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22849904 |
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. |
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20260728105442.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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221102s2023 nju b 001 0 eng |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2022052893 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781119833857 |
| Qualifying information |
(cloth) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Cancelled/invalid ISBN |
9781119833895 |
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(adobe pdf) |
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| Cancelled/invalid ISBN |
9781119833901 |
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(epub) |
| 035 ## - SYSTEM CONTROL NUMBER |
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22849904 |
| 041 ## - LANGUAGE CODE |
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| Language code of text/sound track or separate title |
eng |
| 042 ## - AUTHENTICATION CODE |
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| Authentication code |
pcc |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA371 |
| Item number |
.R37 2023 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
660/.284015118 |
| Edition number |
23/eng20230317 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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Rice, Richard G., |
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author. |
| 245 10 - TITLE STATEMENT |
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| Title |
Applied mathematics and modeling for chemical engineers / |
| Statement of responsibility, etc |
Richard G. Rice, Emeritus Professor (LSU), Punta Gorda, Florida, USA, Duong D. Do, Emeritus Professor (University of Queensland), Middle Park, Queensland, Australia, James E. Maneval, Department of Chemical Engineering, Bucknell University, Lewisburg, Pennsylvania, USA. |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
Third edition. |
| 264 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Hoboken, New Jersey : |
| Name of publisher, distributor, etc |
Wiley, |
| Date of publication, distribution, etc |
2023. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xv, 408 pages : |
| Dimensions |
28 cm |
| 336 ## - CONTENT TYPE |
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text |
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txt |
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rdacontent |
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unmediated |
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n |
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rdamedia |
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volume |
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nc |
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rdacarrier |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 ## - CONTENTS |
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| Formatted contents note |
Table of Contents<br/>Preface to the Third Edition xv<br/><br/>Part I 1<br/><br/>1 Formulation of Physicochemical Problems 3<br/><br/>1.1 Introduction 3<br/><br/>1.2 Illustration of the Formulation Process (Cooling of Fluids) 3<br/><br/>1.2.1 Model I: Plug Flow 3<br/><br/>1.2.2 Model II: Parabolic Velocity 6<br/><br/>1.3 Combining Rate and Equilibrium Concepts (Packed-Bed Adsorber) 7<br/><br/>1.4 Boundary Conditions and Sign Conventions 8<br/><br/>1.5 Summary of the Model Building Process 9<br/><br/>1.6 Model Hierarchy and its Importance in Analysis 10<br/><br/>1.6.1 Level 1 10<br/><br/>1.6.2 Level 2 11<br/><br/>1.6.3 Level 3 13<br/><br/>1.6.4 Level 4 13<br/><br/>Problems 15<br/><br/>References 20<br/><br/>2 Modeling with Linear Algebra and Matrices 21<br/><br/>2.1 Introduction 21<br/><br/>2.2 Basic Concepts of Systems of Linear Equations 21<br/><br/>2.3 Matrix Notation 22<br/><br/>2.3.1 Matrices 22<br/><br/>2.3.2 Vectors 22<br/><br/>2.3.3 Scalars 22<br/><br/>2.3.4 Matrices and Vectors with Special Structure 22<br/><br/>2.4 Matrix Algebra and Calculus Operations 24<br/><br/>2.4.1 Equality 24<br/><br/>2.4.2 Addition and Subtraction 24<br/><br/>2.4.3 Multiplication 24<br/><br/>2.4.4 Division 26<br/><br/>2.4.5 Further Algebraic Properties of Matrices 27<br/><br/>2.4.6 Basic Differential and Integral Relations for Matrices 28<br/><br/>2.5 Problem 1: Solution of N Equations in N Unknowns 29<br/><br/>2.5.1 Analytical Results 29<br/><br/>2.5.2 Computational Approach: Gauss Elimination 30<br/><br/>2.6 Problem 2: The Matrix Eigenvalue Problem 32<br/><br/>2.6.1 Problem Statement and Formal Solution 32<br/><br/>2.6.2 Computing Eigensystems: Basic Procedure 33<br/><br/>2.7 Singular Systems 34<br/><br/>2.7.1 Consistent and Inconsistent Systems 34<br/><br/>2.7.2 Solution Structure for Consistent Systems 35<br/><br/>2.7.3 Formulation and Characteristics of Non-Square Problems 36<br/><br/>2.7.4 Over-Determined Systems: Least-Squares Solution 37<br/><br/>2.7.5 Under-Determined Systems 38<br/><br/>2.8 Computational Linear Algebra 40<br/><br/>2.8.1 The LU Factorization 40<br/><br/>2.8.2 The QR Factorization 40<br/><br/>2.8.3 The SVD Factorization 40<br/><br/>2.8.4 Large-Scale Problems and Iterative Methods 41<br/><br/>Problems 42<br/><br/>References 47<br/><br/>3 Solution Techniques for Models Yielding Ordinary Differential Equations 49<br/><br/>3.1 Geometric Basis and Functionality 49<br/><br/>3.2 Classification of ODE 50<br/><br/>3.3 First-Order Equations 50<br/><br/>3.3.1 Exact Solutions 51<br/><br/>3.3.2 Equations Composed of Homogeneous Functions 52<br/><br/>3.3.3 Bernoulli’s Equation 52<br/><br/>3.3.4 Riccati’s Equation 52<br/><br/>3.3.5 Linear Coefficients 54<br/><br/>3.3.6 First-Order Equations of Second Degree 54<br/><br/>3.4 Solution Methods for Second-Order Nonlinear Equations 55<br/><br/>3.4.1 Derivative Substitution Method 55<br/><br/>3.4.2 Homogeneous Function Method 58<br/><br/>3.5 Linear Equations of Higher Order 59<br/><br/>3.5.1 Second-Order Unforced Equations: Complementary Solutions 60<br/><br/>3.5.2 Particular Solution Methods for Forced Equations 64<br/><br/>3.5.3 Summary of Particular Solution Methods 70<br/><br/>3.6 Coupled Simultaneous ODE 71<br/><br/>3.7 Eigenproblems 74<br/><br/>3.8 Coupled Linear Differential Equations 74<br/><br/>3.9 Summary of Solution Methods for ODE 75<br/><br/>Problems 75<br/><br/>References 87<br/><br/>4 Series Solution Methods and Special Functions 89<br/><br/>4.1 Introduction to Series Methods 89<br/><br/>4.2 Properties of Infinite Series 90<br/><br/>4.3 Method of Frobenius 91<br/><br/>4.3.1 Indicial Equation and Recurrence Relation 91<br/><br/>4.4 Summary of the Frobenius Method 98<br/><br/>4.5 Special Functions 98<br/><br/>4.5.1 Bessel’s Equation 99<br/><br/>4.5.2 Modified Bessel’s Equation 100<br/><br/>4.5.3 Generalized Bessel’s Equation 100<br/><br/>4.5.4 Properties of Bessel Functions 102<br/><br/>4.5.5 Differential Integral and Recurrence Relations 103<br/><br/>Problems 105<br/><br/>References 107<br/><br/>5 Integral Functions 109<br/><br/>5.1 Introduction 109<br/><br/>5.2 The Error Function 109<br/><br/>5.2.1 Properties of Error Function 110<br/><br/>5.3 The Gamma and Beta Functions 110<br/><br/>5.3.1 The Gamma Function 110<br/><br/>5.3.2 The Beta Function 111<br/><br/>5.4 The Elliptic Integrals 111<br/><br/>5.5 The Exponential and Trigonometric Integrals 113<br/><br/>Problems 113<br/><br/>References 116<br/><br/>6 Staged-Process Models: The Calculus of Finite Differences 117<br/><br/>6.1 Introduction 117<br/><br/>6.1.1 Modeling Multiple Stages 117<br/><br/>6.2 Solution Methods for Linear Finite Difference Equations 118<br/><br/>6.2.1 Complementary Solutions 118<br/><br/>6.3 Particular Solution Methods 121<br/><br/>6.3.1 Method of Undetermined Coefficients 121<br/><br/>6.3.2 Inverse Operator Method 122<br/><br/>6.4 Nonlinear Equations (Riccati Equation) 122<br/><br/>Problems 124<br/><br/>References 126<br/><br/>7 Probability and Statistical Modeling 127<br/><br/>7.1 Concepts and Results From Probability Theory 127<br/><br/>7.1.1 Experiments and Random Variables 127<br/><br/>7.1.2 Probabilities and Distribution Functions 128<br/><br/>7.1.3 Characteristics of Distributions Functions 131<br/><br/>7.1.4 The Cumulative Distribution Function 132<br/><br/>7.2 Concepts and Results From Mathematical Statistics 134<br/><br/>7.2.1 Populations Samples and Sampling 134<br/><br/>7.2.2 Sample Statistics and Sampling Distributions 134<br/><br/>7.3 Statistical Analysis and Modeling 137<br/><br/>7.3.1 Confidence Interval for the Mean of a Population 137<br/><br/>7.3.2 Hypothesis Tests for the Population Mean 138<br/><br/>7.3.3 Hypothesis Tests: Comparing Multiple Means 140<br/><br/>7.3.4 Linear Models and Linear Regression 143<br/><br/>Problems 150<br/><br/>References 154<br/><br/>8 Approximate Solution Methods for ODE: Perturbation Methods 155<br/><br/>8.1 Perturbation Methods 155<br/><br/>8.1.1 Introduction 155<br/><br/>8.2 The Basic Concepts 157<br/><br/>8.2.1 Gauge Functions 157<br/><br/>8.2.2 Order Symbols 158<br/><br/>8.2.3 Asymptotic Expansions and Sequences 158<br/><br/>8.2.4 Sources of Nonuniformity 159<br/><br/>8.3 The Method of Matched Asymptotic Expansion 160<br/><br/>8.3.1 Outer Solutions 160<br/><br/>8.3.2 Inner Solutions 160<br/><br/>8.3.3 Matching 161<br/><br/>8.3.4 Composite Solutions 161<br/><br/>8.3.5 General Matching Principle 162<br/><br/>8.3.6 Composite Solution of Higher Order 162<br/><br/>8.4 Matched Asymptotic Expansions for Coupled Equations 163<br/><br/>8.4.1 Outer Expansion 163<br/><br/>8.4.2 Inner Expansion 164<br/><br/>8.4.3 Matching 164<br/><br/>Problems 165<br/><br/>References 173<br/><br/>Part II 175<br/><br/>9 Numerical Solution Methods (Initial Value Problems) 177<br/><br/>9.1 Introduction 177<br/><br/>9.2 Type of Method 179<br/><br/>9.3 Stability 180<br/><br/>9.4 Stiffness 185<br/><br/>9.5 Interpolation and Quadrature 186<br/><br/>9.6 Explicit Integration Methods 187<br/><br/>9.7 Implicit Integration Methods 188<br/><br/>9.8 Predictor–Corrector Methods and Runge–Kutta Methods 189<br/><br/>9.8.1 Predictor–Corrector Methods 189<br/><br/>9.9 Runge–Kutta Methods 189<br/><br/>9.10 Extrapolation 191<br/><br/>9.11 Step Size Control 192<br/><br/>9.12 Higher-Order Integration Methods 192<br/><br/>Problems 192<br/><br/>References 195<br/><br/>10 Approximate Methods for Boundary Value Problems: Weighted Residuals 197<br/><br/>10.1 The Method of Weighted Residuals 197<br/><br/>10.1.1 Variations on a Theme of Weighted Residuals 198<br/><br/>10.2 Jacobi Polynomials 205<br/><br/>10.2.1 Rodrigues Formula 205<br/><br/>10.2.2 Orthogonality Conditions 205<br/><br/>10.3 Lagrange Interpolation Polynomials 206<br/><br/>10.4 Orthogonal Collocation Method 206<br/><br/>10.4.1 Differentiation of a Lagrange Interpolation Polynomial 206<br/><br/>10.4.2 Gauss–Jacobi Quadrature 207<br/><br/>10.4.3 Radau and Lobatto Quadrature 208<br/><br/>10.5 Linear Boundary Value Problem: Dirichlet Boundary Condition 209<br/><br/>10.6 Linear Boundary Value Problem: Robin Boundary Condition 211<br/><br/>10.7 Nonlinear Boundary Value Problem: Dirichlet Boundary Condition 213<br/><br/>10.8 One-Point Collocation 215<br/><br/>10.9 Summary of Collocation Methods 215<br/><br/>10.10 Concluding Remarks 216<br/><br/>Problems 217<br/><br/>References 225<br/><br/>11 Introduction to Complex Variables and Laplace Transforms 227<br/><br/>11.1 Introduction 227<br/><br/>11.2 Elements of Complex Variables 227<br/><br/>11.3 Elementary Functions of Complex Variables 228<br/><br/>11.4 Multivalued Functions 229<br/><br/>11.5 Continuity Properties for Complex Variables: Analyticity 230<br/><br/>11.5.1 Exploiting Singularities 231<br/><br/>11.6 Integration: Cauchy’s Theorem 232<br/><br/>11.7 Cauchy’s Theory of Residues 233<br/><br/>11.7.1 Practical Evaluation of Residues 234<br/><br/>11.7.2 Residues at Multiple Poles 235<br/><br/>11.8 Inversion of Laplace Transforms by Contour Integration 235<br/><br/>11.8.1 Summary of Inversion Theorem for Pole Singularities 237<br/><br/>11.9 Laplace Transformations: Building Blocks 237<br/><br/>11.9.1 Taking the Transform 237<br/><br/>11.9.2 Transforms of Derivatives and Integrals 238<br/><br/>11.9.3 The Shifting Theorem 240<br/><br/>11.9.4 Transform of Distribution Functions 240<br/><br/>11.10 Practical Inversion Methods 242<br/><br/>11.10.1 Partial Fractions 242<br/><br/>11.10.2 Convolution Theorem 243<br/><br/>11.11 Applications of Laplace Transforms for Solutions of ODE 243<br/><br/>11.12 Inversion Theory for Multivalued Functions: The Second Bromwich Path 248<br/><br/>11.12.1 Inversion When Poles and Branch Points Exist 250<br/><br/>11.13 Numerical Inversion Techniques 250<br/><br/>11.13.1 The Zakian Method 250<br/><br/>11.13.2 The Fourier Series Approximation 252<br/><br/>Problems 253<br/><br/>References 257<br/><br/>12 Solution Techniques for Models Producing PDEs 259<br/><br/>12.1 Introduction 259<br/><br/>12.1.1 Classification and Characteristics of Linear Equations 261<br/><br/>12.2 Particular Solutions for PDEs 263<br/><br/>12.2.1 Boundary and Initial Conditions 263<br/><br/>12.3 Combination of Variables Method 264<br/><br/>12.4 Separation of Variables Method 269<br/><br/>12.4.1 Coated Wall Reactor 269<br/><br/>12.5 Orthogonal Functions and Sturm–Liouville Conditions 272<br/><br/>12.5.1 The Sturm–Liouville Equation 272<br/><br/>12.6 Inhomogeneous Equations 275<br/><br/>12.7 Applications of Laplace Transforms for Solutions of PDEs 279<br/><br/>Problems 285<br/><br/>References 302<br/><br/>13 Transform Methods for Linear PDEs 305<br/><br/>13.1 Introduction 305<br/><br/>13.2 Transforms in Finite Domain: Sturm–Liouville Transforms 305<br/><br/>13.2.1 Development of Integral Transform Pairs 306<br/><br/>13.2.2 The Eigenvalue Problem and the Orthogonality Condition 309<br/><br/>13.2.3 Inhomogeneous Boundary Conditions 313<br/><br/>13.2.4 Inhomogeneous Equations 316<br/><br/>13.2.5 Time-Dependent Boundary Conditions 317<br/><br/>13.2.6 Elliptic Partial Differential Equations 317<br/><br/>13.3 Generalized Sturm–Liouville Integral Transform 320<br/><br/>13.3.1 Introduction 320<br/><br/>13.3.2 The Batch Adsorber Problem 320<br/><br/>Problems 327<br/><br/>References 331<br/><br/>14 Approximate and Numerical Solution Methods for PDEs 333<br/><br/>14.1 Polynomial Approximation 333<br/><br/>14.2 Singular Perturbation 338<br/><br/>14.3 Finite Difference 343<br/><br/>14.3.1 Notations 343<br/><br/>14.3.2 Essence of the Method 344<br/><br/>14.3.3 Tridiagonal Matrix and the Thomas Algorithm 345<br/><br/>14.3.4 Linear Parabolic Partial Differential Equations 345<br/><br/>14.3.5 Nonlinear Parabolic Partial Differential Equations 349<br/><br/>14.4 Orthogonal Collocation for Solving PDEs 350<br/><br/>14.4.1 Elliptic PDE 350<br/><br/>14.4.2 Parabolic PDE: Example 1 353<br/><br/>14.4.3 Coupled Parabolic PDE: Example 2 354<br/><br/>Problems 355<br/><br/>References 362<br/><br/>Appendix A: Review of Methods for Nonlinear Algebraic Equations 363<br/><br/>A.1 The Bisection Algorithm 363<br/><br/>A.2 The Successive Substitution Method 364<br/><br/>A.3 The Newton–Raphson Method 366<br/><br/>A.4 Rate of Convergence 367<br/><br/>A.4.1 Definition of Speed of Convergence 367<br/><br/>A.5 Multiplicity 368<br/><br/>A.5.1 Multiplicity 368<br/><br/>A.6 Accelerating Convergence 369<br/><br/>References 369<br/><br/>Appendix B: Derivation of the Fourier–Mellin Inversion Theorem 371<br/><br/>References 374<br/><br/>Appendix C: Table of Laplace Transforms 375<br/><br/>Appendix D: Numerical Integration 381<br/><br/>D.1 Basic Idea of Numerical Integration 381<br/><br/>D.2 Newton Forward Difference Polynomial 381<br/><br/>D.3 Basic Integration Procedure 382<br/><br/>D.3.1 Trapezoid Rule 382<br/><br/>D.3.2 Simpson’s Rule 383<br/><br/>D.4 Error Control and Extrapolation 384<br/><br/>D.5 Gaussian Quadrature 384<br/><br/>D.6 Radau Quadrature 386<br/><br/>D.7 Lobatto Quadrature 388<br/><br/>D.8 Concluding Remarks 389<br/><br/>References 389<br/><br/>Appendix E: Nomenclature 391<br/><br/>Appendix F: Statistical Tables 395<br/><br/>Postface 399<br/><br/>Index 401 |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
"The book introduces traditional techniques of applied mathematics for chemical engineers. It shows the reader how to solve ordinary differential equations (ODEs) while adding new material on approximate solution methods such as perturbation techniques and elementary numerical solutions. The book also includes basics of linear algebra and statistical methods along with analytical techniques to deal with important classes of finite-difference equations while also discussing analytical, numerical and approximate solution techniques applied to solution of partial differential equations (PDEs). The reader will then have had the practical training to apply mathematics in the formulation of problems in Chemical Engineering, Bioengineering, Chemistry and Physics. The first and second editions of Applied Mathematics and Modeling for Chemical Engineers have served a generation of chemical engineers well. The new edition revises and updates to bring new contemporary examples to bear on emerging technology in biochemical engineering and nanotechnology. Updates throughout the text along with two added chapters, one on Linear Algebra and the other on Applied Statistics, satisfies the need for more analysis on laboratory data and statistical quality control in the engineering curricula"-- |
| Assigning source |
Provided by publisher. |
| 545 0# - BIOGRAPHICAL OR HISTORICAL DATA |
|---|
| Biographical or historical note |
About the Author<br/>Richard G. Rice, PhD is Emeritus Professor in the Department of Chemical Engineering at Louisiana State University, Baton Rouge, LA, USA.<br/><br/>Duong D. Do, PhD is Emeritus Professor in the School of Chemical Engineering at the University of Queensland, Australia.<br/><br/>James E. Maneval, PhD is Professor in the Department of Chemical Engineering at Bucknell University, Lewisburg, PA, USA. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Differential equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Chemical processes |
| General subdivision |
Mathematical models. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Chemical engineering |
| General subdivision |
Mathematics. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Do, Duong D., |
| Relator term |
author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Maneval, James E., |
| Relator term |
author. |
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BOOK |