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Book
ix, 502 pages : illustrations ; 25 cm
Science Library (Li and Ma)
CHEMENG-100-01
Book
xix, 809 pages : illustrations ; 27 cm
  • Chapter 1 Introduction 1 1.1 Some Basic Mathematical Models-- Direction Fields 1 1.2 Solutions of Some Differential Equations 10 1.3 Classification of Differential Equations 19 1.4 Historical Remarks 26 Chapter 2 First Order Differential Equations 31 2.1 Linear Equations-- Method of Integrating Factors 31 2.2 Separable Equations 42 2.3 Modeling with First Order Equations 51 2.4 Differences Between Linear and Nonlinear Equations 68 2.5 Autonomous Equations and Population Dynamics 78 2.6 Exact Equations and Integrating Factors 95 2.7 Numerical Approximations: Euler's Method 102 2.8 The Existence and Uniqueness Theorem 112 2.9 First Order Difference Equations 122 Chapter 3 Second Order Linear Equations 137 3.1 Homogeneous Equations with Constant Coefficients 137 3.2 Solutions of Linear Homogeneous Equations-- the Wronskian 145 3.3 Complex Roots of the Characteristic Equation 158 3.4 Repeated Roots-- Reduction of Order 167 3.5 Nonhomogeneous Equations-- Method of Undetermined Coefficients 175 3.6 Variation of Parameters 186 3.7 Mechanical and Electrical Vibrations 192 3.8 Forced Vibrations 207 Chapter 4 Higher Order Linear Equations 221 4.1 General Theory of nth Order Linear Equations 221 4.2 Homogeneous Equations with Constant Coefficients 228 4.3 The Method of Undetermined Coefficients 236 4.4 The Method of Variation of Parameters 241 Chapter 5 Series Solutions of Second Order Linear Equations 247 5.1 Review of Power Series 247 5.2 Series Solutions Near an Ordinary Point, Part I 254 5.3 Series Solutions Near an Ordinary Point, Part II 265 5.4 Euler Equations-- Regular Singular Points 272 5.5 Series Solutions Near a Regular Singular Point, Part I 282 5.6 Series Solutions Near a Regular Singular Point, Part II 288 5.7 Bessel's Equation 296 Chapter 6 The Laplace Transform 309 6.1 Definition of the Laplace Transform 309 6.2 Solution of Initial Value Problems 317 6.3 Step Functions 327 6.4 Differential Equations with Discontinuous Forcing Functions 336 6.5 Impulse Functions 343 6.6 The Convolution Integral 350 Chapter 7 Systems of First Order Linear Equations 359 7.1 Introduction 359 7.2 Review of Matrices 368 7.3 Systems of Linear Algebraic Equations-- Linear Independence, Eigenvalues, Eigenvectors 378 7.4 Basic Theory of Systems of First Order Linear Equations 390 7.5 Homogeneous Linear Systems with Constant Coefficients 396 7.6 Complex Eigenvalues 408 7.7 Fundamental Matrices 421 7.8 Repeated Eigenvalues 429 7.9 Nonhomogeneous Linear Systems 440 Chapter 8 Numerical Methods 451 8.1 The Euler or Tangent Line Method 451 8.2 Improvements on the Euler Method 462 8.3 The Runge--Kutta Method 468 8.4 Multistep Methods 472 8.5 Systems of First Order Equations 478 8.6 More on Errors-- Stability 482 Chapter 9 Nonlinear Differential Equations and Stability 495 9.1 The Phase Plane: Linear Systems 495 9.2 Autonomous Systems and Stability 508 9.3 Locally Linear Systems 519 9.4 Competing Species 531 9.5 Predator--Prey Equations 544 9.6 Liapunov's Second Method 554 9.7 Periodic Solutions and Limit Cycles 565 9.8 Chaos and Strange Attractors: The Lorenz Equations 577 Chapter 10 Partial Differential Equations and Fourier Series 589 10.1 Two-Point Boundary Value Problems 589 10.2 Fourier Series 596 10.3 The Fourier Convergence Theorem 607 10.4 Even and Odd Functions 614 10.5 Separation of Variables-- Heat Conduction in a Rod 623 10.6 Other Heat Conduction Problems 632 10.7 TheWave Equation: Vibrations of an Elastic String 643 10.8 Laplace's Equation 658 AppendixA Derivation of the Heat Conduction Equation 669 Appendix B Derivation of theWave Equation 673 Chapter 11 Boundary Value Problems and Sturm--Liouville Theory 677 11.1 The Occurrence of Two-Point Boundary Value Problems 677 11.2 Sturm--Liouville Boundary Value Problems 685 11.3 Nonhomogeneous Boundary Value Problems 699 11.4 Singular Sturm--Liouville Problems 714 11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion 721 11.6 Series of Orthogonal Functions: Mean Convergence 728 Answers to Problems 739 Index 799.
  • (source: Nielsen Book Data)9780470458310 20160612
The 10th edition of "Elementary Differential Equationsand Boundary Value Problems, " like its predecessors, is writtenfrom the viewpoint of the applied mathematician, whose interest indifferential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. Theauthors have sought to combine a sound and accurate (but notabstract) exposition of the elementary theory of differentialequations with considerable material on methods of solution, analysis, and approximation that have proved useful in a widevariety of applications. While the general structure of the bookremains unchanged, some notable changes have been made to improvethe clarity and readability of basic material about differentialequations and their applications. In addition to expandedexplanations, the 10th edition includes new problems, updatedfigures and examples to help motivate students.The book is written primarily for undergraduate students ofmathematics, science, or engineering, who typically take a courseon differential equations during their first or second year ofstudy. The main prerequisite for reading the book is a workingknowledge of calculus, gained from a normal two or three semestercourse sequence or its equivalent. Some familiarity with matriceswill also be helpful in the chapters on systems of differentialequations.WileyPLUS sold separately from text.
(source: Nielsen Book Data)9780470458310 20160612
Science Library (Li and Ma)
CHEMENG-100-01
Book
xx, 602 pages : illustrations ; 24 cm.
  • Ch. 1. Introductory Concepts
  • pt. I. Modeling for Process Dynamics
  • Ch. 2. Modeling Tools for Process Dynamics
  • Ch. 3. Inversion by Partial Fractions
  • pt. II. Linear Open-Loop Systems
  • Ch. 4. Response of First-Order Systems
  • Ch. 5. Physical Examples of First-Order Systems
  • Ch. 6. Response of First-Order Systems in Series
  • Ch. 7. Higher-Order Systems: Second-Order and Transportation Lag
  • pt. III. Linear Closed-Loop Systems
  • Ch. 8. The Control System
  • Ch. 9. Controllers and Final Control Elements
  • Ch. 10. Block Diagram of a Chemical-Reactor Control System
  • Ch. 11. Closed-Loop Transfer Functions
  • Ch. 12. Transient Response of Simple Control Systems
  • Ch. 13. Stability
  • Ch. 14. Root Locus.
The third edition of "Process Systems Analysis and Control" retains the excellent style for which this book is well known: short, clearly written chapters. The book is an ideal teaching and learning tool for a semester-long undergraduate chemical engineering course in process dynamics and control. It avoids the encyclopedic approach that many texts on this topic fall into. The third edition is updated to include new topics, including model predictive control and digital control, that are introduced at a level appropriate for the undergraduate chemical engineering curriculum. Computer examples using MATLAB and Simulink have been introduced throughout the book to supplement and enhance standard hand-solved examples. These packages allow the easy construction of block diagrams and quick analysis of control concepts to enable the student to explore "what-if" type problems that would be much more difficult and time consuming by hand. Many new homework problems have been added to each chapter. The new problems are a mixture of hand-solved and computer exercises. One-page capsule summaries have been added to the end of each chapter to help students review and study the most important concepts in each chapter.
(source: Nielsen Book Data)9780071121866 20181015
Process Systems Analysis and Control, third edition retains the clarity of presentation for which this book is well known. It is an ideal teaching and learning tool for a semester-long undergraduate chemical engineering course in process dynamics and control. It avoids the encyclopedic approach of many other texts on this topic. Computer examples using MATLAB(R) and Simulink(R) have been introduced throughout the book to supplement and enhance standard hand-solved examples. These packages allow the easy construction of block diagrams and quick analysis of control concepts to enable the student to explore "what-if" type problems that would be much more difficult and time consuming by hand.
(source: Nielsen Book Data)9780073397894 20181015
Science Library (Li and Ma)
CHEMENG-100-01
Book
xix, 1324 p. : ill. ; 26 cm.
  • I. ORDINARY DIFFERENTIAL EQUATIONS. 1. Introduction to Differential Equations. 2. Equations of First Order. 3. Linear Differential Equations of Second Order and Higher. 4. Power Series Solutions. 5. Laplace Transform. 6. Quantitative Methods: Numerical Solution of Differential Equations. 7. Qualitative Methods: Phase Plane and Nonlinear Differential Equations. II. LINEAR ALGEBRA. 8. Systems of Linear Algebraic Equations-- Gauss Elimination. 9. Vector Space. 10. Matrices and Linear Equations. 11. The Eigenvalue Problem. 12. Extension to Complex Case (Optional). III. SCALAR and VECTOR FIELD THEORY. 13. Differential Calculus of Functions of Several Variables. 14. Vectors in 3-Space. 15.Curves, Surfaces, and Volumes. 16. Scalar and Vector Field Theory. IV. FOURIER SERIES AND PARTIAL DIFFERENTIAL EQUATIONS. 17. Fourier Series, Fourier Integral, Fourier Transform. 18. Diffusion Equation. 19. Wave Equation. 20. Laplace Equation. V. COMPLEX VARIABLE THEORY. 21. Functions of a Complex Variable. 22. Conformal Mapping. 23. The Complex Integral Calculus. 24. Taylor Series, Laurent Series, and the Residue Theorem. Appendix A: Review of Partial Fraction Expansions. Appendix B: Existence and Uniqueness of Solutions of Systems of Linear Algebraic Equations. Appendix C: Table of Laplace Transforms. Appendix D: Table of Fourier Transforms. Appendix E: Table of Fourier Cosine and Sine Transforms. Appendix F: Table of Conformal Maps.
  • (source: Nielsen Book Data)9780133214314 20160528
Appropriate for one- or two-semester Advanced Engineering Mathematics courses in departments of Mathematics and Engineering. This clear, pedagogically rich book develops a strong understanding of the mathematical principles and practices that today's engineers and scientists need to know. Equally effective as either a textbook or reference manual, it approaches mathematical concepts from a practical-use perspective making physical applications more vivid and substantial. Its comprehensive instructional framework supports a conversational, down-to-earth narrative style offering easy accessibility and frequent opportunities for application and reinforcement.
(source: Nielsen Book Data)9780133214314 20160528
Science Library (Li and Ma)
CHEMENG-100-01