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Book
xvi, 461 pages : illustrations ; 25 cm.
  • Chapter 1. Complex Numbers Chapter 2. Analytic Functions Chapter 3. Elementary Functions Chapter 4. Integrals Chapter 5. Series Chapter 6. Residues and Poles Chapter 7. Applications of Residues Chapter 8. Mapping by Elementary Functions Chapter 9. Conformal Mapping Chapter 10. Applications of Conformed Mapping Chapter 11. The Schwarz-Christoffel Transformation Chapter 12. Integral Formulas of the Poisson Type Appendixes.
  • (source: Nielsen Book Data)9781259072772 20160614
Complex Variables and Applications, 9e will serve, just as the earlier editions did, as a textbook for an introductory course in the theory and application of functions of a complex variable. This new edition preserves the basic content and style of the earlier editions. The text is designed to develop the theory that is prominent in applications of the subject. You will find a special emphasis given to the application of residues and conformal mappings. To accommodate the different calculus backgrounds of students, footnotes are given with references to other texts that contain proofs and discussions of the more delicate results in advanced calculus. Improvements in the text include extended explanations of theorems, greater detail in arguments, and the separation of topics into their own sections.
(source: Nielsen Book Data)9781259072772 20160614
Science Library (Li and Ma)
CHEMENG-300-01
Book
xi, 468 p. : ill. ; 25 cm.
  • 1 Complex Numbers Sums and Products Basic Algebraic Properties Further Properties Vectors and Moduli Complex Conjugates Exponential Form Products and Powers in Exponential Form Arguments of Products and Quotients Roots of Complex Numbers Examples Regions in the Complex Plane 2 Analytic Functions Functions of a Complex Variable Mappings Mappings by the Exponential Function Limits Theorems on Limits Limits Involving the Point at Infinity Continuity Derivatives Differentiation Formulas Cauchy--Riemann Equations Sufficient Conditions for Differentiability Polar Coordinates Analytic Functions Examples Harmonic Functions Uniquely Determined Analytic Functions Reflection Principle 3 Elementary Functions The Exponential Function The Logarithmic Function Branches and Derivatives of Logarithms Some Identities Involving Logarithms Complex Exponents Trigonometric Functions Hyperbolic Functions Inverse Trigonometric and Hyperbolic Functions 4 Integrals Derivatives of Functions w(t) Definite Integrals of Functions w(t) Contours Contour Integrals Some Examples Examples with Branch Cuts Upper Bounds for Moduli of Contour Integrals Antiderivatives Proof of the Theorem Cauchy--Goursat Theorem Proof of the Theorem Simply Connected Domains Multiply Connected Domains Cauchy Integral Formula An Extension of the Cauchy Integral Formula Some Consequences of the Extension Liouville's Theorem and the Fundamental Theorem of Algebra Maximum Modulus Principle 5 Series Convergence of Sequences Convergence of Series Taylor Series Proof of Taylor's Theorem Examples Laurent Series Proof of Laurent's Theorem Examples Absolute and Uniform Convergence of Power Series Continuity of Sums of Power Series Integration and Differentiation of Power Series Uniqueness of Series Representations Multiplication and Division of Power Series 6 Residues and Poles Isolated Singular Points Residues Cauchy's Residue Theorem Residue at Infinity The Three Types of Isolated Singular Points Residues at Poles Examples Zeros of Analytic Functions Zeros and Poles Behavior of Functions Near Isolated Singular Points 7 Applications of Residues Evaluation of Improper Integrals Example Improper Integrals from Fourier Analysis Jordan's Lemma Indented Paths An Indentation Around a Branch Point Integration Along a Branch Cut Definite Integrals Involving Sines and Cosines Argument Principle Rouche's Theorem Inverse Laplace Transforms Examples 8 Mapping by Elementary Functions Linear Transformations The Transformation w = 1/z Mappings by 1/z Linear Fractional Transformations An Implicit Form Mappings of the Upper Half Plane The Transformation w = sin z Mappings by z2 and Branches of z1/2 Square Roots of Polynomials Riemann Surfaces Surfaces for Related Functions 9 Conformal Mapping Preservation of Angles Scale Factors Local Inverses Harmonic Conjugates Transformations of Harmonic Functions Transformations of Boundary Conditions 10 Applications of Conformal Mapping Steady Temperatures Steady Temperatures in a Half Plane A Related Problem Temperatures in a Quadrant Electrostatic Potential Potential in a Cylindrical Space Two-Dimensional Fluid Flow The Stream Function Flows Around a Corner and Around a Cylinder 11 The Schwarz--Christoffel Transformation Mapping the Real Axis onto a Polygon Schwarz--Christoffel Transformation Triangles and Rectangles Degenerate Polygons Fluid Flow in a Channel Through a Slit Flow in a Channel with an Offset Electrostatic Potential about an Edge of a Conducting Plate 12 Integral Formulas of the Poisson Type Poisson Integral Formula Dirichlet Problem for a Disk Related Boundary Value Problems Schwarz Integral Formula Dirichlet Problem for a Half Plane Neumann Problems Appendixes Bibliography Table of Transformations of Regions Index.
  • (source: Nielsen Book Data)9780071263283 20160527
"Complex Variables and Applications, 8E" will serve, just as the earlier editions did, as a textbook for an introductory course in the theory and application of functions of a complex variable. This new edition preserves the basic content and style of the earlier editions. The text is designed to develop the theory that is prominent in applications of the subject. You will find a special emphasis given to the application of residues and conformal mappings. To accommodate the different calculus backgrounds of students, footnotes are given with references to other texts that contain proofs and discussions of the more delicate results in advanced calculus. Improvements in the text include extended explanations of theorems, greater detail in arguments, and the separation of topics into their own sections.
(source: Nielsen Book Data)9780073051949 20160528
Science Library (Li and Ma)
CHEMENG-300-01
Book
viii, 163 p. : ill. ; 24 cm.
This well-written new edition contains a healthy balance of explicit and implied calculation. It updates the notation to bring it in line with modern usage and adds new example exercises.
(source: Nielsen Book Data)9780393925166 20160528
Green Library, Science Library (Li and Ma)
CHEMENG-300-01
Book
xvii, 639 p. : ill ; 24 cm.
  • Preface to the Second Edition. Chapter 1. Catalizing the Generation of Knowledge. 1.1. The Learning Process. 1.2. Important Considerations. 1.3. The Experimenter's Problem and Statistical Methods. 1.4. A Typical Investigation. 1.5. How to Use Statistical Techniques. References and Further Reading. Chapter 2. Basics: Probability, Parameters and Statistics. 2.1. Experimental Error. 2.2. Distributions. 2.3. Statistics and Parameters. 2.4. Measures of Location and Spread. 2.5. The Normal Distribution. 2.6. Normal Probability Plots. 2.7. Randomness and Random Variables. 2.8. Covariance and Correlation as Measures of Linear Dependence. 2.9. Student's t Distribution. 2.10. Estimates of Parameters. 2.11. Random Sampling from a Normal Population. 2.12. The Chi-Square and F Distributions. 2.13. The Binomial Distribution. 2.14. The Poisson Distribution. Appendix 2A. Mean and Variance of Linear Combinations of Observations. References and Further Reading. Chapter 3. Comparing Two Entities: Relevant Reference Distributions, Tests and Confidence Intervals. 3.1. Relevant Reference Sets and Distributions. 3.2. Randomized Paired Comparison Design: Boys' Shoes Example. 3.3. Blocking and Randomization. 3.4. Reprise: Comparison, Replication, Randomization, and Blocking in Simple Experiments. 3.5. More on Significance Tests. 3.6. Inferences About Data that are Discrete: Binomial Distribution. 3.7. Inferences about Frequencies (Counts Per Unit): The Poisson Distribution. 3.8. Contingency Tables and Tests of Association. Appendix 3A. Comparison of the Robustness of Tests to Compare Two Entities. Appendix 3B. Calculation of reference distribution from past data. References and Further Reading. Chapter 4. Comparing a Number of Entities: Randomized Blocks and Latin Squares. 4.1. Comparing k Treatments in a Fully Randomized Design. 4.2. Randomized Block Designs. 4.3. A Preliminary Note on Split-Plot Experiments and their Relationship to Randomized Blocks. 4.4. More than one blocking component: Latin Squares. 4.5. Balanced Incomplete Block Designs. Appendix 4A. The Rationale for the Graphical ANOVA. Appendix 4B. Some Useful Latin Square, Graeco-Latin Square, and Hyper-Graeco-Latin Square Designs. References and Further Reading. Chapter 5. Factorial Designs at Two Levels: Advantages of Experimental Design. 5.1. Introduction. 5.2. Example 1: The Effects of Three Factors (Variables) on Clarity of Film. 5.3. Example 2: The Effects of Three Factors on Three Physical Properties of a Polymer Solution. 5.4. A 23 Factorial Design: Pilot Plant Investigation. 5.5. Calculation of Main Effects. 5.6. Interaction Effects. 5.7. Genuine Replicate Runs. 5.8. Interpretation of Results. 5.9. The Table of Contrasts. 5.10. Misuse of the ANOVA for 2k Factorial Experiments. 5.11. Eyeing the Data. 5.12. Dealing with More Than One Response: A Pet Food Experiment. 5.13. A 24 Factorial Design: Process Development Study. 5.14. Analysis Using Normal and Lenth Plots. 5.15. Other Models for Factorial Data. 5.16. Blocking the 2k Factorial Designs. 5.17. Learning by Doing. 5.18. Summary. Appendix 5A. Blocking Larger Factorial Designs. Appendix 5B. Partial Confounding. References and Further Reading. Chapter 6. Fraction Factorial Designs: Economy in Experimentation. 6.1. Effects of Five Factors on Six Properties of Films in Eight Runs. 6.2. Stability of New Product, Four Factors in Eight Runs, a 24 1 Design. 6.3. A Half-Fraction Example: The Modification of a Bearing. 6.4. The Anatomy of the Half Fraction. 6.5. The 27 4III Design: A Bicycle Example. 6.6. Eight-Run Designs. 6.7. Using Table 6.6: An Illustration. 6.8. Sign Switching, Foldover, and Sequential Assembly. 6.9. An Investigation Using Multiple-Column Foldover. 6.10. Increasing Design Resolution from III to IV by Foldover. 6.11. Sixteen-Run Designs. 6.12. The 25 1 Nodal Half Replicate of the 25 Factorial: Reactor Example. 6.13. The 28 4 IV Nodal Sixteenth Fraction of a 28 Factorial. 6.14. The 215 11 III Nodal Design: The Sixty-Fourth Fraction of the 215 Factorial. 6.15. Constructing Other Two-Level Fractions. 6.16. Elimination of Block Effects. References and Further Reading. Chapter 7. Other Fractionals, Analysis and Choosing Follow-up Runs. 7.1. Plackett and Burman Designs. 7.2. Choosing Follow-Up Runs. 7.3. Justifications for the Use of Fractionals. Appendix 7A. Technical Details. Appendix 7B. An Approximate Partial Analysis for PB Designs. Appendix 7C. Hall's Orthogonal Designs. References and Further Reading. Chapter 8. Factorial Designs and Data Transformation. 8.1. A Two-Way (Factorial) Design. 8.2. Simplification and Increased Sensitivity from Transformation. Appendix 8A. Rationale for Data Transformation. Appendix 8B. Bartlett's chi2nu for Testing Inhomogeneity of Variance. References and Further Reading. Chapter 9. Multiple Sources of Variation: Split Plot Designs, Variance Components and Error Transmission. 9.1. Split-Plot Designs, Variance Components, and Error Transmission. 9.2. Split-Plot Designs. 9.3. Estimating Variance Components. 9.4. Transmission of Error. References and Further Reading. Chapter 10. Least Squares and Why You Need to Design Experiments. 10.1. Estimation With Least Squares. 10.2. The Versatility of Least Squares. 10.3. The Origins of Experimental Design. 10.4. Nonlinear Models. Appendix 10A. Vector Representation of Statistical Concepts. Appendix 10B. Matrix Version of Least Squares. Appendix 10C. Analysis of Factorials, Botched and Otherwise. Appendix 10D. Unweighted and Weighted Least Squares. References and Further Reading. Chapter 11. Modelling Relationships, Sequential Assembly: Basics for Response Surface Methods. 11.1. Some Empirical Models. 11.2. Some Experimental Designs and the Design Information Function. 11.3. Is the Surface Sufficiently Well Estimated? 11.4. Sequential Design Strategy. 11.5. Canonical Analysis. 11.6. Box-Behnken Designs. References and Further Reading. Chapter 12. Some Applications of Response Surface Methods. 12.1. Iterative Experimentation To Improve a Product Design. 12.2. Simplification of a Response Function by Data Transformation. 12.3. Detecting and Exploiting Active and Inactive Factor Spaces for Multiple-Response Data. 12.4. Exploring Canonical Factor Spaces. 12.5. From Empiricism to Mechanism. 12.6. Uses of RSM. Appendix 12A. Average Variance of y. Appendix 12B. References and Further Reading. Chapter 13. Designing Robust Products: An Introduction. 13.1. Environmental Robustness. 13.2. Robustness To Component Variation. Appendix 13A. A Mathematical Formulation for Environmental Robustness. Appendix 13B. Choice of Criteria. References and Further Reading. Chapter 14. Process Control, Forecasting and Times Series: An Introduction. 14.1. Process Monitoring. 14.2. The Exponentially Weighted Moving Average. 14.3. The CuSum Chart. 14.4. Process Adjustment. 14.5. A Brief Look At Some Time Series Models and Applications. 14.6. Using a Model to Make a Forecast. 14.7. Intervention Analysis: A Los Angeles Air Pollution Example. References and Further Reading. Chapter 15. Evolutionary Process Operation. 15.1. More than One Factor. 15.2. Multiple Responses. 15.3. The Evolutionary Process Operation Committee. References and Further Reading. Appendix Tables. Author Index. Subject Index.
  • (source: Nielsen Book Data)9780471718130 20160528
A Classic adapted to modern times Rewritten and updated, this new edition of Statistics for Experimenters adopts the same approaches as the landmark First Edition by teaching with examples, readily understood graphics, and the appropriate use of computers. Catalyzing innovation, problem solving, and discovery, the Second Edition provides experimenters with the scientific and statistical tools needed to maximize the knowledge gained from research data, illustrating how these tools may best be utilized during all stages of the investigative process. The authors' practical approach starts with a problem that needs to be solved and then examines the appropriate statistical methods of design and analysis. Providing even greater accessibility for its users, the Second Edition is thoroughly revised and updated to reflect the changes in techniques and technologies since the publication of the classic First Edition. Among the new topics included are: * Graphical Analysis of Variance * Computer Analysis of Complex Designs * Simplification by transformation * Hands-on experimentation using Response Service Methods * Further development of robust product and process design using split plot arrangements and minimization of error transmission * Introduction to Process Control, Forecasting and Time Series * Illustrations demonstrating how multi-response problems can be solved using the concepts of active and inert factor spaces and canonical spaces * Bayesian approaches to model selection and sequential experimentation An appendix featuring Quaquaversal quotes from a variety of sources including noted statisticians and scientists to famous philosophers is provided to illustrate key concepts and enliven the learning process. All the computations in the Second Edition can be done utilizing the statistical language R. Functions for displaying ANOVA and lamba plots, Bayesian screening, and model building are all included and R packages are available online. All theses topics can also be applied utilizing easy-to-use commercial software packages. Complete with applications covering the physical, engineering, biological, and social sciences, Statistics for Experimenters is designed for individuals who must use statistical approaches to conduct an experiment, but do not necessarily have formal training in statistics. Experimenters need only a basic understanding of mathematics to master all the statistical methods presented. This text is an essential reference for all researchers and is a highly recommended course book for undergraduate and graduate students.
(source: Nielsen Book Data)9780471718130 20160528
Science Library (Li and Ma)
CHEMENG-300-01
Book
viii, 164 p. : ill. ; 24 cm.
Science Library (Li and Ma)
CHEMENG-300-01
Book
xiv, 690 p. : ill. ; 24 cm.
  • 1. Matrices and Their Application-- 2. First-Order Nonlinear Ordinary Differential Equations and Stability Theory-- 3. Theory of Linear Ordinary Differential Equations (ODEs)-- 4. Series Solutions and Special Functions-- 5. Fundamentals of Partial Differential Equations-- 6. First-Order Partial Differential Equations-- 7. Generalized Fourier Transform Methods for Linear Partial Differential Equations-- 8. Laplace Transform-- 9. Perturbation Methods.
  • (source: Nielsen Book Data)9780195098211 20160528
Designed to provide a firm grounding in mathematical methods for chemical engineering practitioners in academic institutions and industry, this volume builds on the reader's previous knowledge of calculus, differential equations and linear algebra. Varma and Morbidelli offer an integrated treatment of linear operator theory from determinants through partial differential equations, and feature extensive chapters on both ordinary differential equations and perturbation methods. Numerous high-quality diagrams and examples from chemical engineering illustrate the textual material and enhance the reader's understanding of complex mathematical systems.
(source: Nielsen Book Data)9780195098211 20160528
Science Library (Li and Ma)
CHEMENG-300-01
Book
578 p. : ill. ; 25 cm.
  • Chapter 1 First-order differential equations * Chapter 2 Second-order linear differential equations * Chapter 3 Systems of differential equations * Chapter 4 Qualitative theory of differential equations * Chapter 5 Separation of variables and Fourier series * Chapter 6 Sturm -Liouville boundary value problems * Appendix A Some simple facts concerning functions of several variables * Appendix B Sequences and series * Appendix C C Programs * Answers to odd-numbered exercises * Index.
  • (source: Nielsen Book Data)9783540978947 20160528
Designed for undergraduate classrooms, this is an introduction to differential equations and their applications. The fourth edition incorporates earlier introductory material on bifurcation theory and adds a new chapter on Sturm-Liouville boundary value problems. Computer programmes in C, PASCAL and FORTRAN are presented throughout the text to show the reader how to apply differential equations toward quantitative problems.
(source: Nielsen Book Data)9783540978947 20160528
Used in undergraduate classrooms across the country, this book is a clearly written, rigorous introduction to differential equations and their applications. Fully understandable to students who have had one year of calculus, this book differentiates itself from other differential equations texts through its engaging application of the subject matter to interesting scenarios. This fourth edition incorporates earlier introductory material on bifurcation theory and adds a new chapter on Sturm-Liouville boundary value problems. Computer programs in C, Pascal, and Fortran are presented throughout the text to show the read how to apply differential equations towards quantitative problems.
(source: Nielsen Book Data)9780387978949 20160528
Science Library (Li and Ma)
CHEMENG-300-01