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Mathematics for Enzyme Reaction Kinetics and Reactor Performance
ISBN-13: 9781119490289 / Angielski / Twarda / 2020 / 1072 str.
Mathematics for Enzyme Reaction Kinetics and Reactor Performance
ISBN-13: 9781119490289 / Angielski / Twarda / 2020 / 1072 str.
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About the Author
Series Preface
Preface
Volume One
1. Basic Concepts of Algebra 2
17.1. Scalars, vectors, matrices and determinants 3
17.2. Function features 8
17.2.1. Series 20
17.2.1.1. Arithmetic series 21
17.2.1.2. Geometric series 24
17.2.1.3. Arithmetic/geometric series 28
17.2.2. Multiplication and division of polynomials 34
17.2.2.1. Product 35
17.2.2.2. Quotient 36
17.2.2.3. Factorization 41
17.2.2.4. Splitting 46
17.2.2.5. Power 57
17.2.3. Trigonometric functions 66
17.2.3.1. Definition and major features 67
17.2.3.2. Angle transformation formulae 73
17.2.3.3. Fundamental theorem of trigonometry 91
17.2.3.4. Inverse functions 99
17.2.4. Hyperbolic functions 100
17.2.4.1. Definition and major features 101
17.2.4.2. Argument transformation formulae 107
17.2.4.3. Euler s form of complex numbers 112
17.2.4.4. Inverse functions 114
17.3. Vector operations 120
17.3.1. Addition of vectors 123
17.3.2. Multiplication of scalar by vector 125
17.3.3. Scalar multiplication of vectors 128
17.3.4. Vector multiplication of vectors 140
17.4. Matrix operations 147
17.4.1. Addition of matrices 148
17.4.2. Multiplication of scalar by matrix 150
17.4.3. Multiplication of matrices 153
17.4.4. Transposal of matrices 162
17.4.5. Inversion of matrices 165
17.4.5.1. Full matrix 166
17.4.5.2. Block matrix 172
17.4.6. Combined features 175
17.4.6.1. Symmetric matrix 176
17.4.6.2. Positive semidefinite matrix 178
17.5. Tensor operations 181
17.6. Determinants 187
17.6.1. Definition 188
17.6.2. Calculation 195
17.6.2.1. Laplace s theorem 197
17.6.2.2. Major features 201
17.6.2.3. Tridiagonal matrix 221
17.6.2.4. Block matrix 223
17.6.2.5. Matrix inversion 228
17.6.3. Eigenvalues and –vectors 233
17.6.3.1. Characteristic polynomial 235
17.6.3.2. Cayley & Hamilton s theorem 239
17.7. Solution of algebraic equations250
17.7.1. Linear systems of equations 251
17.7.1.1. Jacobi s method 256
17.7.1.2. Explicitation 268
17.7.1.3. Cramer s rule 269
17.7.1.4. Matrix inversion 273
17.7.2. Quadratic equation 278
17.7.3. Lambert s W function 283
17.7.4. Numerical approaches 288
17.7.4.1. Double–initial estimate methods 289
17.7.4.2. Single–initial estimate methods 307
17.8. Further reading 326
Volume Two
1. Basic Concepts of Calculus 1
18.1. Limits, derivatives, integrals and differential equations 2
18.2. Limits and continuity 3
18.2.1. Univariate limit 4
18.2.1.1. Definition 4
18.2.1.2. Basic calculation 9
18.2.2. Multivariate limit 14
18.2.3. Basic theorems on limits 16
18.2.4. Definition of continuity 26
18.2.5. Basic theorems on continuity 29
18.2.5.1. Bolzano s theorem 30
18.2.5.2. Weierstrass theorem 35
18.3. Differentials, derivatives and partial derivatives 38
18.3.1. Differential 39
18.3.2. Derivative 43
18.3.2.1. Definition 43
18.3.2.2. Rules of differentiation of univariate functions 63
18.3.2.3. Rules of differentiation of multivariate functions 85
18.3.2.4. Implicit differentiation 86
18.3.2.5. Parametric differentiation 89
18.3.2.6. Basic theorems of differential calculus 93
18.3.2.7. Derivative of matrix 116
18.3.2.8. Derivative of determinant 123
18.3.3. Dependence between functions 127
18.3.4. Optimization of univariate continuous functions 131
18.3.4.1. Constraint–free 132
18.3.4.2. Subjected to constraints 135
18.3.5. Optimization of multivariate continuous functions 139
18.3.5.1. Constraint–free 139
18.3.5.2. Subjected to constraints 145
18.4. Integrals 146
18.4.1. Univariate integral 149
18.4.1.1. Indefinite integral 149
18.4.1.2. Definite integral 165
18.4.2. Multivariate integral 185
18.4.2.1. Definition 185
18.4.2.2. Basic theorems 191
18.4.2.3. Change of variables 200
18.4.2.4. Differentiation of integral 204
18.4.3. Optimization of single integral 207
18.4.4. Optimization of set of derivatives 217
18.5. Infinite series and integrals 222
18.5.1. Definition and criteria of convergence 223
18.5.1.1. Comparison test 225
18.5.1.2. Ratio test 226
18.5.1.3. D Alembert s test 228
18.5.1.4. Cauchy s integral test 231
18.5.1.5. Leibnitz s test 234
18.5.2. Taylor s series 237
18.5.2.1. Analytical functions 255
18.5.2.2. Euler s infinite product 293
18.5.3. Gamma function and factorial 304
18.5.3.1. Integral definition and major features 305
18.5.3.2. Euler s definition 312
18.5.3.3. Stirling s approximation 319
18.6. Analytical geometry 325
18.6.1. Straight line 326
18.6.2. Simple polygons 329
18.6.3. Conical curves 333
18.6.4. Length of line 340
18.6.5. Curvature of line 353
18.6.6. Area of plane surface 359
18.6.7. Outer area of revolution solid 367
18.6.8. Volume of revolution solid 387
18.7. Transforms 395
18.7.1. Laplace s transform 396
18.7.1.1. Definition 396
18.7.1.2. Major features 411
18.7.1.3. Inversion 427
18.7.2. Legendre s transform 438
18.8. Solution of differential equations 447
18.8.1. Ordinary differential equations 448
18.8.1.1. Single first order 449
18.8.1.2. Single second order 456
18.8.1.3. Linear higher order 522
18.8.2. Partial differential equations 535
18.9. Vector calculus 543
18.9.1. Rectangular coordinates 544
18.9.1.1. Definition and representation 544
18.9.1.2. Definition of nabla operator, Ñ 546
18.9.1.3. Algebraic properties of Ñ 553
18.9.1.4. Multiple products involving Ñ 556
18.9.2. Cylindrical coordinates 588
18.9.2.1. Definition and representation 588
18.9.1.2. Redefinition of nabla operator, Ñ 594
18.9.3. Spherical coordinates 601
18.9.3.1. Definition and representation 601
18.9.3.2. Redefinition of nabla operator, Ñ 615
18.9.4. Curvature of three–dimensional surface 636
18.9.5. Three–dimensional integration 646
18.10. Numerical approaches to integration 650
18.10.1. Calculation of definite integrals 651
18.10.1.1. Zero–th order interpolation 653
18.10.1.2. First and second order interpolation 664
18.10.1.3. Composite methods 693
18.10.1.4. Infinite and multidimensional integrals 699
18.10.2. Integration of differential equations 702
18.10.2.1. Single–step methods 705
18.10.2.2. Multiple–step methods 709
18.10.2.3. Multiple–stage methods 718
18.10.2.4. Integral versus differential equation 734
18.11. Further reading
3. Basic Concepts of Statistics 1
19.1. Continuous probability functions2
19.1.1. Basic statistical descriptors 4
19.1.2. Normal distribution 12
19.1.2.1. Derivation 13
19.1.2.2. Justification 20
19.1.2.3. Operational features 27
19.1.2.4. Moment–generating function 31
19.1.2.5. Standard probability density function 48
19.1.2.6. Central limit theorem 52
19.1.2.7. Standard probability cumulative function 64
19.1.3. Other relevant distributions 68
19.1.3.1. Lognormal distribution 69
19.1.3.2. Chi–square distribution 78
19.1.3.3. Student s t–distribution 94
19.1.3.4. Fisher s F–distribution 112
19.2. Statistical hypothesis testing 147
19.3. Linear regression 156
19.3.1. Parameter fitting 158
19.3.2. Residual characterization 162
19.3.3. Parameter inference 166
19.3.3.1. Multivariate models 166
19.3.3.2. Univariate models 171
19.3.4. Unbiased estimation 175
19.3.4.1. Multivariate models 175
19.3.4.2. Univariate models 179
19.3.5. Prediction inference 189
19.3.6. Multivariate correction 192
19.4. Further reading 207
F. Xavier Malcata, PhD, is Full Professor at in the Department of Chemical Engineering at the University of Porto in Portugal, and Researcher at LEPABE Laboratory for Process Engineering, Environment, Biotechnology and Energy. He is the author of more than 400 highly cited journal papers, eleven books, four edited books, and fifty chapters in edited books. He has been awarded the Elmer Marth Educator Award by the International Association of Food Protection (USA), and the William V. Cruess Award for excellence in teaching by the Institute of Food Technologists (USA).
This two volume set details the mathematical background required for systematic and rational simulation of both enzyme reaction kinetics and enzyme reactor performance (and related areas)
Mathematics for Enzyme Reaction Kinetics and Reactor Performance is the first set in a unique 11 volume–collection on Enzyme Reaction Engineering. This two volume–set relates specifically to the wide mathematical background required for systematic and rational simulation of both reaction kinetics and reactor performance; and to fully understand and capitalize on the modelling concepts developed. It accordingly reviews basic and useful concepts of Algebra (first volume), and Calculus and Statistics (second volume).
A brief overview of such native algebraic entities as scalars, vectors, matrices and determinants constitutes the starting point of the first volume; the major features of germane functions are then addressed. Vector operations ensue, followed by calculation of determinants. Finally, exact methods for solution of selected algebraic equations including sets of linear equations, are considered, as well as numerical methods for utilization at large.
The second volume begins with an introduction to basic concepts in calculus, i.e. limits, derivatives, integrals and differential equations; limits, along with continuity, are further expanded afterwards, covering uni– and multivariate cases, as well as classical theorems. After recovering the concept of differential and applying it to generate (regular and partial) derivatives, the most important rules of differentiation of functions, in explicit, implicit and parametric form, are retrieved together with the nuclear theorems supporting simpler manipulation thereof. The book then tackles strategies to optimize uni– and multivariate functions, before addressing integrals in both indefinite and definite forms. Next, the book touches on the methods of solution of differential equations for practical applications, followed by analytical geometry and vector calculus. Brief coverage of statistics including continuous probability functions, statistical descriptors and statistical hypothesis testing, brings the second volume to a close.
SERIES INFORMATION
Enzyme Reactor Engineering is organized into four major sets: Enzyme Reaction Kinetics and Reactor Performance; Analysis of Enzyme Reaction Kinetics; Analysis of Enzyme Reactor Performance; and Mathematics for Enzyme Reaction Kinetics and Reactor Performance. In particular, Enzyme Reaction Kinetics and Reactor Performance provides an overview of the behavior of both biocatalyst and bioreactor, including biochemical relevance and industrial applications. Analysis of Enzyme Reaction Kinetics covers analysis of rate expressions and effects of processing conditions upon enzyme reactions. Analysis of Enzyme Reactor Performance looks at analysis of reactor design and performance using enzymes as catalysts, departing from the simplest cases of ideal (single and multiple) reactors, and expanding toward nonideal hydrodynamic patterns and multiphasic systems. Mathematics for Enzyme Reaction Kinetics and Reactor Performance finally examines mathematical background from trivial to advanced mathematical concepts of algebra, calculus and statistics, useful for all aforementioned analyses.
- Presents true engineering aspects departing from first principles, and systematically emphasizes their rationale
- Pays special attention to stepwise derivation of the underlying equations
- Offers an unparalleled way of viewing enzyme reactors, by focusing on the reactor component
- Features a selection of mathematical tools, suitable for modeling at large and for simulation specifically of enzyme reactions and reactors
- Includes selected papers, chapters, and books recommended for more in–depth, complementary reading
Mathematics for Enzyme Reaction Kinetics and Reactor Performance is an excellent reference book for students in the fields of chemical, biological and biochemical engineering, and will appeal to all those interested in the fascinating area of white biotechnology.
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