Applied mathematics and modeling for chemical engineers
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| 245 | 1 | 0 | |a Applied mathematics and modeling for chemical engineers |c Richard G. Rice ; Duong D. Do |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2012 | |
| 300 | |a XII, 383 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0302 CIT 009f 2013 B 182 |
|---|---|
| DE-BY-TUM_katkey | 1904537 |
| DE-BY-TUM_location | 03 |
| DE-BY-TUM_media_number | 040030497044 |
| _version_ | 1820893715020906496 |
| adam_text | CONTENTS
Preface to the Second Edition
xi
PARTI
1
Formulation of Physicochemical Problems
1.1
Introduction,
3
1.2
Illustration of the Formulation Process (Cooling of Fluids),
3
1.2.1
Model I: Plug Row,
3
1.2.2
Model II: Parabolic Velocity,
6
1.3
Combining Rate and Equilibrium Concepts (Packed Bed Adsorber),
7
1.4
Boundary Conditions and Sign Conventions,
8
1.5
Models with Many Variables: Vectors and Matrices,
10
1.6
Matrix Definition,
10
1.6.1
The Matrix,
10
1.6.2
The Vector,
11
1.7
Types of Matrices,
11
1.7.1
Square Matrix,
11
1.7.2
Diagonal Matrix,
11
1.7.3
Triangular Matrix,
11
1.7.4
Tridiagonal Matrix,
11
1.7.5
Symmetric Matrix,
11
1.7.6
Sparse Matrix,
11
1.7.7
Diagonally Dominant Matrix,
11
1.8
Matrix Algebra,
12
1.8.1
Addition and Subtraction,
12
1.8.2
Multiplication,
12
1.8.3
Inverse,
12
1.8.4
Matrix Decomposition or Factorization,
13
1.9
Useful Row Operations,
13
1.9.1
Scaling,
13
1.9.2
Pivoting,
13
1.9.3
Elimination,
13
1.10
Direct Elimination Methods,
14
vi
CONTENTS
1.10.1
Basic Procedure,
14
1.10.2
Augmented
Matrix, 14
1.10.3
Pivoting,
15
1.10.4
Scaling,
16
1.10.5
Gauss Elimination,
16
1.10.6
Gauss-Jordan Elimination: Solving Linear Equations,
17
1.10.7
LU
Decomposition,
17
1.11
Iterative Methods,
18
1.11.1
Jacobi Method,
18
1.11.2
Gauss-Seidel Iteration Method,
18
1.11.3
Successive Overrelaxation Method,
18
1.12
Summary of the Model Building Process,
19
1.13
Model Hierarchy and its Importance in Analysis,
19
Problems,
25
References,
30
2
Solution Techniques for Models Yielding Ordinary Differential Equations
31
2.1
Geometric Basis and Functionality,
31
2.2
Classification of ODE,
32
2.3
First-Order Equations,
32
2.3.1
Exact Solutions,
33
2.3.2
Equations Composed of Homogeneous Functions,
34
2.3.3
Bernoulli s Equation,
34
2.3.4
Riccati
s
Equation,
35
2.3.5
Linear Coefficients,
36
2.3.6
First-Order Equations of Second Degree,
37
2.4
Solution Methods for Second-Order Nonlinear Equations,
37
2.4.1
Derivative Substitution Method,
38
2.4.2
Homogeneous Function Method,
41
2.5
Linear Equations of Higher Order,
42
2.5.1
Second-Order Unforced Equations: Complementary Solutions,
43
2.5.2
Particular Solution Methods for Forced Equations,
47
2.5.3
Summary of Particular Solution Methods,
55
2.6
Coupled Simultaneous ODE,
55
2.7 Eigenproblems, 59
2.8
Coupled Linear Differential Equations,
59
2.9
Summary of Solution Methods for ODE,
60
Problems,
60
References,
73
3
Series Solution Methods and Special Functions
75
3.1
Introduction to Series Methods,
75
3.2
Properties of Infinite Series,
76
3.3
Method of Frobenius,
77
3.3.1
Indiciai
Equation and Recurrence Relation,
77
3.4
Summary of the Frobenius Method,
85
3.5
Special Functions,
86
3.5.1
Besseľs
Equation,
86
3.5.2
Modified
Besseľ s
Equation,
87
3.5.3
Generalized Bessel s Equation,
88
3.5.4
Properties of Bessel Functions,
89
3.5.5
Differential, Integral, and Recurrence Relations,
91
CONTENTS
Problems, 93
References,
95
4 Integral
Functions
97
4.1
Introduction,
97
4.2
The Error Function,
97
4.2.1
Properties of Error Function,
97
4.3
The Gamma and Beta Functions,
98
4.3.1
The Gamma Function,
98
4.3.2
The Beta Function,
99
4.4
The Elliptic Integrals,
99
4.5
The Exponential and Trigonometric Integrals,
101
Problems,
102
References,
104
5
Staged-Process Models: The Calculus of Finite Differences
105
5.1
Introduction,
105
5.1.1
Modeling Multiple Stages,
105
5.2
Solution Methods for Linear Finite Difference Equations,
106
5.2.1
Complementary Solutions,
106
5.3
Particular Solution Methods,
109
5.3.1
Method of Undetermined Coefficients,
109
5.3.2
Inverse Operator Method,
110
5.4
Nonlinear Equations (Riccati Equation),
111
Problems,
112
References,
115
6
Approximate Solution Methods for ODE: Perturbation Methods
117
6.1
Perturbation Methods,
117
6.1.1
Introduction,
117
6.2
The Basic Concepts,
120
6.2.1
Gauge Functions,
120
6.2.2
Order Symbols,
120
6.2.3
Asymptotic Expansions and Sequences,
120
6.2.4
Sources of Nonuniformity,
121
6.3
The Method of Matched Asymptotic Expansion,
122
6.3.1
Outer Solutions,
123
6.3.2
Inner Solutions,
123
6.3.3
Matching,
124
6.3.4
Composite Solutions,
124
6.3.5
General Matching Principle,
124
6.3.6
Composite Solution of Higher Order,
125
6.4
Matched Asymptotic Expansions for Coupled Equations,
125
6.4.1
Outer Expansion,
126
6.4.2
Inner Expansion,
126
6.4.3
Matching,
127
Problems,
128
References,
136
viii CONTENTS
PART II
137
7
Numerical Solution Methods (Initial Value Problems)
139
7.1
Introduction,
139
7.2
Type of Method,
142
7.3
Stability,
142
7.4
Stiffness,
147
7.5
Interpolation and Quadrature,
149
7.6
Explicit Integration Methods,
150
7.7
Implicit Integration Methods,
152
7.8
Predictor-Corrector Methods and Runge-Kutta Methods,
152
7.8.1
Predictor-Corrector Methods,
152
7.9
Runge-Kutta Methods,
153
7.10
Extrapolation,
155
7.11
Step Size Control,
155
7.12
Higher Order Integration Methods,
156
Problems,
156
References,
159
8
Approximate Methods for Boundary Value Problems:
Weighted Residuals
161
8.1
The Method of Weighted Residuals,
161
8.1.1
Variations on a Theme of Weighted Residuals,
162
8.2
Jacobi Polynomials,
170
8.2.1
Rodrigues
Formula,
170
8.2.2
Orthogonality Conditions,
170
8.3 Lagrange
Interpolation Polynomials,
172
8.4
Orthogonal Collocation Method,
172
8.4.1
Differentiation of
a
Lagrange
Interpolation Polynomial,
172
8.4.2
Gauss-Jacobi Quadrature,
173
8.4.3
Radau and Lobatto Quadrature,
175
8.5
Linear Boundary Value Problem: Dirichlet Boundary Condition,
175
8.6
Linear Boundary Value Problem: Robin Boundary Condition,
177
8.7
Nonlinear Boundary Value Problem: Dirichlet Boundary Condition,
179
8.8
One-Point Collocation,
181
8.9
Summary of Collocation Methods,
182
8.10
Concluding Remarks,
183
Problems,
184
References,
192
9
Introduction to Complex Variables and Laplace Transforms
193
9.1
Introduction,
193
9.2
Elements of Complex Variables,
193
9.3
Elementary Functions of Complex Variables,
194
9.4
Multivalued Functions,
195
9.5
Continuity Properties for Complex Variables: Analyticity,
196
9.5.1
Exploiting Singularities,
198
9.6
Integration: Cauchy
s
Theorem,
198
9.7
Cauchy
s
Theory of Residues,
200
9.7.1
Practical Evaluation of Residues,
201
9.7.2
Residues at Multiple Poles,
202
CONTENTS
9.8 Inversion
of Laplace Transforms by Contour Integration,
202
9.8.1
Summary of Inversion Theorem for Pole Singularities,
204
9.9
Laplace Transformations: Building Blocks,
204
9.9.1
Taking the Transform,
204
9.9.2
Transforms of Derivatives and Integrals,
206
9.9.3
The Shifting Theorem,
207
9.9.4
Transform of Distribution Functions,
207
9.10
Practical Inversion Methods,
209
9.10.1
Partial Fractions,
209
9.10.2
Convolution Theorem,
210
9.11
Applications of Laplace Transforms for Solutions of ODE,
211
9.12
Inversion Theory for Multivalued Functions: the Second
Bromwich
Path,
215
9.12.1
Inversion When Poles and Branch Points Exist,
218
9.13
Numerical Inversion Techniques,
218
9.13.1
The Zakian Method,
218
9.13.2
The Fourier Series Approximation,
220
Problems,
221
References,
225
10
Solution Techniques for Models Producing PDEs
227
10.1
Introduction,
227
10.1.1
Classification and Characteristics of Linear Equations,
229
10.2
Particular Solutions for PDEs,
231
10.2.1
Boundary and Initial Conditions,
231
10.3
Combination of Variables Method,
233
10.4
Separation of Variables Method,
238
10.4.1
Coated Wall Reactor,
238
10.5
Orthogonal Functions and Sturm-Liouville Conditions,
241
10.5.1
The Sturm-Liouville Equation,
241
10.6
Inhomogeneous Equations,
245
10.7
Applications of Laplace Transforms for Solutions of PDEs,
248
Problems,
254
References,
271
11
Transform Methods for Linear PDEs
273
11.1
Introduction,
273
11.2
Transforms in Finite Domain: Sturm-Liouville Transforms,
273
11.2.1
Development of Integral Transform Pairs,
274
11.2.2
The Eigenvalue Problem and the Orthogonality Condition,
277
11.2.3
Inhomogeneous Boundary Conditions,
282
11.2.4
Inhomogeneous Equations,
285
11.2.5
Time-Dependent Boundary Conditions,
286
11.2.6
Elliptic Partial Differential Equations,
287
11.3
Generalized Sturm-Liouville Integral Transform,
289
11.3.1
Introduction,
289
11.3.2
The Batch Adsorber Problem,
290
Problems,
297
References,
301
12
Approximate and Numerical Solution Methods for PDEs
303
12.1
Polynomial Approximation,
303
12.2
Singular Perturbation,
310
12.3
Finite Difference,
315
%
CONTENTS
12.3.1
Notations,
316
12.3.2
Essence
of the Method,
316
12.3.3
Tridiagonal Matrix and the Thomas Algorithm,
317
12.3.4
Linear Parabolic Partial Differential Equations,
318
12.3.5
Nonlinear Parabolic Partial Differential Equations,
321
12.3.6
Elliptic Equations,
322
12.4
Orthogonal Collocation for Solving PDEs,
324
12.4.1
Elliptic PDE,
324
12.4.2
Parabolic PDE: Example
1, 327
12.4.3
Coupled Parabolic PDE: Example
2, 328
12.5
Orthogonal Collocation on Finite Elements,
330
Problems,
335
References,
342
Appendix A: Review of Methods for Nonlinear Algebraic Equations
343
A.I The Bisection Algorithm,
343
A.
2
The Successive Substitution Method,
344
A.3 The Newton-Raphson Method,
346
A.4 Rate of Convergence,
348
A.5 Multiplicity,
349
A.
6
Accelerating Convergence,
349
References,
350
Appendix B: Derivation of the Fourier-Mellin Inversion Theorem
351
Appendix
С
:
Table of Laplace Transforms
357
Appendix D: Numerical Integration
363
D.I Basic Idea of Numerical Integration,
363
D.2 Newton Forward Difference Polynomial,
364
D.3 Basic Integration Procedure,
364
D.3.1
Trapezoid
Rule,
364
D.3.
2
Simpson s Rule,
365
D.4 Error Control and Extrapolation,
366
D.5 Gaussian Quadrature,
367
D.6 Radau Quadrature,
369
D.7 Lobatto Quadrature,
370
D.8 Concluding Remarks,
372
References,
372
Appendix E: Nomenclature
373
Postface
377
Index
379
Enables chemical engineers to use
mathematics to solve common
on-the-job problems
With its clear explanations, examples, and problem sets, Applied Mathematics and Modeling for Chemical
Engineers has enabled thousands of chemical engineers to apply mathematical principles to successfully solve
practical problems. The book introduces traditional techniques to solve ordinary differential equations as well
as analytical methods to deal with important classes of finite-difference equations. It then explores techniques
for solving partial differential equations from classical methods to finite-transforms, culminating with numerical
methods including orthogonal collocation.
This Second Edition demonstrates how classical mathematics solves a broad range of new applications that have
arisen since the publication of the acclaimed first edition. Readers will find new materials and problems dealing
with such topics as:
•
Brain implant drug delivery
•
Carbon dioxide storage
•
Chemical reactions in nanotubes
•
Dissolution of pills and pharmaceutical capsules
•
Honeycomb reactors used in catalytic converters
•
New models of physical phenomena such as bubble coalescence
Like the first edition, this Second Edition provides plenty of worked examples that explain each step on the way to
finding a problem s solution. Homework problems at the end of each chapter are designed to encourage readers to
more deeply examine the underlying logic of the mathematical techniques used to arrive at the answers. Readers
can refer to the references, also at the end of each chapter, to explore individual topics in greater depth. Finally,
the text s appendices provide additional information on numerical methods for solving algebraic equations as well
as a detailed explanation of numerical integration algorithms.
Applied Mathematics and Modeling for Chemical Ejigineers is recommended for all students in chemical
engineering as well as professional chemical engineers who want to improve their ability to use mathematics to
solve common on-the-job problems.
RICHARD G. RICE, PhD, is Emeritus Professor at Louisiana State University and widely published in the areas
<if chemical separations and two-phase flow.
DUONG D. DO, PhD, is University Professor at the University of Queensland, Australia, and is well-known in
the area of adsorption science.
Cmer
Illustration:
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Subscribe to our free Engineering eNewsletter at
ISBN 17fl-l-llfl-DE47a-0
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|
| any_adam_object | 1 |
| author | Rice, Richard G. Do, Duong D. |
| author_GND | (DE-588)1028333552 (DE-588)1028334133 |
| author_facet | Rice, Richard G. Do, Duong D. |
| author_role | aut aut |
| author_sort | Rice, Richard G. |
| author_variant | r g r rg rgr d d d dd ddd |
| building | Verbundindex |
| bvnumber | BV040605939 |
| classification_rvk | SK 950 VN 7030 |
| classification_tum | CIT 001f MAT 022f CIT 009f |
| ctrlnum | (OCoLC)819367815 (DE-599)BSZ372668399 |
| dewey-full | 660.0151 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 660 - Chemical engineering |
| dewey-raw | 660.0151 |
| dewey-search | 660.0151 |
| dewey-sort | 3660.0151 |
| dewey-tens | 660 - Chemical engineering |
| discipline | Chemie / Pharmazie Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV040605939 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T02:54:50Z |
| institution | BVB |
| isbn | 9781118024720 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025433606 |
| oclc_num | 819367815 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-29T |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-29T |
| physical | XII, 383 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Wiley |
| record_format | marc |
| spellingShingle | Rice, Richard G. Do, Duong D. Applied mathematics and modeling for chemical engineers Mathematik (DE-588)4037944-9 gnd Computerunterstütztes Verfahren (DE-588)4139030-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Angewandte Mathematik (DE-588)4142443-8 gnd Simulation (DE-588)4055072-2 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd Technische Mathematik (DE-588)4827059-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4139030-1 (DE-588)4128130-5 (DE-588)4114528-8 (DE-588)4142443-8 (DE-588)4055072-2 (DE-588)4069941-9 (DE-588)4827059-3 (DE-588)4012249-9 |
| title | Applied mathematics and modeling for chemical engineers |
| title_auth | Applied mathematics and modeling for chemical engineers |
| title_exact_search | Applied mathematics and modeling for chemical engineers |
| title_full | Applied mathematics and modeling for chemical engineers Richard G. Rice ; Duong D. Do |
| title_fullStr | Applied mathematics and modeling for chemical engineers Richard G. Rice ; Duong D. Do |
| title_full_unstemmed | Applied mathematics and modeling for chemical engineers Richard G. Rice ; Duong D. Do |
| title_short | Applied mathematics and modeling for chemical engineers |
| title_sort | applied mathematics and modeling for chemical engineers |
| topic | Mathematik (DE-588)4037944-9 gnd Computerunterstütztes Verfahren (DE-588)4139030-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Angewandte Mathematik (DE-588)4142443-8 gnd Simulation (DE-588)4055072-2 gnd Chemische Verfahrenstechnik (DE-588)4069941-9 gnd Technische Mathematik (DE-588)4827059-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Mathematik Computerunterstütztes Verfahren Numerisches Verfahren Mathematisches Modell Angewandte Mathematik Simulation Chemische Verfahrenstechnik Technische Mathematik Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025433606&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025433606&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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