Kooperativer Bibliotheksverbund

UID:

Format: 1 online resource (204 p.)

ISBN: 1-283-52648-4 , 9786613838933 , 0-08-095779-X

Series Statement: Mathematics in science and engineering

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Note: Description based upon print version of record. , Front Cover; The Optimal Design of Chemical Reactors; Copyright Page; Preface; Contents; Chapter 1. Introduction; 1.1. The Principle of Optimality; 1.2. Review of Cognate Work; 1.3. The Scope of the Present Monograph; Chapter 2. The Principal Notions of Dynamic Programming; 2.1. Multistage Decision Processes and the Principle of Optimality; 2.2. The Discrete Deterministic Process; 2.3. The Discrete Stochastic Process; 2.4. The Continuous Deterministic Process; 2.5. The Dynamic Programming Approach to the Calculus of Variations; 2.6. The Use and Interpretation of the Lagrange MuItiplier , Chapter 3. Mathematical Models for Reactor Design3.1. Systems of Chemical Reactions; 3.2. The Continuous Flow Stirred Tank Reactor; 3.3. The Multibed Adiabatic Reactor; 3.4. The Tubular Reactor; 3.5. The Stirred Tank Sequence as a Model for the Tubular Reactor; 3.6. The Batch Reactor; 3.7. Cooling; Chapter 4. The Objective Function; 4.1. Stoichiometric Objective Functions; 4.2. Material Objective Functions; 4.3. Objective Functions with Operating Costs; 4.4. An Example of Cost Estimation; 4.5. The Relation of the Objective Function to the Optimal Problem , Chapter 5. The Continuous Flow Stirred Tank Reactor5.1. The Disjoint Character of the Optimal Temperature Policy with a Single Reaction; 5.2. The Sequence of Reactors of Equal Size; 5.3. The Optimal Choice of Temperature and Holding Time with a Single Reaction; 5.4. Parametric Studies; 5.5. Two Consecutive Reactions; 5.6. Denbigh's System of Reactions; 5.7. General Problems with Sequences of Stirred Tanks; 5.8. Sequences of Stirred Tanks with Bypassing of the Feed Stream; 5.9. The Adiabatic Sequence of Reactors with a Single Reaction; Chapter 6. The Multibed Adiabatic Reactor , 6.1. Interchanger Cooling with a Single Reaction6.2. Extended Results of the Simple Model; 6.3. Interchanger Cooling with Simultaneous Reactions; 6.4. Cold Shot Cooling with a Single Reaction; 6.5. Cold Shot Cooling with Simultaneous Reactions; 6.6. Cooling bay an Alien Cold Shot; 6.7. The Removal of Sundry Approximations; Chapter 7. The Tubular Reactor; 7.1. Optimal Temperature Policy with a Single Reaction; 7.2. Alternative Forms of the Optimal Problem with a Single Reaction; 7.3. Two Consecutive Reactions; 7.4. Two Simultaneous Reactions in General; 7.5. The General Problem , Chapter 8. Stochastic Problems8.1. Optimal Replication of Processes Subject to Failure; 8.2. Stochastic Gold Making; 8.3. Optimal Catalyst Replacement Policies; Chapter 9. The Optimal Operation of Existing Reactors; 9.1. The Stirred Tank Reactor Sequence; 9.2. The Multibed Adiabatic Reactor; 9.3. Control with a Decaying Catalyst; 9.4. The Optimal Control of a Batch Reactor; 9.5. Further Problems in Batch Reactor Control; References; Index , English

Additional Edition: ISBN 0-12-374916-6

Language: English

UID:

Format: 1 online resource (455 p.)

ISBN: 1-283-52557-7 , 9786613838025 , 0-08-095557-6

Series Statement: Mathematics in science and engineering

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Note: Description based upon print version of record. , Front Cover; Differential Geometry and the Calculus of Variations; Copyright Page; Contents; Preface; Part 1: Differential and Integral Calculus on Manifolds; Chapter 1. Introduction; Chapter 2. Tangent Vector-Vector Field Formalism; Chapter 3. Differential Forms; Chapter 4. Specialization to Euclidean Spaces: Differential Manifolds; Chapter 5. Mappings, Submanifolds, and the Implicit Function Theorem; Chapter 6. The Jacobi Bracket and the Lie Theory of Ordinary Differential Equations; Chapter 7. Lie Derivation and Exterior Derivative; Integration on Manifolds , Chapter 8. The Frobenius Complete Integrability TheoremChapter 9. Reduction of Dimension When a Lie Algebra of Vector Fields Leaves a Vector-Field Invariant; Chapter 10. Lie Groups; Chapter 11. Classical Mechanics of Particles and Continua; Part 2: The Hamilton-Jacobi Theory and Calculus of Variations; Chapter 12. Differential Forms and Variational Problems; Chapter 13. Hamilton-Jacobi Theory; Chapter 14. Extremal Fields and Sufficient Conditions for a Minimum; Chapter 15. The Ordinary Problems of the Calculus of Variations , Chapter 16. Groups of Symmetries of Variational Problems: Applications to MechanicsChapter 17. Elliptic Functions; Chapter 18. Accessibility Problems for Path Systems; Part 3: Global Riemannian Geometry; Chapter 19. Affine Connections on Differential Manifolds; Chapter 20. The Riemannian Affine Connection and the First Variation Formula; Chapter 21. The Hopf-Rinow Theorem; Applications to the Theory of Covering Spaces; Chapter 22. The Second Variation Formula and Jacobi Vector Fields; Chapter 23. Sectional Curvature and the Elementary Comparison Theorems , Chapter 24. Submanifolds of Riemannian ManifoldsChapter 25. Groups of Isometries; Chapter 26. Deformation of Submanifolds in Riemannian Spaces; Part 4: Differential Geometry and the Calculus of Variations: Additional Topics in Differential Geometry; Chapter 27. First-Order Invariants of Submanifolds and Convexity for Affinely Connected Manifolds; Chapter 28. Affine Groups of Automorphisms. Induced Connections on Submanifolds. Projective Changes of Connection; Chapter 29. The Laplace-Beltrami Operator; Chapter 30. Characteristics and Shock Waves; Chapter 31. The Morse Index Theorem , Chapter 32. Complex Manifolds and Their SubmanifoldsChapter 33. Mechanics on Riemannian Manifolds; Bibliography; Subject Index; Mathematics in Science and Engineering , English

Additional Edition: ISBN 0-12-342150-0

Language: English

UID:

Format: 1 online resource (239 p.)

ISBN: 1-283-52567-4 , 9786613838124 , 0-08-095556-8

Series Statement: Mathematics in science and engineering

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Note: Description based upon print version of record. , Front Cover; Comparison and Oscillation Theory of Linear Differential Equations; Copyright Page; Contents; Preface; Chapter 1. Sturm-Type Theorems for Second Order Ordinary Equations; 1. Comparison Theorems for Self-Adjoint Equations; 2. Additional Results of Leighton; 3. Extension to General Second Order Equations; 4. Comparison Theorems for Singular Equations; 5. Comparison Theorems for Eigenfunctions; 6. Reid's Comparison Theorems on Focal Points; 7. Levin's Comparison Theorems; 8. The Order of Zeros; Chapter 2. Oscillation and Nonoscillation Theorems for Second Order Ordinary Equations , 1. The Oscillation Criteria of Hille and Nehari2. Conditionally Oscillatory Equations; 3. Nehari's Comparison Theorems; 4. The Hille-Wintner Comparison Theorem; 5. Hille's Necessary and Sufficient Conditions for Nonoscillatory Equations; 6. Leighton's Oscillation Criteria; 7. Potter's Oscillation Criteria; 8. Hille's Kneser-Type Oscillation Criteria; 9. Nonoscillation Theorems of Hartman and Wintner; 10. Asymptotic Estimates for the Number of Zeros of a Solution of (1.1) or (2.1); 11. Nonoscillation Criteria for Hill's Equation; 12. Nonoscillation Criteria for Complex Equations , Chapter 3. Fourth Order Ordinary Equations1. Introduction; 2. Separation Theorems; 3. Comparison Theorems for (3.2) and (3.3); 4. Comparison Theorems for Other Fourth Order Equations; 5. Comparison Theorems for Eigenfunctions; 6. Nonoscillation Theorems; 7. Leighton and Nehari's Sufficient Conditions for Nonoscillatory Equations; 8. Comparison Theorems for Nonoscillation; 9. Howard's Comparison Theorems for Eigenvalue Problems; Chapter 4. Third Order Ordinary Equations, nth Order Ordinary Equations and Systems; 1. Introduction; 2. Separation Theorems for Third Order Equations , 3. Comparison Theorems for Third Order Equations4. Oscillation Criteria for Third Order Equations; 5. Separation and Comparison Theorems for nth Order Equations; 6. General Oscillation Theorems; 7. Nonoscillation Theorems for Systems of Differential Equations; 8. Whyburn's Second Order System; Chapter 5. Partial Differential Equations; 1. Introduction; 2. Comparison Theorems for Self-Adjoint Equations in Bounded Domains; 3. Comparison Theorems for General Second Order Elliptic Equations; 4. Comparison Theorems on Unbounded Domains; 5. Extension to Complex-Valued Solutions and Subsolutions , 6. Lower Bounds for Eigenvalues7. Oscillation Theorems; 8. Comparison Theorems for Eigenfunctions; Bibliography; Author Index; Subject Index; Mathematics in Science and Engineering , English

Additional Edition: ISBN 0-12-678950-9

Language: English

UID:

Format: 1 online resource (129 p.)

ISBN: 1-283-52604-2 , 9786613838490 , 0-08-095778-1

Series Statement: Mathematics in science and engineering

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Note: Description based upon print version of record. , Front Cover; Concepts From Tensor Analysis and Differential Geometry; Copyright Page; Contents; Preface; Chapter 1. Coordinate Manifolds; Chapter 2. Scalars; Chapter 3. Vectors and Tensors; Chapter 4. A Special Skew-symmetric Tensor; Chapter 5. The Vector Product. Curl of a Vector; Chapter 6. Riemann Spaces; Chapter 7. Affinely Connected Spaces; Chapter 8. Normal Coordinates; Chapter 9. General Theory of Extension; Chapter 10. Absolute Differentiation; Chapter 11. Differential Invariants; Chapter 12. Transformation Groups; Chapter 13. Euclidean Metric Space , Chapter 14. Homogeneous and Isotropic TensorsChapter 15. Curves in Space. Frenet Formulae; Chapter 16. Surfaces in Space; Chapter 17. Mixed Surface and Space Tensors. Coordinate Extension and Absolute Differentiation; Chapter 18. Formulae of Gauss and Weingarten; Chapter 19. Gaussian and Mean Curvature of a Surface; Chapter 20. Equations of Gauss and Codazzi; Chapter 21. Principal Curvatures and Principal Directions; Chapter 22. Asymptotic Lines; Chapter 23. Orthogonal Ennuples and Normal Congruences; Chapter 24. Families of Parallel Surfaces , Chapter 25. Developable Surfaces. Minimal SurfacesGeneral References; Subject Index , English

Additional Edition: ISBN 0-12-374915-8

Language: English

UID:

Format: 1 online resource (239 p.)

ISBN: 1-283-52567-4 , 9786613838124 , 0-08-095556-8

Series Statement: Mathematics in science and engineering

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Note: Description based upon print version of record. , Front Cover; Comparison and Oscillation Theory of Linear Differential Equations; Copyright Page; Contents; Preface; Chapter 1. Sturm-Type Theorems for Second Order Ordinary Equations; 1. Comparison Theorems for Self-Adjoint Equations; 2. Additional Results of Leighton; 3. Extension to General Second Order Equations; 4. Comparison Theorems for Singular Equations; 5. Comparison Theorems for Eigenfunctions; 6. Reid's Comparison Theorems on Focal Points; 7. Levin's Comparison Theorems; 8. The Order of Zeros; Chapter 2. Oscillation and Nonoscillation Theorems for Second Order Ordinary Equations , 1. The Oscillation Criteria of Hille and Nehari2. Conditionally Oscillatory Equations; 3. Nehari's Comparison Theorems; 4. The Hille-Wintner Comparison Theorem; 5. Hille's Necessary and Sufficient Conditions for Nonoscillatory Equations; 6. Leighton's Oscillation Criteria; 7. Potter's Oscillation Criteria; 8. Hille's Kneser-Type Oscillation Criteria; 9. Nonoscillation Theorems of Hartman and Wintner; 10. Asymptotic Estimates for the Number of Zeros of a Solution of (1.1) or (2.1); 11. Nonoscillation Criteria for Hill's Equation; 12. Nonoscillation Criteria for Complex Equations , Chapter 3. Fourth Order Ordinary Equations1. Introduction; 2. Separation Theorems; 3. Comparison Theorems for (3.2) and (3.3); 4. Comparison Theorems for Other Fourth Order Equations; 5. Comparison Theorems for Eigenfunctions; 6. Nonoscillation Theorems; 7. Leighton and Nehari's Sufficient Conditions for Nonoscillatory Equations; 8. Comparison Theorems for Nonoscillation; 9. Howard's Comparison Theorems for Eigenvalue Problems; Chapter 4. Third Order Ordinary Equations, nth Order Ordinary Equations and Systems; 1. Introduction; 2. Separation Theorems for Third Order Equations , 3. Comparison Theorems for Third Order Equations4. Oscillation Criteria for Third Order Equations; 5. Separation and Comparison Theorems for nth Order Equations; 6. General Oscillation Theorems; 7. Nonoscillation Theorems for Systems of Differential Equations; 8. Whyburn's Second Order System; Chapter 5. Partial Differential Equations; 1. Introduction; 2. Comparison Theorems for Self-Adjoint Equations in Bounded Domains; 3. Comparison Theorems for General Second Order Elliptic Equations; 4. Comparison Theorems on Unbounded Domains; 5. Extension to Complex-Valued Solutions and Subsolutions , 6. Lower Bounds for Eigenvalues7. Oscillation Theorems; 8. Comparison Theorems for Eigenfunctions; Bibliography; Author Index; Subject Index; Mathematics in Science and Engineering , English

Additional Edition: ISBN 0-12-678950-9

Language: English

UID:

Format: 1 online resource (239 p.)

ISBN: 1-283-52567-4 , 9786613838124 , 0-08-095556-8

Series Statement: Mathematics in science and engineering

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Note: Description based upon print version of record. , Front Cover; Comparison and Oscillation Theory of Linear Differential Equations; Copyright Page; Contents; Preface; Chapter 1. Sturm-Type Theorems for Second Order Ordinary Equations; 1. Comparison Theorems for Self-Adjoint Equations; 2. Additional Results of Leighton; 3. Extension to General Second Order Equations; 4. Comparison Theorems for Singular Equations; 5. Comparison Theorems for Eigenfunctions; 6. Reid's Comparison Theorems on Focal Points; 7. Levin's Comparison Theorems; 8. The Order of Zeros; Chapter 2. Oscillation and Nonoscillation Theorems for Second Order Ordinary Equations , 1. The Oscillation Criteria of Hille and Nehari2. Conditionally Oscillatory Equations; 3. Nehari's Comparison Theorems; 4. The Hille-Wintner Comparison Theorem; 5. Hille's Necessary and Sufficient Conditions for Nonoscillatory Equations; 6. Leighton's Oscillation Criteria; 7. Potter's Oscillation Criteria; 8. Hille's Kneser-Type Oscillation Criteria; 9. Nonoscillation Theorems of Hartman and Wintner; 10. Asymptotic Estimates for the Number of Zeros of a Solution of (1.1) or (2.1); 11. Nonoscillation Criteria for Hill's Equation; 12. Nonoscillation Criteria for Complex Equations , Chapter 3. Fourth Order Ordinary Equations1. Introduction; 2. Separation Theorems; 3. Comparison Theorems for (3.2) and (3.3); 4. Comparison Theorems for Other Fourth Order Equations; 5. Comparison Theorems for Eigenfunctions; 6. Nonoscillation Theorems; 7. Leighton and Nehari's Sufficient Conditions for Nonoscillatory Equations; 8. Comparison Theorems for Nonoscillation; 9. Howard's Comparison Theorems for Eigenvalue Problems; Chapter 4. Third Order Ordinary Equations, nth Order Ordinary Equations and Systems; 1. Introduction; 2. Separation Theorems for Third Order Equations , 3. Comparison Theorems for Third Order Equations4. Oscillation Criteria for Third Order Equations; 5. Separation and Comparison Theorems for nth Order Equations; 6. General Oscillation Theorems; 7. Nonoscillation Theorems for Systems of Differential Equations; 8. Whyburn's Second Order System; Chapter 5. Partial Differential Equations; 1. Introduction; 2. Comparison Theorems for Self-Adjoint Equations in Bounded Domains; 3. Comparison Theorems for General Second Order Elliptic Equations; 4. Comparison Theorems on Unbounded Domains; 5. Extension to Complex-Valued Solutions and Subsolutions , 6. Lower Bounds for Eigenvalues7. Oscillation Theorems; 8. Comparison Theorems for Eigenfunctions; Bibliography; Author Index; Subject Index; Mathematics in Science and Engineering , English

Additional Edition: ISBN 0-12-678950-9

Language: English

UID:

Format: XI, 397 S. : , Ill., graph. Darst.

Edition: 1. ed.

ISBN: 978-0-444-53044-8 , 0-444-53044-4

Series Statement: Mathematics in science and engineering 212

Language: English

Subjects: Mathematics

Keywords: Nichtlineares System ; Mathematisches Modell ; Numerisches Verfahren

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020106955&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

UID:

Format: 1 online resource (204 p.)

ISBN: 1-283-52648-4 , 9786613838933 , 0-08-095779-X

Series Statement: Mathematics in science and engineering

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Note: Description based upon print version of record. , Front Cover; The Optimal Design of Chemical Reactors; Copyright Page; Preface; Contents; Chapter 1. Introduction; 1.1. The Principle of Optimality; 1.2. Review of Cognate Work; 1.3. The Scope of the Present Monograph; Chapter 2. The Principal Notions of Dynamic Programming; 2.1. Multistage Decision Processes and the Principle of Optimality; 2.2. The Discrete Deterministic Process; 2.3. The Discrete Stochastic Process; 2.4. The Continuous Deterministic Process; 2.5. The Dynamic Programming Approach to the Calculus of Variations; 2.6. The Use and Interpretation of the Lagrange MuItiplier , Chapter 3. Mathematical Models for Reactor Design3.1. Systems of Chemical Reactions; 3.2. The Continuous Flow Stirred Tank Reactor; 3.3. The Multibed Adiabatic Reactor; 3.4. The Tubular Reactor; 3.5. The Stirred Tank Sequence as a Model for the Tubular Reactor; 3.6. The Batch Reactor; 3.7. Cooling; Chapter 4. The Objective Function; 4.1. Stoichiometric Objective Functions; 4.2. Material Objective Functions; 4.3. Objective Functions with Operating Costs; 4.4. An Example of Cost Estimation; 4.5. The Relation of the Objective Function to the Optimal Problem , Chapter 5. The Continuous Flow Stirred Tank Reactor5.1. The Disjoint Character of the Optimal Temperature Policy with a Single Reaction; 5.2. The Sequence of Reactors of Equal Size; 5.3. The Optimal Choice of Temperature and Holding Time with a Single Reaction; 5.4. Parametric Studies; 5.5. Two Consecutive Reactions; 5.6. Denbigh's System of Reactions; 5.7. General Problems with Sequences of Stirred Tanks; 5.8. Sequences of Stirred Tanks with Bypassing of the Feed Stream; 5.9. The Adiabatic Sequence of Reactors with a Single Reaction; Chapter 6. The Multibed Adiabatic Reactor , 6.1. Interchanger Cooling with a Single Reaction6.2. Extended Results of the Simple Model; 6.3. Interchanger Cooling with Simultaneous Reactions; 6.4. Cold Shot Cooling with a Single Reaction; 6.5. Cold Shot Cooling with Simultaneous Reactions; 6.6. Cooling bay an Alien Cold Shot; 6.7. The Removal of Sundry Approximations; Chapter 7. The Tubular Reactor; 7.1. Optimal Temperature Policy with a Single Reaction; 7.2. Alternative Forms of the Optimal Problem with a Single Reaction; 7.3. Two Consecutive Reactions; 7.4. Two Simultaneous Reactions in General; 7.5. The General Problem , Chapter 8. Stochastic Problems8.1. Optimal Replication of Processes Subject to Failure; 8.2. Stochastic Gold Making; 8.3. Optimal Catalyst Replacement Policies; Chapter 9. The Optimal Operation of Existing Reactors; 9.1. The Stirred Tank Reactor Sequence; 9.2. The Multibed Adiabatic Reactor; 9.3. Control with a Decaying Catalyst; 9.4. The Optimal Control of a Batch Reactor; 9.5. Further Problems in Batch Reactor Control; References; Index , English

Additional Edition: ISBN 0-12-374916-6

Language: English

UID:

Format: 1 online resource (204 p.)

ISBN: 1-283-52648-4 , 9786613838933 , 0-08-095779-X

Series Statement: Mathematics in science and engineering

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Note: Description based upon print version of record. , Front Cover; The Optimal Design of Chemical Reactors; Copyright Page; Preface; Contents; Chapter 1. Introduction; 1.1. The Principle of Optimality; 1.2. Review of Cognate Work; 1.3. The Scope of the Present Monograph; Chapter 2. The Principal Notions of Dynamic Programming; 2.1. Multistage Decision Processes and the Principle of Optimality; 2.2. The Discrete Deterministic Process; 2.3. The Discrete Stochastic Process; 2.4. The Continuous Deterministic Process; 2.5. The Dynamic Programming Approach to the Calculus of Variations; 2.6. The Use and Interpretation of the Lagrange MuItiplier , Chapter 3. Mathematical Models for Reactor Design3.1. Systems of Chemical Reactions; 3.2. The Continuous Flow Stirred Tank Reactor; 3.3. The Multibed Adiabatic Reactor; 3.4. The Tubular Reactor; 3.5. The Stirred Tank Sequence as a Model for the Tubular Reactor; 3.6. The Batch Reactor; 3.7. Cooling; Chapter 4. The Objective Function; 4.1. Stoichiometric Objective Functions; 4.2. Material Objective Functions; 4.3. Objective Functions with Operating Costs; 4.4. An Example of Cost Estimation; 4.5. The Relation of the Objective Function to the Optimal Problem , Chapter 5. The Continuous Flow Stirred Tank Reactor5.1. The Disjoint Character of the Optimal Temperature Policy with a Single Reaction; 5.2. The Sequence of Reactors of Equal Size; 5.3. The Optimal Choice of Temperature and Holding Time with a Single Reaction; 5.4. Parametric Studies; 5.5. Two Consecutive Reactions; 5.6. Denbigh's System of Reactions; 5.7. General Problems with Sequences of Stirred Tanks; 5.8. Sequences of Stirred Tanks with Bypassing of the Feed Stream; 5.9. The Adiabatic Sequence of Reactors with a Single Reaction; Chapter 6. The Multibed Adiabatic Reactor , 6.1. Interchanger Cooling with a Single Reaction6.2. Extended Results of the Simple Model; 6.3. Interchanger Cooling with Simultaneous Reactions; 6.4. Cold Shot Cooling with a Single Reaction; 6.5. Cold Shot Cooling with Simultaneous Reactions; 6.6. Cooling bay an Alien Cold Shot; 6.7. The Removal of Sundry Approximations; Chapter 7. The Tubular Reactor; 7.1. Optimal Temperature Policy with a Single Reaction; 7.2. Alternative Forms of the Optimal Problem with a Single Reaction; 7.3. Two Consecutive Reactions; 7.4. Two Simultaneous Reactions in General; 7.5. The General Problem , Chapter 8. Stochastic Problems8.1. Optimal Replication of Processes Subject to Failure; 8.2. Stochastic Gold Making; 8.3. Optimal Catalyst Replacement Policies; Chapter 9. The Optimal Operation of Existing Reactors; 9.1. The Stirred Tank Reactor Sequence; 9.2. The Multibed Adiabatic Reactor; 9.3. Control with a Decaying Catalyst; 9.4. The Optimal Control of a Batch Reactor; 9.5. Further Problems in Batch Reactor Control; References; Index , English

Additional Edition: ISBN 0-12-374916-6

Language: English

UID:

Format: 1 online resource (455 p.)

ISBN: 1-283-52557-7 , 9786613838025 , 0-08-095557-6

Series Statement: Mathematics in science and engineering

Content: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Note: Description based upon print version of record. , Front Cover; Differential Geometry and the Calculus of Variations; Copyright Page; Contents; Preface; Part 1: Differential and Integral Calculus on Manifolds; Chapter 1. Introduction; Chapter 2. Tangent Vector-Vector Field Formalism; Chapter 3. Differential Forms; Chapter 4. Specialization to Euclidean Spaces: Differential Manifolds; Chapter 5. Mappings, Submanifolds, and the Implicit Function Theorem; Chapter 6. The Jacobi Bracket and the Lie Theory of Ordinary Differential Equations; Chapter 7. Lie Derivation and Exterior Derivative; Integration on Manifolds , Chapter 8. The Frobenius Complete Integrability TheoremChapter 9. Reduction of Dimension When a Lie Algebra of Vector Fields Leaves a Vector-Field Invariant; Chapter 10. Lie Groups; Chapter 11. Classical Mechanics of Particles and Continua; Part 2: The Hamilton-Jacobi Theory and Calculus of Variations; Chapter 12. Differential Forms and Variational Problems; Chapter 13. Hamilton-Jacobi Theory; Chapter 14. Extremal Fields and Sufficient Conditions for a Minimum; Chapter 15. The Ordinary Problems of the Calculus of Variations , Chapter 16. Groups of Symmetries of Variational Problems: Applications to MechanicsChapter 17. Elliptic Functions; Chapter 18. Accessibility Problems for Path Systems; Part 3: Global Riemannian Geometry; Chapter 19. Affine Connections on Differential Manifolds; Chapter 20. The Riemannian Affine Connection and the First Variation Formula; Chapter 21. The Hopf-Rinow Theorem; Applications to the Theory of Covering Spaces; Chapter 22. The Second Variation Formula and Jacobi Vector Fields; Chapter 23. Sectional Curvature and the Elementary Comparison Theorems , Chapter 24. Submanifolds of Riemannian ManifoldsChapter 25. Groups of Isometries; Chapter 26. Deformation of Submanifolds in Riemannian Spaces; Part 4: Differential Geometry and the Calculus of Variations: Additional Topics in Differential Geometry; Chapter 27. First-Order Invariants of Submanifolds and Convexity for Affinely Connected Manifolds; Chapter 28. Affine Groups of Automorphisms. Induced Connections on Submanifolds. Projective Changes of Connection; Chapter 29. The Laplace-Beltrami Operator; Chapter 30. Characteristics and Shock Waves; Chapter 31. The Morse Index Theorem , Chapter 32. Complex Manifolds and Their SubmanifoldsChapter 33. Mechanics on Riemannian Manifolds; Bibliography; Subject Index; Mathematics in Science and Engineering , English

Additional Edition: ISBN 0-12-342150-0

Language: English