Linear mathematical models in chemical engineering:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 507 S. graph. Darst. |
| ISBN: | 9789812794154 9812794158 |
Internformat
MARC
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| 008 | 081128s2010 d||| |||| 00||| eng d | ||
| 015 | |a GBA8B2740 |2 dnb | ||
| 020 | |a 9789812794154 |9 978-981-279-415-4 | ||
| 020 | |a 9812794158 |9 981-279-415-8 | ||
| 035 | |a (OCoLC)213479547 | ||
| 035 | |a (DE-599)HBZHT016347527 | ||
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| 050 | 0 | |a TP155.2.M35 | |
| 082 | 0 | |a 660.015118 |2 22 | |
| 084 | |a VN 7030 |0 (DE-625)147599:253 |2 rvk | ||
| 084 | |a 92E99 |2 msc | ||
| 084 | |a 00A06 |2 msc | ||
| 100 | 1 | |a Hjortsø, Martin A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear mathematical models in chemical engineering |c Martin A. Hjortso and Peter Wolenski |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2010 | |
| 300 | |a XV, 507 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Chemical engineering / Mathematical models | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Chemical engineering |x Mathematical models | |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chemische Verfahrenstechnik |0 (DE-588)4069941-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Chemische Verfahrenstechnik |0 (DE-588)4069941-9 |D s |
| 689 | 0 | 1 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Wolenski, Peter |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016992764&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016992764 | ||
Datensatz im Suchindex
| _version_ | 1804138361809534976 |
|---|---|
| adam_text | Contents
Preface v
1.
Model
Formulation
1
1.1
Classical models
............................ 1
1.1.1
Macroscopic balances
..................... 2
1.1.1.1
Mass and energy balances
............. 2
1.1.1.2
Balances involving chemical kinetics
....... 18
1.1.2
The quasi steady state assumption
.............. 27
1.1.3
Differential balances
...................... 32
1.1.3.1
Coordinate systems
................. 32
1.1.3.2
Constitutive equations
............... 36
1.1.3.3
Operator notation
................. 38
1.1.3.4
Mass and energy balances
............. 42
1.1.3.5
Problems in fluid mechanics
............ 59
1.1.3.6
Summary of common boundary conditions
.... 64
1.1.3.7
Symmetry
...................... 66
1.2
Abstract control volumes
....................... 69
2.
Some Ordinary Differential Equations
79
2.1
First order equations
.......................... 79
2.1.1
Separable equations
...................... 79
2.1.2
Linear, first order equations
................. 80
2.1.3
Exact equations
........................ 82
2.1.4
Homogeneous equations
.................... 83
2.1.5
Bernoulli equation
....................... 85
2.1.6
Clairauťs
equation
...................... 86
2.1.7
Riccati equation
........................ 87
2.2
Second order equations
......................... 89
2.2.1
Dependent variable does not occur explicitly
........ 89
2.2.2
Free variable does not occur explicitly
............ 90
xii
Linear Mathematical Models in Chemical
Engineering
2.2.3
Homogeneous equations
.................... 91
2.3
Higher order equations
......................... 92
2.4
Variable transformations
........................ 92
2.5
The importance of being Lipschitz
.................. 94
3.
Finite Dimensional Vector Spaces
97
3.1
Basic concepts
............................. 97
3.2
Examples
................................ 99
3.3
Span, linear independence, and basis
................. 101
3.3.1
Coordinates
.......................... 106
3.4
Isomorphisms
.............................. 107
3.4.1
Isomorphisms of vector spaces
................ 107
3.4.2
Subspaces
........................... 109
3.4.3
Sums
..............................
Ш
3.4.4
Representation of subspaces
................. 113
3.5
Matrices
................................. 116
3.5.1
Matrix algebra
.........................117
3.5.2
Gauss elimination
.......................119
3.5.3
Determinants
.........................123
3.5.3.1
Basic properties of determinants
......... 124
3.5.3.2
Calculation of determinants
............ 127
3.5.3.3
The derivative of a determinant
.......... 129
3.5.4
The classical adjoint matrix
................. 129
3.6
Systems of linear algebraic equations
................. 130
3.6.1
Rank
.............................. 131
3.6.2
Applications of rank
...................... 135
3.6.3
Solution structure
....................... 141
3.6.4
The null and range space of a matrix
............ 148
3.6.5
Overdetermined systems
................... 151
3.7
The algebraic eigenvalue problem
................... 152
3.7.1
Finding eigenvalues and eigenvectors
............ 153
3.7.2
Multiplicity
.......................... 160
3.7.3
Similar matrices
........................ 161
3.7.3.1
Equivalence relations
................ 163
3.7.4 Eigenspaces
and eigenbases
.................. 164
3.7.4.1
Diagonalization of simple and semi-simple
matrices
....................... 166
3.7.5
Generalized eigenspaces
.................... 167
3.7.5.1
Generalized eigenbases
............... 171
3.7.6
Jordan canonical form
..................... 175
3.7.7
Jordan form of real matrices with complex eigenvalues
. . 179
3.7.8
Powers and exponentials of matrices
............. 183
Contents
x¡¡¡
3.7.9
Location of eigenvalues
.................... 186
3.8
Geometry of vector spaces
......................
ig$
3.8.1
Vector products
........................ 188
3.8.1.1
Inner product
.................... 188
3.8.1.2
Cross product
.................... 190
3.8.1.3
Triple scalar product
................ 191
3.8.1.4
Dyad or outer product
............... 193
3.8.2
Gram-Schmidt orthogonalization
............... 194
3.8.3
Eigenrows
........................... 197
3.8.4
Real, symmetric matrices
................... 198
4.
Tensors
201
4.1
Definitions and basic concepts
..................... 202
4.2
Examples
................................ 203
4.2.1
Matrices as operators
..................... 204
4.2.2
Equivalence transformations
................. 208
4.3
The adjoint operator
.......................... 210
4.4
Tensors
................................. 212
4.4.1
Transformation rules
..................... 214
4.4.2
Invariants of tensors
...................... 218
4.5
Some tensors from physics and engineering
............. 220
4.5.1
Fourier s law
.......................... 221
4.5.2
The stress tensor
....................... 227
4.6
Vectors and tensors in curvilinear coordinates
............ 235
4.6.1
Proper transformations
.................... 237
4.6.2
Vectors and transformations at a point
........... 238
4.6.3
Covariance and contravariance
................ 240
4.6.4
The physical components
................... 246
5.
Linear Difference Equations
249
5.1
Linear equations with constant coefficients
.............. 259
5.1.1
Homogeneous solutions
.................... 260
5.1.2
Particular solutions
...................... 263
5.2
Single, first order equations
...................... 266
5.3
Single, higher order equations
..................... 267
5.3.1
Solution by variable transformation
............. 268
5.3.1.1
Euler s equation
................... 268
5.3.2
Reduction of order
....................... 268
5.3.3
Particular solution by variation of parameters
....... 270
5.4
Systems of linear difference equations
................ 272
5.4.1
Basic theorems
......................... 273
5.4.2
Particular solution by variation of parameters
....... 275
xiv
Linear Mathematical Models in Chemical Engineering
5.4.3
Equations with constant coefficients
............. 277
5.4.3.1
Homogeneous solutions
............... 277
5.4.3.2
Particular solutions for constant inhomogeneous
term
......................... 282
5.5
Non
linear equations
.......................... 285
5.5.1
Riccatľs
equation
....................... 286
6.
Linear Differential Equations
287
6.1
Linear equations with constant coefficients
.............. 288
6.1.1
Homogeneous solutions
.................... 288
6.1.2
Particular solutions
...................... 290
6.2
Single, higher order equations
..................... 293
6.2.1
Solution by variable transformation
............. 294
6.2.1.1
Euler s equation
................... 294
6.2.2
Reduction of order
....................... 295
6.2.3
Particular solution by variation of parameters
....... 296
6.3
Systems of linear differential equations
................ 299
6.3.1
Basic theorems
......................... 300
6.3.2
Particular solution by variation of parameters
....... 301
6.3.3
Equations with constant coefficients
............. 302
6.3.3.1
Homogeneous solutions
............... 303
6.3.3.2
Particular solutions for constant inhomogeneous
term
......................... 307
6.3.3.3
Dealing with complex eigenvalues
......... 310
6.3.3.4
Classification of steady states
........... 311
6.3.3.5
Stability of nonlinear ODEs
............ 319
6.4
Series solutions
............................. 325
6.5
Some common functions defined by ODEs
.............. 333
6.5.1
Exponential and trigonometric functions
.......... 333
6.5.2
Bessel functions
........................ 334
6.5.3
Legendre functions
...................... 340
7.
Hubert Spaces
345
7.1
Infinite dimensional vector spaces
................... 346
7.1.1
Countable and uncountable infinities
............ 346
7.1.2
Normed spaces
......................... 348
7.1.3
Bases in infinite dimensional spaces
............. 351
7.1.4
The function spaces £p[0,
1] ................. 353
7.2
Hubert spaces
.............................. 354
7.2.1
Inner products
......................... 354
7.2.2
Examples
............................ 356
7.2.3
Orthogonality
......................... 357
Contents xv
7.2.4 Orthogonal
projections
.................... 361
7.2.5 Orthogonal
complements
................... 363
7.3 Linear
operators in Hubert spaces
.................. 363
7.3.1
The adjoint operator.....................
364
7.3.2
Examples
............................
З65
7.3.3 Sturm-Liouville
operators
................... 367
7.4
Eigenvalue problems
.......................... 368
7.4.1
Sturm-Liouville Problems
................... 372
7.4.2
Conversion of linear equations to SLP
............ 370
7.5
Fourier series
.............................. 377
7.5.1
Fourier sine series
....................... 377
7.5.2
Fourier cosine series
...................... 378
7.5.3
Complete Fourier series
.................... 378
7.5.4
Gibb s phenomena
....................... 381
7.5.5
Generalized Fourier series
................... 383
8.
Partial Differential Equations
389
8.1
Fourier series methods
......................... 389
8.1.1
Classification of second order PDEs
............. 390
8.1.2
Inner product method
..................... 392
8.1.3
PDEs with Sturm-Liouville operators
............ 396
8.1.3.1
Homogeneous problem
............... 397
8.1.3.2
Homogeneous problem with transcendental
equation for eigenvalues
.............. 399
8.1.3.3
Inhomogeneous PDE
................ 409
8.1.3.4
Inhomogeneous, time varying boundary
conditions
...................... 411
8.1.4
Other self-adjoint PDEs
.................... 415
8.2
Finite Fourier transform
........................ 425
8.3
First order PDEs
............................ 428
8.4
First order PDE and Cauchy s method
................ 432
8.4.1
Cauchy s method for linear equations
............ 434
8.5
Similarity transformation
....................... 448
9.
Problems
455
Appendix
497
A.I Complex numbers
........................... 497
Index <r>01
|
| adam_txt |
Contents
Preface v
1.
Model
Formulation
1
1.1
Classical models
. 1
1.1.1
Macroscopic balances
. 2
1.1.1.1
Mass and energy balances
. 2
1.1.1.2
Balances involving chemical kinetics
. 18
1.1.2
The quasi steady state assumption
. 27
1.1.3
Differential balances
. 32
1.1.3.1
Coordinate systems
. 32
1.1.3.2
Constitutive equations
. 36
1.1.3.3
Operator notation
. 38
1.1.3.4
Mass and energy balances
. 42
1.1.3.5
Problems in fluid mechanics
. 59
1.1.3.6
Summary of common boundary conditions
. 64
1.1.3.7
Symmetry
. 66
1.2
Abstract control volumes
. 69
2.
Some Ordinary Differential Equations
79
2.1
First order equations
. 79
2.1.1
Separable equations
. 79
2.1.2
Linear, first order equations
. 80
2.1.3
Exact equations
. 82
2.1.4
Homogeneous equations
. 83
2.1.5
Bernoulli equation
. 85
2.1.6
Clairauťs
equation
. 86
2.1.7
Riccati equation
. 87
2.2
Second order equations
. 89
2.2.1
Dependent variable does not occur explicitly
. 89
2.2.2
Free variable does not occur explicitly
. 90
xii
Linear Mathematical Models in Chemical
Engineering
2.2.3
Homogeneous equations
. 91
2.3
Higher order equations
. 92
2.4
Variable transformations
. 92
2.5
The importance of being Lipschitz
. 94
3.
Finite Dimensional Vector Spaces
97
3.1
Basic concepts
. 97
3.2
Examples
. 99
3.3
Span, linear independence, and basis
. 101
3.3.1
Coordinates
. 106
3.4
Isomorphisms
. 107
3.4.1
Isomorphisms of vector spaces
. 107
3.4.2
Subspaces
. 109
3.4.3
Sums
.
Ш
3.4.4
Representation of subspaces
. 113
3.5
Matrices
. 116
3.5.1
Matrix algebra
.117
3.5.2
Gauss elimination
.119
3.5.3
Determinants
.123
3.5.3.1
Basic properties of determinants
. 124
3.5.3.2
Calculation of determinants
. 127
3.5.3.3
The derivative of a determinant
. 129
3.5.4
The classical adjoint matrix
. 129
3.6
Systems of linear algebraic equations
. 130
3.6.1
Rank
. 131
3.6.2
Applications of rank
. 135
3.6.3
Solution structure
. 141
3.6.4
The null and range space of a matrix
. 148
3.6.5
Overdetermined systems
. 151
3.7
The algebraic eigenvalue problem
. 152
3.7.1
Finding eigenvalues and eigenvectors
. 153
3.7.2
Multiplicity
. 160
3.7.3
Similar matrices
. 161
3.7.3.1
Equivalence relations
. 163
3.7.4 Eigenspaces
and eigenbases
. 164
3.7.4.1
Diagonalization of simple and semi-simple
matrices
. 166
3.7.5
Generalized eigenspaces
. 167
3.7.5.1
Generalized eigenbases
. 171
3.7.6
Jordan canonical form
. 175
3.7.7
Jordan form of real matrices with complex eigenvalues
. . 179
3.7.8
Powers and exponentials of matrices
. 183
Contents
x¡¡¡
3.7.9
Location of eigenvalues
. 186
3.8
Geometry of vector spaces
.
ig$
3.8.1
Vector products
. 188
3.8.1.1
Inner product
. 188
3.8.1.2
Cross product
. 190
3.8.1.3
Triple scalar product
. 191
3.8.1.4
Dyad or outer product
. 193
3.8.2
Gram-Schmidt orthogonalization
. 194
3.8.3
Eigenrows
. 197
3.8.4
Real, symmetric matrices
. 198
4.
Tensors
201
4.1
Definitions and basic concepts
. 202
4.2
Examples
. 203
4.2.1
Matrices as operators
. 204
4.2.2
Equivalence transformations
. 208
4.3
The adjoint operator
. 210
4.4
Tensors
. 212
4.4.1
Transformation rules
. 214
4.4.2
Invariants of tensors
. 218
4.5
Some tensors from physics and engineering
. 220
4.5.1
Fourier's law
. 221
4.5.2
The stress tensor
. 227
4.6
Vectors and tensors in curvilinear coordinates
. 235
4.6.1
Proper transformations
. 237
4.6.2
Vectors and transformations at a point
. 238
4.6.3
Covariance and contravariance
. 240
4.6.4
The physical components
. 246
5.
Linear Difference Equations
249
5.1
Linear equations with constant coefficients
. 259
5.1.1
Homogeneous solutions
. 260
5.1.2
Particular solutions
. 263
5.2
Single, first order equations
. 266
5.3
Single, higher order equations
. 267
5.3.1
Solution by variable transformation
. 268
5.3.1.1
Euler's equation
. 268
5.3.2
Reduction of order
. 268
5.3.3
Particular solution by variation of parameters
. 270
5.4
Systems of linear difference equations
. 272
5.4.1
Basic theorems
. 273
5.4.2
Particular solution by variation of parameters
. 275
xiv
Linear Mathematical Models in Chemical Engineering
5.4.3
Equations with constant coefficients
. 277
5.4.3.1
Homogeneous solutions
. 277
5.4.3.2
Particular solutions for constant inhomogeneous
term
. 282
5.5
Non
linear equations
. 285
5.5.1
Riccatľs
equation
. 286
6.
Linear Differential Equations
287
6.1
Linear equations with constant coefficients
. 288
6.1.1
Homogeneous solutions
. 288
6.1.2
Particular solutions
. 290
6.2
Single, higher order equations
. 293
6.2.1
Solution by variable transformation
. 294
6.2.1.1
Euler's equation
. 294
6.2.2
Reduction of order
. 295
6.2.3
Particular solution by variation of parameters
. 296
6.3
Systems of linear differential equations
. 299
6.3.1
Basic theorems
. 300
6.3.2
Particular solution by variation of parameters
. 301
6.3.3
Equations with constant coefficients
. 302
6.3.3.1
Homogeneous solutions
. 303
6.3.3.2
Particular solutions for constant inhomogeneous
term
. 307
6.3.3.3
Dealing with complex eigenvalues
. 310
6.3.3.4
Classification of steady states
. 311
6.3.3.5
Stability of nonlinear ODEs
. 319
6.4
Series solutions
. 325
6.5
Some common functions defined by ODEs
. 333
6.5.1
Exponential and trigonometric functions
. 333
6.5.2
Bessel functions
. 334
6.5.3
Legendre functions
. 340
7.
Hubert Spaces
345
7.1
Infinite dimensional vector spaces
. 346
7.1.1
Countable and uncountable infinities
. 346
7.1.2
Normed spaces
. 348
7.1.3
Bases in infinite dimensional spaces
. 351
7.1.4
The function spaces £p[0,
1] . 353
7.2
Hubert spaces
. 354
7.2.1
Inner products
. 354
7.2.2
Examples
. 356
7.2.3
Orthogonality
. 357
Contents xv
7.2.4 Orthogonal
projections
. 361
7.2.5 Orthogonal
complements
. 363
7.3 Linear
operators in Hubert spaces
. 363
7.3.1
The adjoint operator.
364
7.3.2
Examples
.
З65
7.3.3 Sturm-Liouville
operators
. 367
7.4
Eigenvalue problems
. 368
7.4.1
Sturm-Liouville Problems
. 372
7.4.2
Conversion of linear equations to SLP
. 370
7.5
Fourier series
. 377
7.5.1
Fourier sine series
. 377
7.5.2
Fourier cosine series
. 378
7.5.3
Complete Fourier series
. 378
7.5.4
Gibb's phenomena
. 381
7.5.5
Generalized Fourier series
. 383
8.
Partial Differential Equations
389
8.1
Fourier series methods
. 389
8.1.1
Classification of second order PDEs
. 390
8.1.2
Inner product method
. 392
8.1.3
PDEs with Sturm-Liouville operators
. 396
8.1.3.1
Homogeneous problem
. 397
8.1.3.2
Homogeneous problem with transcendental
equation for eigenvalues
. 399
8.1.3.3
Inhomogeneous PDE
. 409
8.1.3.4
Inhomogeneous, time varying boundary
conditions
. 411
8.1.4
Other self-adjoint PDEs
. 415
8.2
Finite Fourier transform
. 425
8.3
First order PDEs
. 428
8.4
First order PDE and Cauchy's method
. 432
8.4.1
Cauchy's method for linear equations
. 434
8.5
Similarity transformation
. 448
9.
Problems
455
Appendix
497
A.I Complex numbers
. 497
Index <r>01 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Hjortsø, Martin A. Wolenski, Peter |
| author_facet | Hjortsø, Martin A. Wolenski, Peter |
| author_role | aut aut |
| author_sort | Hjortsø, Martin A. |
| author_variant | m a h ma mah p w pw |
| building | Verbundindex |
| bvnumber | BV035186076 |
| callnumber-first | T - Technology |
| callnumber-label | TP155 |
| callnumber-raw | TP155.2.M35 |
| callnumber-search | TP155.2.M35 |
| callnumber-sort | TP 3155.2 M35 |
| callnumber-subject | TP - Chemical Technology |
| classification_rvk | VN 7030 |
| ctrlnum | (OCoLC)213479547 (DE-599)HBZHT016347527 |
| dewey-full | 660.015118 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 660 - Chemical engineering |
| dewey-raw | 660.015118 |
| dewey-search | 660.015118 |
| dewey-sort | 3660.015118 |
| dewey-tens | 660 - Chemical engineering |
| discipline | Chemie / Pharmazie |
| discipline_str_mv | Chemie / Pharmazie |
| format | Book |
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| id | DE-604.BV035186076 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:59:44Z |
| indexdate | 2024-07-09T21:26:58Z |
| institution | BVB |
| isbn | 9789812794154 9812794158 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016992764 |
| oclc_num | 213479547 |
| open_access_boolean | |
| owner | DE-703 DE-83 |
| owner_facet | DE-703 DE-83 |
| physical | XV, 507 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Hjortsø, Martin A. Verfasser aut Linear mathematical models in chemical engineering Martin A. Hjortso and Peter Wolenski Singapore [u.a.] World Scientific 2010 XV, 507 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chemical engineering / Mathematical models Mathematisches Modell Chemical engineering Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Chemische Verfahrenstechnik (DE-588)4069941-9 gnd rswk-swf Chemische Verfahrenstechnik (DE-588)4069941-9 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Wolenski, Peter Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016992764&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hjortsø, Martin A. Wolenski, Peter Linear mathematical models in chemical engineering Chemical engineering / Mathematical models Mathematisches Modell Chemical engineering Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4069941-9 |
| title | Linear mathematical models in chemical engineering |
| title_auth | Linear mathematical models in chemical engineering |
| title_exact_search | Linear mathematical models in chemical engineering |
| title_exact_search_txtP | Linear mathematical models in chemical engineering |
| title_full | Linear mathematical models in chemical engineering Martin A. Hjortso and Peter Wolenski |
| title_fullStr | Linear mathematical models in chemical engineering Martin A. Hjortso and Peter Wolenski |
| title_full_unstemmed | Linear mathematical models in chemical engineering Martin A. Hjortso and Peter Wolenski |
| title_short | Linear mathematical models in chemical engineering |
| title_sort | linear mathematical models in chemical engineering |
| topic | Chemical engineering / Mathematical models Mathematisches Modell Chemical engineering Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd |
| topic_facet | Chemical engineering / Mathematical models Mathematisches Modell Chemical engineering Mathematical models Chemische Verfahrenstechnik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016992764&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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