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Book
xix, 756 p. : ill. ; 24 cm.
This book emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, Green's functions, and transform methods. This text is ideal for readers interested in science, engineering, and applied mathematics.
(source: Nielsen Book Data)9780321797056 20160608
Engineering Library (Terman)
CME-204-01, ME-300B-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
Engineering Library (Terman)
CME-204-01, ME-300B-01
Book
xxi, 1113, 109, 130 p. : col. ill. ; 26 cm.
The tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. It goes into the following topics at great depth differential equations, partial differential equations, Fourier analysis, vector analysis, complex analysis, and linear algebra/differential equations.
(source: Nielsen Book Data)9780470458365 20160610
Green Library, Engineering Library (Terman)
CME-204-01, ME-300B-01, CME-102-01
Book
x, 454 p. : ill. ; 24 cm.
  • Chapter 1: Where PDEs Come From 1.1 What is a Partial Differential Equation? 1.2 First-Order Linear Equations 1.3 Flows, Vibrations, and Diffusions 1.4 Initial and Boundary Conditions 1.5 Well-Posed Problems 1.6 Types of Second-Order EquationsChapter 2: Waves and Diffusions 2.1 The Wave Equation 2.2 Causality and Energy 2.3 The Diffusion Equation 2.4 Diffusion on the Whole Line 2.5 Comparison of Waves and DiffusionsChapter 3: Reflections and Sources 3.1 Diffusion on the Half-Line 3.2 Reflections of Waves 3.3 Diffusion with a Source 3.4 Waves with a Source 3.5 Diffusion RevisitedChapter 4: Boundary Problems 4.1 Separation of Variables, The Dirichlet Condition 4.2 The Neumann Condition 4.3 The Robin ConditionChapter 5: Fourier Series 5.1 The Coefficients 5.2 Even, Odd, Periodic, and Complex Functions 5.3 Orthogonality and the General Fourier Series 5.4 Completeness 5.5 Completeness and the Gibbs Phenomenon 5.6 Inhomogeneous Boundary ConditionsChapter 6: Harmonic Functions 6.1 Laplace's Equation 6.2 Rectangles and Cubes 6.3 Poisson's Formula 6.4 Circles, Wedges, and AnnuliChapter 7: Green's Identities and Green's Functions 7.1 Green's First Identity 7.2 Green's Second Identity 7.3 Green's Functions 7.4 Half-Space and SphereChapter 8: Computation of Solutions 8.1 Opportunities and Dangers 8.2 Approximations of Diffusions 8.3 Approximations of Waves 8.4 Approximations of Laplace's Equation 8.5 Finite Element MethodChapter 9: Waves in Space 9.1 Energy and Causality 9.2 The Wave Equation in Space-Time 9.3 Rays, Singularities, and Sources 9.4 The Diffusion and Schrodinger Equations 9.5 The Hydrogen AtomChapter 10: Boundaries in the Plane and in Space 10.1 Fourier's Method, Revisited 10.2 Vibrations of a Drumhead 10.3 Solid Vibrations in a Ball 10.4 Nodes 10.5 Bessel Functions 10.6 Legendre Functions 10.7 Angular Momentum in Quantum MechanicsChapter 11: General Eigenvalue Problems 11.1 The Eigenvalues Are Minima of the Potential Energy 11.2 Computation of Eigenvalues 11.3 Completeness 11.4 Symmetric Differential Operators 11.5 Completeness and Separation of Variables 11.6 Asymptotics of the EigenvaluesChapter 12: Distributions and Transforms 12.1 Distributions 12.2 Green's Functions, Revisited 12.3 Fourier Transforms 12.4 Source Functions 12.5 Laplace Transform TechniquesChapter 13: PDE Problems for Physics 13.1 Electromagnetism 13.2 Fluids and Acoustics 13.3 Scattering 13.4 Continuous Spectrum 13.5 Equations of Elementary ParticlesChapter 14: Nonlinear PDEs 14.1 Shock Waves 14.2 Solitions 14.3 Calculus of Variations 14.4 Bifurcation Theory 14.5 Water WavesAppendix A.1 Continuous and Differentiable Functions A.2 Infinite Sets of Functions A.3 Differentiation and Integration A.4 Differential Equations A.5 The Gamma FunctionReferencesAnswers and Hints to Selected ExercisesIndex.
  • (source: Nielsen Book Data)9780470054567 20160528
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). This second edition of "Partial Differential Equations" provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs, the wave, heat and Lapace equations. In this book, advanced concepts are introduced frequently but with the least possible technicalities. This book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
(source: Nielsen Book Data)9780470385531 20160527
Engineering Library (Terman)
CME-204-01, ME-300B-01
Book
1 v. (various pagings) : ill. ; 27 cm.
  • PART A: ORDINARY DIFFERENTIAL EQUATIONS (ODE'S). Chapter 1. First-Order ODE's. Chapter 2. Second Order Linear ODE's. Chapter 3. Higher Order Linear ODE's. Chapter 4. Systems of ODE's Phase Plane, Qualitative Methods. Chapter 5. Series Solutions of ODE's Special Functions. Chapter 6. Laplace Transforms. PART B: LINEAR ALGEBRA, VECTOR CALCULUS. Chapter 7. Linear Algebra: Matrices, Vectors, Determinants: Linear Systems. Chapter 8. Linear Algebra: Matrix Eigenvalue Problems. Chapter 9. Vector Differential Calculus: Grad, Div, Curl. Chapter 10. Vector Integral Calculus: Integral Theorems. PART C: FOURIER ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS. Chapter 11. Fourier Series, Integrals, and Transforms. Chapter 12. Partial Differential Equations (PDE's). Chapter 13. Complex Numbers and Functions. Chapter 14. Complex Integration. Chapter 15. Power Series, Taylor Series. Chapter 16. Laurent Series: Residue Integration. Chapter 17. Conformal Mapping. Chapter 18. Complex Analysis and Potential Theory. PART E: NUMERICAL ANALYSIS SOFTWARE. Chapter 19. Numerics in General. Chapter 20. Numerical Linear Algebra. Chapter 21. Numerics for ODE's and PDE's. PART F: OPTIMIZATION, GRAPHS. Chapter 22. Unconstrained Optimization: Linear Programming. Chapter 23. Graphs, Combinatorial Optimization. PART G: PROBABILITY-- STATISTICS. Chapter 24. Data Analysis: Probability Theory. Chapter 25. Mathematical Statistics. Appendix 1: References. Appendix 2: Answers to Odd-Numbered Problems. Appendix 3: Auxiliary Material. Appendix 4: Additional Proofs. Appendix 5: Tables. Index.
  • (source: Nielsen Book Data)9780471728979 20160528
  • How to Use this Student Solutions Manual and Study Guide.PART A: ORDINARY DIFERENTIAL EQUATIONS (ODEs).Chapter 1. First-Order ODEs.Chapter 2. Second-Order Linear ODEs.Chapter 3. Higher Order Linear ODEs.Chapter 4. Systems of ODEs. Phase Plane. Qualitative Methods.Chapter 5. Series Solutions of ODEs. Special Functions.Chapter 6. Laplace Transforms.PART B: LINEAR ALGEBRA, VECTOR CALCULUS.Chapter 7. Matrices, Vectors, Determinants. Linear Systems.Chapter 8. Linear Algebra: Matrix Eigenvalue Problems.Chapter 9. Vector Differential Calculus. Grad, Div, Curl.Chapter 10. Vector Integral Calculus. Integral Theorems.PART C: FOURIER ANALYSIS. PARTIAL DIFFERENTIAL EQUATIONS.Chapter 11. Fourier Series, Integrals, and Transforms.Chapter 12. Partial Differential Equations (PDEs).PART D: COMPLEX ANALYSIS.Chapter 13. Complex Numbers and Functions.Chapter 14. Complex Integration.Chapter 15. Power Series, Taylor Series.Chapter 16. Laurent Series. Residue Integration.Chapter 17. Conformal Mapping.Chapter 18. Complex Analysis and Potential theory.PART E: NUMERIC ANALYSIS.Chapter 19. Numerics in General.Chapter 20. Numeric Linear Algebra.Chapter 21. Numerics for ODEs and PDEs.PART F: OPTIMIZATION, GRAPHS.Chapter 22. Unconstrained Optimization. Linear Programming.Chapter 23. Graphs and Combinatorial Optimization.PART G: PROBABILITY, STATISTICS.Chapter 24. Data Analysis. Probability Theory.Chapter 25. Mathematical Statistics.Photo Credits P1.
  • (source: Nielsen Book Data)9780471726449 20160528
  • Introduction, General Commands.PART A. ORDINARY DIFFERENTAIL EQUATIONS (ODEs).Chapter 1. First-Order ODEs.Chapter 2 and 3. Linear ODEs of Second and Higher Order.Chapter 4. Systems of ODEs. Phase Plane, Qualitative Methods.Chapter 5. Series Solution of ODEs.Chapter 6. Laplace Transform Method for Solving ODEs.PART B. LINEAR ALGEBRA, VECTOR CALCULUS.Chapter 7. Matrices, Vectors, Determinants. Linear Systems of Equations.Chapter 8. Matrix Eigenvalue Problems.Chapter 9. Vector Differential Calculus Grad, Div, Curl.Chapter 10. Vector Integral Calculus. Integral Theorems.PART C. FOURIER ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS (PDEs).Chapter 11. Fourier Series, Integrals, and Transforms.Chapter 12. Partial Differential Equations (PDEs).PART D. COMPLEX ANALYSIS.CHAPTER 13. AND 17. Complex Numbers and Functions. Conformal Mapping.Chapter 14. Complex Integration.Chapter 15. Power Series, Taylor Series.Chapter 16. Laurent Series. Residue Integration.Chapter 17. See before.Chapter 18. Complex Analysis in Potential Theory.PART E. NUMERIC ANALYSIS.Chapter 19. Numerics in General.Chapter 20. Numeric Linear Algebra.Chapter 21. Numerics for ODEs and PDEs.PART F. OPTIMIZATION GRAPHS.Chapter 22. Unconstrained Optimization, Linear Programming.Chapter 23. No examples, no problems.PART G. PROBABILITY AND STATISTICS.Chapter 24. Data Analysis. Probability Theory.Chapter 25. Mathematical Statistics.Appendix 1. References.Appendix 2. Answers to Odd-Numbered Problems.Index.
  • (source: Nielsen Book Data)9780471726463 20160528
This market leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises and self contained subject matter parts for maximum flexibility. Thoroughly updated and streamlined to reflect new developments in the field, the ninth edition of this best-selling text features modern engineering applications and the uses of technology. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. The material is arranged into seven independent parts: ODE; Linear Algebra, Vector Calculus; Fourier Analysis and Partial Differential Equations; Complex Analysis; Numerical methods; Optimization, graphs; and Probability and Statistics.
(source: Nielsen Book Data)9780471728979 20160528
Engineering Library (Terman)
CME-204-01, ME-300B-01
Book
xviii, 769 p. : ill. ; 24 cm.
  • 1. Heat Equation. 2. Method of Separation of Variables. 3. Fourier Series. 4. Vibrating Strings and Membranes. 5. Sturm-Liouville Eigenvalue Problems. 6. Finite Difference Numerical Methods for Partial Differential Equations. 7. Partial Differential Equations with at Least Three Independent Variables. 8. Nonhomogeneous Problems. 9. Green's Functions for Time-Independent Problems. 10. Infinite Domain Problems--Fourier Transform Solutions of Partial Differential Equations. 11. Green's Functions for Wave and Heat Equations. 12. The Method of Characteristics for Linear and Quasi-Linear Wave Equations. 13. A Brief Introduction to Laplace Transform Solution of Partial Differential Equations. 14. Topics: Dispersive Waves, Stability, Nonlinearity, and Perturbation Methods. Bibliography. Selected Answers to Starred Exercises. Index.
  • (source: Nielsen Book Data)9780130652430 20160528
Appropriate for an elementary or advanced undergraduate first course of varying lengths. Also appropriate for beginning graduate students. Its in-depth elementary presentation is intended primarily for students in science, engineering, and applied mathematics. Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations.
(source: Nielsen Book Data)9780130652430 20160528
Engineering Library (Terman)
CME-204-01, ME-300B-01
Book
xvi, 745 p. : ill. (some col.) ; 26 cm.
  • First Order Differential Equations-- Second Order Linear Equations-- Higher Order Linear Equations-- Series Solutions of Second Order Linear Equations-- The Laplace Transform-- Systems of First Order Linear Equations-- Numerical Methods-- Nonlinear Differential Equations and Stability-- Partial Differential Equations and Fourier Series-- Boundary Value Problems and Sturm-Liouville Theory-- Answers to Problems-- Index.
  • (source: Nielsen Book Data)9780471319993 20160527
Written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year. The main prerequisite is a working knowledge of calculus. The environment in which instructors teach, and students learn differential equations has changed enormously in the past few years and continues to evolve at a rapid pace. Computing equipment of some kind, whether a graphing calculator, a notebook computer, or a desktop workstation is available to most students. The seventh edition of this classic text reflects this changing environment, while at the same time, it maintains its great strengths - a contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. In addition many new problems have been added and a reorganisation of the material makes the concepts even clearer and more comprehensible. Like its predecessors, this edition is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of differential equations as they apply to engineering and the sciences.
(source: Nielsen Book Data)9780471319993 20160527
Engineering Library (Terman)
CME-204-01, ME-300B-01
Book
xii, 471 p. : ill. ; 25 cm.
  • One--Dimensional Problems--Separation of Variables. Laplace Transform Method. Two and Three Dimensions. Green's Functions. Spherical Geometry. Fourier Transform Methods. Perturbation Methods. Generalizations and First Order Equations. Selected Topics. Appendices. References. Index.
  • (source: Nielsen Book Data)9780471311232 20160528
INTRODUCTORY APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS With Emphasis on Wave Propagation and Diffusion This is the ideal text for students and professionals who have some familiarity with partial differential equations, and who now wish to consolidate and expand their knowledge. Unlike most other texts on this topic, it interweaves prior knowledge of mathematics and physics, especially heat conduction and wave motion, into a presentation that demonstrates their interdependence. The result is a superb teaching text that reinforces the reader's understanding of both mathematics and physics. Rather than presenting the mathematics in isolation and out of context, problems in this text are framed to show how partial differential equations can be used to obtain specific information about the physical system being analyzed. Designed for upper-level students, professionals and researchers in engineering, applied mathematics, physics, and optics, Professor Lamb's text is lucid in its presentation and comprehensive in its coverage of all the important topic areas, including: * One-Dimensional Problems * The Laplace Transform Method * Two and Three Dimensions * Green's Functions * Spherical Geometry * Fourier Transform Methods * Perturbation Methods * Generalizations and First Order Equations In addition, this text includes a supplementary chapter of selected topics and handy appendices that review Fourier Series, Laplace Transform, Sturm-Liouville Equations, Bessel Functions, and Legendre Polynomials.
(source: Nielsen Book Data)9780471311232 20160528
Engineering Library (Terman), eReserve
CME-204-01, ME-300B-01
Book
ix, 425 p. : ill. ; 25 cm.
  • Where PDE's come from-- waves and diffusions-- reflections and sources-- boundary problems-- Fourier series-- harmonic functions-- Green's identities and Green's functions-- computation of solutions-- three-dimensional waves.
  • (source: Nielsen Book Data)9780471548683 20160527
This volume covers the fundamental properties of partial differential equations (PDEs) and the proven techniques useful in analyzing them. It uses a broad approach to illustrate the rich diversity of phenomena such as the vibrations of solids, fluid flow, molecular structure, photon and electron interactions, and the radiation of electomagnetic waves, as well as the role PDEs play in modern mathematics, especially geometry and analysis.
(source: Nielsen Book Data)9780471548683 20160527
Engineering Library (Terman)
CME-204-01, ME-300B-01
Book
xiii, 733 p. : ill. ; 24 cm.
  • 1. Ordinary Differential Equations. 2. The Laplace Transform. 3. Numerical Methods for Solving Ordinary Differential Equations. 4. Series Solutions of Differential Equations-- Special Functions. Boundary-Value Problems and Characteristic-Function Representations. 5. Vector Analysis. 6. Topics in Higher-Dimensional Calculus. 7. Partial Differential Equations. 8. Solutions of Partial Differential Equations. 9. Solutions of Partial Differential Equations of Mathematical Physics. 10. Functions of a Complex Variable. 11. Applications of Analytic Function Theory.
  • (source: Nielsen Book Data)9780130111890 20160528
Two-term text for juniors in physics and engineering. Most often taught out of math departments. Can also work as a good applied math text.
(source: Nielsen Book Data)9780130111890 20160528
Engineering Library (Terman)
CME-204-01, ME-300B-01
Book
xi, 458 p. illus. 27 cm.
Engineering Library (Terman)
CME-204-01, ME-300B-01
Book
ix, 446 p. ; 27 cm.
Engineering Library (Terman)
CME-204-01, ME-300B-01
Book
ix, 446 p. 26 cm.
Engineering Library (Terman)
CME-204-01, ME-300B-01
Engineering Library (Terman)
CME-204-01, ME-300B-01
Engineering Library (Terman)
CME-204-01, ME-300B-01