of Symbols 457
Author Index 461
Subject Index 463
|
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| id | DE-604.BV002044662 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:39:25Z |
| institution | BVB |
| isbn | 0135373417 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001337256 |
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| owner_facet | DE-91 DE-BY-TUM DE-29T DE-83 |
| physical | XV, 471 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Prentice-Hall |
| record_format | marc |
| series2 | Prentice-Hall international series in the physical and chemical engineering sciences |
| spelling | Ramkrishna, Doraiswami Verfasser aut Linear operator methods in chemical engineering with applications to transport and chemical reaction systems Doraiswami Ramkrishna ; Neal R. Amundson Englewood Cliffs, NJ Prentice-Hall 1985 XV, 471 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Prentice-Hall international series in the physical and chemical engineering sciences Mathematik Chemical engineering Mathematics Linear operators Verfahrenstechnik (DE-588)4062781-0 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Linearer Operator (DE-588)4167721-3 s Verfahrenstechnik (DE-588)4062781-0 s DE-604 Amundson, Neal Russell 1916- Verfasser (DE-588)118502689 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001337256&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ramkrishna, Doraiswami Amundson, Neal Russell 1916- Linear operator methods in chemical engineering with applications to transport and chemical reaction systems Mathematik Chemical engineering Mathematics Linear operators Verfahrenstechnik (DE-588)4062781-0 gnd Linearer Operator (DE-588)4167721-3 gnd |
| subject_GND | (DE-588)4062781-0 (DE-588)4167721-3 |
| title | Linear operator methods in chemical engineering with applications to transport and chemical reaction systems |
| title_auth | Linear operator methods in chemical engineering with applications to transport and chemical reaction systems |
| title_exact_search | Linear operator methods in chemical engineering with applications to transport and chemical reaction systems |
| title_full | Linear operator methods in chemical engineering with applications to transport and chemical reaction systems Doraiswami Ramkrishna ; Neal R. Amundson |
| title_fullStr | Linear operator methods in chemical engineering with applications to transport and chemical reaction systems Doraiswami Ramkrishna ; Neal R. Amundson |
| title_full_unstemmed | Linear operator methods in chemical engineering with applications to transport and chemical reaction systems Doraiswami Ramkrishna ; Neal R. Amundson |
| title_short | Linear operator methods in chemical engineering |
| title_sort | linear operator methods in chemical engineering with applications to transport and chemical reaction systems |
| title_sub | with applications to transport and chemical reaction systems |
| topic | Mathematik Chemical engineering Mathematics Linear operators Verfahrenstechnik (DE-588)4062781-0 gnd Linearer Operator (DE-588)4167721-3 gnd |
| topic_facet | Mathematik Chemical engineering Mathematics Linear operators Verfahrenstechnik Linearer Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001337256&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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