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Mathematics for Enzyme Reaction Kinetics and Reactor Performance


Mathematics for Enzyme Reaction Kinetics and Reactor Performance


Enzyme Reaction Engineering 1. Aufl.

von: F. Xavier Malcata

254,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 30.04.2020
ISBN/EAN: 9781119490326
Sprache: englisch
Anzahl Seiten: 1072

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Beschreibungen

<p><i>Mathematics for Enzyme Reaction Kinetics and Reactor Performance</i> is the first set in a unique 11 volume-collection on <i>Enzyme Reactor Engineering</i>. 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.</p> <p>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.</p>
<p>About the Author xv</p> <p>Series Preface xix</p> <p>Preface xxiii</p> <p><b>Volume 1</b></p> <p><b>Part 1 Basic Concepts of Algebra 1</b></p> <p><b>1 Scalars, Vectors, Matrices, and Determinants 3</b></p> <p><b>2 Function Features 7</b></p> <p>2.1 Series 17</p> <p>2.1.1 Arithmetic Series 17</p> <p>2.1.2 Geometric Series 19</p> <p>2.1.3 Arithmetic/Geometric Series 22</p> <p>2.2 Multiplication and Division of Polynomials 26</p> <p>2.2.1 Product 27</p> <p>2.2.2 Quotient 28</p> <p>2.2.3 Factorization 31</p> <p>2.2.4 Splitting 35</p> <p>2.2.5 Power 43</p> <p>2.3 Trigonometric Functions 52</p> <p>2.3.1 Definition and Major Features 52</p> <p>2.3.2 Angle Transformation Formulae 57</p> <p>2.3.3 Fundamental Theorem of Trigonometry 73</p> <p>2.3.4 Inverse Functions 79</p> <p>2.4 Hyperbolic Functions 80</p> <p>2.4.1 Definition and Major Features 80</p> <p>2.4.2 Argument Transformation Formulae 85</p> <p>2.4.3 Euler’s Form of Complex Numbers 89</p> <p>2.4.4 Inverse Functions 90</p> <p><b>3 Vector Operations 97</b></p> <p>3.1 Addition of Vectors 99</p> <p>3.2 Multiplication of Scalar by Vector 101</p> <p>3.3 Scalar Multiplication of Vectors 103</p> <p>3.4 Vector Multiplication of Vectors 111</p> <p><b>4 Matrix Operations 119</b></p> <p>4.1 Addition of Matrices 120</p> <p>4.2 Multiplication of Scalar by Matrix 121</p> <p>4.3 Multiplication of Matrices 124</p> <p>4.4 Transposal of Matrices 131</p> <p>4.5 Inversion of Matrices 133</p> <p>4.5.1 Full Matrix 134</p> <p>4.5.2 Block Matrix 138</p> <p>4.6 Combined Features 140</p> <p>4.6.1 Symmetric Matrix 141</p> <p>4.6.2 Positive Semidefinite Matrix 142</p> <p><b>5 Tensor Operations 145</b></p> <p><b>6 Determinants 151</b></p> <p>6.1 Definition 152</p> <p>6.2 Calculation 157</p> <p>6.2.1 Laplace’s Theorem 159</p> <p>6.2.2 Major Features 161</p> <p>6.2.3 Tridiagonal Matrix 177</p> <p>6.2.4 Block Matrix 179</p> <p>6.2.5 Matrix Inversion 181</p> <p>6.3 Eigenvalues and Eigenvectors 185</p> <p>6.3.1 Characteristic Polynomial 186</p> <p>6.3.2 Cayley–Hamilton’s Theorem 190</p> <p><b>7 Solution of Algebraic Equations 199</b></p> <p>7.1 Linear Systems of Equations 199</p> <p>7.1.1 Jacobi’s Method 203</p> <p>7.1.2 Explicitation 212</p> <p>7.1.3 Cramer’s Rule 213</p> <p>7.1.4 Matrix Inversion 216</p> <p>7.2 Quadratic Equation 220</p> <p>7.3 Lambert’s <i>W</i> Function 224</p> <p>7.4 Numerical Approaches 228</p> <p>7.4.1 Double-initial Estimate Methods 229</p> <p>7.4.1.1 Bisection 229</p> <p>7.4.1.2 Linear Interpolation 232</p> <p>7.4.2 Single-initial Estimate Methods 242</p> <p>7.4.2.1 Newton and Raphson’s Method 242</p> <p>7.4.2.2 Direct Iteration 250</p> <p>Further Reading 255</p> <p><b>Volume 2</b></p> <p><b>Part 2 Basic Concepts of Calculus 259</b></p> <p><b>8 Limits, Derivatives, Integrals, and Differential Equations 261</b></p> <p><b>9 Limits and Continuity 263</b></p> <p>9.1 Univariate Limit 263</p> <p>9.1.1 Definition 263</p> <p>9.1.2 Basic Calculation 267</p> <p>9.2 Multivariate Limit 271</p> <p>9.3 Basic Theorems on Limits 272</p> <p>9.4 Definition of Continuity 280</p> <p>9.5 Basic Theorems on Continuity 282</p> <p>9.5.1 Bolzano’s Theorem 282</p> <p>9.5.2 Weierstrass’ Theorem 286</p> <p><b>10 Differentials, Derivatives, and Partial Derivatives 291</b></p> <p>10.1 Differential 291</p> <p>10.2 Derivative 294</p> <p>10.2.1 Definition 294</p> <p>10.2.1.1 Total Derivative 295</p> <p>10.2.1.2 Partial Derivatives 300</p> <p>10.2.1.3 Directional Derivatives 307</p> <p>10.2.2 Rules of Differentiation of Univariate Functions 308</p> <p>10.2.3 Rules of Differentiation of Multivariate Functions 325</p> <p>10.2.4 Implicit Differentiation 325</p> <p>10.2.5 Parametric Differentiation 327</p> <p>10.2.6 Basic Theorems of Differential Calculus 331</p> <p>10.2.6.1 Rolle’s Theorem 331</p> <p>10.2.6.2 Lagrange’s Theorem 332</p> <p>10.2.6.3 Cauchy’s Theorem 334</p> <p>10.2.6.4 L’Hôpital’s Rule 337</p> <p>10.2.7 Derivative of Matrix 349</p> <p>10.2.8 Derivative of Determinant 356</p> <p>10.3 Dependence Between Functions 358</p> <p>10.4 Optimization of Univariate Continuous Functions 362</p> <p>10.4.1 Constraint-free 362</p> <p>10.4.2 Subjected to Constraints 364</p> <p>10.5 Optimization of Multivariate Continuous Functions 367</p> <p>10.5.1 Constraint-free 367</p> <p>10.5.2 Subjected to Constraints 371</p> <p><b>11 Integrals 373</b></p> <p>11.1 Univariate Integral 374</p> <p>11.1.1 Indefinite Integral 374</p> <p>11.1.1.1 Definition 374</p> <p>11.1.1.2 Rules of Integration 377</p> <p>11.1.2 Definite Integral 386</p> <p>11.1.2.1 Definition 386</p> <p>11.1.2.2 Basic Theorems of Integral Calculus 393</p> <p>11.1.2.3 Reduction Formulae 396</p> <p>11.2 Multivariate Integral 400</p> <p>11.2.1 Definition 400</p> <p>11.2.1.1 Line Integral 400</p> <p>11.2.1.2 Double Integral 403</p> <p>11.2.2 Basic Theorems 404</p> <p>11.2.2.1 Fubini’s Theorem 404</p> <p>11.2.2.2 Green’s Theorem 409</p> <p>11.2.3 Change of Variables 411</p> <p>11.2.4 Differentiation of Integral 414</p> <p>11.3 Optimization of Single Integral 416</p> <p>11.4 Optimization of Set of Derivatives 424</p> <p><b>12 Infinite Series and Integrals 429</b></p> <p>12.1 Definition and Criteria of Convergence 429</p> <p>12.1.1 Comparison Test 430</p> <p>12.1.2 Ratio Test 431</p> <p>12.1.3 D’Alembert’s Test 432</p> <p>12.1.4 Cauchy’s Integral Test 434</p> <p>12.1.5 Leibnitz’s Test 436</p> <p>12.2 Taylor’s Series 437</p> <p>12.2.1 Analytical Functions 451</p> <p>12.2.1.1 Exponential Function 451</p> <p>12.2.1.2 Hyperbolic Functions 458</p> <p>12.2.1.3 Logarithmic Function 459</p> <p>12.2.1.4 Trigonometric Functions 463</p> <p>12.2.1.5 Inverse Trigonometric Functions 466</p> <p>12.2.1.6 Powers of Binomials 476</p> <p>12.2.2 Euler’s Infinite Product 479</p> <p>12.3 Gamma Function and Factorial 488</p> <p>12.3.1 Integral Definition and Major Features 489</p> <p>12.3.2 Euler’s Definition 494</p> <p>12.3.3 Stirling’s Approximation 499</p> <p><b>13 Analytical Geometry 505</b></p> <p>13.1 Straight Line 505</p> <p>13.2 Simple Polygons 508</p> <p>13.3 Conical Curves 510</p> <p>13.4 Length of Line 516</p> <p>13.5 Curvature of Line 525</p> <p>13.6 Area of Plane Surface 530</p> <p>13.7 Outer Area of Revolution Solid 536</p> <p>13.8 Volume of Revolution Solid 552</p> <p><b>14 Transforms 559</b></p> <p>14.1 Laplace’s Transform 559</p> <p>14.1.1 Definition 559</p> <p>14.1.2 Major Features 571</p> <p>14.1.3 Inversion 583</p> <p>14.2 Legendre’s Transform 590</p> <p><b>15 Solution of Differential Equations 597</b></p> <p>15.1 Ordinary Differential Equations 597</p> <p>15.1.1 First Order 598</p> <p>15.1.1.1 Nonlinear 598</p> <p>15.1.1.2 Linear 600</p> <p>15.1.2 Second Order 602</p> <p>15.1.2.1 Nonlinear 603</p> <p>15.1.2.2 Linear 613</p> <p>15.1.3 Linear Higher Order 650</p> <p>15.2 Partial Differential Equations 660</p> <p><b>16 Vector Calculus 667</b></p> <p>16.1 Rectangular Coordinates 667</p> <p>16.1.1 Definition and Representation 667</p> <p>16.1.2 Definition of Nabla Operator, ∇ 668</p> <p>16.1.3 Algebraic Properties of ∇ 673</p> <p>16.1.4 Multiple Products Involving ∇ 676</p> <p>16.1.4.1 Calculation of (∇.∇)<i>ϕ </i>676</p> <p>16.1.4.2 Calculation of (∇.∇)<i>u</i> 676</p> <p>16.1.4.3 Calculation of ∇.(<i>ϕ</i><i>u</i>) 677           </p> <p>16.1.4.4 Calculation of ∇.(∇ × <i>u</i>) 679</p> <p>16.1.4.5 Calculation of ∇.(<i>ϕ</i>∇<i>&psi;</i>) 680</p> <p>16.1.4.6 Calculation of ∇.(<i>uu</i>) 682</p> <p>16.1.4.7 Calculation of ∇ × (∇ <i>ϕ</i>) 684</p> <p>16.1.4.8 Calculation of ∇(∇.<i>u</i>) 685</p> <p>16.1.4.9 Calculation of (<i>u</i>.∇)<i>u</i> 690</p> <p>16.1.4.10 Calculation of ∇.(<i>τ.</i><i>u</i>) 693</p> <p>16.2 Cylindrical Coordinates 695</p> <p>16.2.1 Definition and Representation 695</p> <p>16.2.2 Redefinition of Nabla Operator, ∇ 700</p> <p>16.3 Spherical Coordinates 705</p> <p>16.3.1 Definition and Representation 705</p> <p>16.3.2 Redefinition of Nabla Operator, ∇ 715</p> <p>16.4 Curvature of Three-dimensional Surfaces 729</p> <p>16.5 Three-dimensional Integration 737</p> <p><b>17 Numerical Approaches to Integration 741</b></p> <p>17.1 Calculation of Definite Integrals 741</p> <p>17.1.1 Zeroth Order Interpolation 743</p> <p>17.1.2 First- and Second-Order Interpolation 750</p> <p>17.1.2.1 Trapezoidal Rule 751</p> <p>17.1.2.2 Simpson’s Rule 754</p> <p>17.1.2.3 Higher Order Interpolation 768</p> <p>17.1.3 Composite Methods 771</p> <p>17.1.4 Infinite and Multidimensional Integrals 775</p> <p>17.2 Integration of Differential Equations 777</p> <p>17.2.1 Single-step Methods 779</p> <p>17.2.2 Multistep Methods 782</p> <p>17.2.3 Multistage Methods 790</p> <p>17.2.3.1 First Order 790</p> <p>17.2.3.2 Second Order 790</p> <p>17.2.3.3 General Order 793</p> <p>17.2.4 Integral Versus Differential Equation 801</p> <p><b>Part 3 Basic Concepts of Statistics 807</b></p> <p><b>18 Continuous Probability Functions 809</b></p> <p>18.1 Basic Statistical Descriptors 810</p> <p>18.2 Normal Distribution 815</p> <p>18.2.1 Derivation 816</p> <p>18.2.2 Justification 821</p> <p>18.2.3 Operational Features 826</p> <p>18.2.4 Moment-generating Function 829</p> <p>18.2.4.1 Single Variable 829</p> <p>18.2.4.2 Multiple Variables 835</p> <p>18.2.5 Standard Probability Density Function 842</p> <p>18.2.6 Central Limit Theorem 845</p> <p>18.2.7 Standard Probability Cumulative Function 855</p> <p>18.3 Other Relevant Distributions 858</p> <p>18.3.1 Lognormal Distribution 858</p> <p>18.3.1.1 Probability Density Function 858</p> <p>18.3.1.2 Mean and Variance 859</p> <p>18.3.1.3 Probability Cumulative Function 862</p> <p>18.3.1.4 Mode and Median 863</p> <p>18.3.2 Chi-square Distribution 865</p> <p>18.3.2.1 Probability Density Function 865</p> <p>18.3.2.2 Mean and Variance 869</p> <p>18.3.2.3 Asymptotic Behavior 870</p> <p>18.3.2.4 Probability Cumulative Function 872</p> <p>18.3.2.5 Mode and Median 873</p> <p>18.3.2.6 Other Features 874</p> <p>18.3.3 Student’s <i>t</i>-distribution 876</p> <p>18.3.3.1 Probability Density Function 876</p> <p>18.3.3.2 Mean and Variance 879</p> <p>18.3.3.3 Asymptotic Behavior 883</p> <p>18.3.3.4 Probability Cumulative Function 886</p> <p>18.3.3.5 Mode and Median 887</p> <p>18.3.4 Fisher’s <i>F</i>-distribution 888</p> <p>18.3.4.1 Probability Density Function 888</p> <p>18.3.4.2 Mean and Variance 893</p> <p>18.3.4.3 Asymptotic Behavior 896</p> <p>18.3.4.4 Probability Cumulative Function 899</p> <p>18.3.4.5 Mode and Median 902</p> <p>18.3.4.6 Other Features 903</p> <p><b>19 Statistical Hypothesis Testing 915</b></p> <p><b>20 Linear Regression 923</b></p> <p>20.1 Parameter Fitting 924</p> <p>20.2 Residual Characterization 927</p> <p>20.3 Parameter Inference 931</p> <p>20.3.1 Multivariate Models 931</p> <p>20.3.2 Univariate Models 934</p> <p>20.4 Unbiased Estimation 937</p> <p>20.4.1 Multivariate Models 937</p> <p>20.4.2 Univariate Models 940</p> <p>20.5 Prediction Inference 949</p> <p>20.6 Multivariate Correction 951</p> <p>Further Reading 963</p>
<p><b>F. Xavier Malcata, PhD,</b> 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).
<p><b>This two volume set details the mathematical background required for systematic and rational simulation of both enzyme reaction kinetics and enzyme reactor performance</b> <p><i>Mathematics for Enzyme Reaction Kinetics and Reactor Performance</i> is the first set in a unique 11 volume collection on <i>Enzyme Reactor Engineering,</i> and 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). <p>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. <p>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 multi–variate 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. <p><i>Mathematics for Enzyme Reaction Kinetics and Reactor Performance</i> 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. <p><b>SERIES INFORMATION</b> <p><i>Enzyme Reactor Engineering</i> is organized into four major sets: <i>Enzyme Reaction Kinetics and Reactor Performance</i>; <i>Analysis of Enzyme Reaction Kinetics</i>; <i>Analysis of Enzyme Reactor Performance</i>; and <i>Mathematics for Enzyme Reaction Kinetics and Reactor Performance</i>.

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