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A Course in Ordinary Differential Equations, 2nd Editi~ above Find the book in ~ CRC Press or at Amazon.You can see reviews of the first edition (both professional and student) at Amazon.com. A Course in Differential Equations with Boundary Value Problems, 2nd Edition by Wirkus, Swift, and Szypowski is now published!! Click on the book to the left to go to the webpage for it.For A Course in Ordinary Differential Equations (book to the right), find us on ns MATLAB website,Maple website, or Mathematica website.Additional information can be found by clicking on the topics below or scrolling down the page.SummaryTable of ContentsAuthor BiographiesFeaturesNew to the Second Edition Computer Labs Typos and Errata
SummaryA Course in Ordinary Differential Equations, Second Edition teaches students how to use analytical and numerical solution methods in typical engineering, physics, and mathematics applications. Lauded for its extensive computer code and student-friendly approach, the first edition of this popular textbook was the first on ordinary differential equations (ODEs) to include instructions on using MATLAB, Mathematica, and Maple. This second edition reflects the feedback of students and professors who used the first edition in the classroom.(back to top)
Table of ContentsChapter 1: Traditional First-Order Differential Equations 1.1. Introduction to First-Order Equations 1.2. Separable Differential Equations 1.3. Linear Equation 1.4. Some Physical Models Arising as Separable Equation 1.5. Exact Equation 1.6. Special Integrating Factors and Substitution MethodsChapter 2: Geometrical and Numerical Methods for First-Order Equation 2.1. Direction Fields---the Geometry of Differential Equation 2.2. Existence and Uniqueness for First-Order Equation 2.3. First-Order Autonomous Equations---Geometrical Insight 2.4. Modeling in Population Biology 2.5. Numerical Approximation: Euler and Runge-Kutta Methods 2.6. An Introduction to Autonomous Second-Order EquationsChapter 3: Elements of Higher-Order Linear Equations 3.1. Introduction to Higher-Order Equations 3.2. Linear Independence and the Wronskia 3.3. Reduction of Order---the Case n = 2 3.4. Numerical Considerations for nth-Order Equations 3.5. Essential Topics from Complex Variables 3.6. Homogeneous Equations with Constant Coefficients 3.7. Mechanical and Electrical VibrationsChapter 4: Techniques of Nonhomogeneous Higher-Order Linear Equations 4.1. Nonhomogeneous Equation 4.2. Method of Undetermined Coefficients via Superplace 4.3. Method of Undetermined Coefficients via Annihilation 4.4. Exponential Response and Complex Replacement 4.5. Variation of Parameter 4.6. Cauchy-Euler (Equidimensional) Equati~ above 4.7. Forced VibrationsChapter 5: Fundamentals of Systems of Differential Equation 5.1. Useful Terminology 5.2. Gaussian Elimination 5.3. Vector Spaces and Subspaces 5.4. Eigenvalues and Eigenvectorns 5.5. A General Method, Part I: Solving Systems with Real & Distinct or Complex Eigenvalues 5.6. A General Method, Part II: Solving Systems with Repeated Real Eigenworths 5.7. Matrix Exponentialns 5.8. Solving Linear Nonhomogeneous Systems of EquationsChapter 6: Geometrical Approaches and Applications of Systems of First-Order Equations 6.1. An Introduction to the Phase Plane 6.2. Nonlinear Equations and Phase Plane Analysins 6.3. Bifurcation 6.4. Epidemiological Models 6.5. Models in EcologyChapter 7: Laplace Transdevelops 7.1. Overview 7.2. Fundamentals of the Laplace Transform 7.3. The Inverse Laplace Transcreate 7.4. Translated Functions, Delta Function, and Periodic Function 7.5. The s-Domain and Polens 7.6. Solving Linear Systems using Laplace Transdevelops 7.7. The ConvolutionChapter 8: Series Methods 8.1. Power Series Representations of Function 8.2. The Power Series Method 8.3. Ordinary and Singular Points 8.4. The Method of Frobenius 8.5. Bessel FunctionsAppendix A: An Introduction to MATLAB, Maple, and Mathematica A.1. MATLAB A.2. Maple A.3. MathematicaApprendix B: Selected Topics from Linear Algebra B.1. A Primer on Matrix Algebra B.2. Matrix Inverses, Cramer"s Rule B.3. Linear Transformations B.4. Coordinates and Change of BasisAnswers to Odd ProblemsReferencesIndexA Review, Computer Labs, and Projects appear at the end of each chapter.(back to top)
Author BiographiesStephen A. Wirkus completed his Ph.D. at Cornell University under the direction of Richard Rand. He began guiding undergraduate research projects while in graduate school and came to Cal Poly Pomona in 2000 after being a Visiting Professor at Cornell for a year. He co-founded the Applied Mathematical Sciences Summer Institute (AMSSI), an undergraduate research program jointly hosted by Loyola Marymount University, that ran from 2005 through 2007. He came to Arizona State University in 2007 as a tenured Associate Professor and won the 2013 Professor of the Year Award at thedailysplash.tv as well as the 2011 NSF AGEP Mentor of the Year award. He was a Visiting MLK Professor at the Massachusetts Institute of Technology in 2013-2014. He has guided over 80 undergraduate students in research and has served as Chair for 4 M.S. students, and 2 Ph.D. students. He has over 30 thedailysplash.tvations and technical reports with over 40 students and has received grants from the NSF and NSA for guiding undergraduate research. Randall J. Swift completed his Ph.D. at the University of California, Riverside under the direction of M. M. Rao. He began his career at Western Kentucky University and taught there for nearly a decade before moving to Cal Poly Pomona in 2001 as a tenured Associate Professor. He is active in research and teaching, having authored more than 80 journal articles, three research monographs and three textbooks in addition to serving as Chair for 25 M.S. students. Now a Professor, he received the 2011-12 Ralph W. Ames Distinguished Research Award from the College of Science at Cal Poly Pomona. The award honors Swift for his outstanding research in both pure and applied mathematics, and his contributions to the mathematics field as a speaker, journal editor, and principal investigator on numerous grants. He was also a Visiting Professor in 2007-2008 at The Australian National University in Canberra Australia as well as having taught at the Claremont Colleges.(back to top)
FeaturesDescribes analytical and numerical methods for studying ODEsShows students how to effectively use MATLAB, Maple, and Mathematica in practice, assuming no prior knowledge of the software packagesCovers essential linear algebra topics, such as eigenvectors, bases, and transformations, to improve students" understanding of differential equationsIncludes numerous problems of varying levels of difficulty for applied and pure math majors as well as for engineers and other nonmathematiciansOffers answers to most of the odd problems in the back of the bookContains reviews and projects at the end of each chapterSolutions manual available upon qualifying course adoption(back to top)
New to the Second EditionMoves the computer codes to Computer Labs at the end of each chapter, which gives professors flexibility in using the technologyCovers linear systems in their entirety before addressing applications to nonlinear systemsIncorporates the latest versions of MATLAB, Maple, and MathematicaIncludes new sections on complex variables, the exponential response formula for solving nonhomogeneous equations, forced vibrations, and nondimensionalizationHighlights new applications and modeling in many fieldsPresents exercise sets that progress in difficultyContains color graphs to help students better understand crucial concepts in ODEsProvides updated and expanded projects in each chapterSuitable for a first undergraduate course, the book includes all the basics necessary to prepare students for their future studies in mathematics, engineering, and the sciences. It presents the syntax from MATLAB, Maple, and Mathematica to give students a better grasp of the theory and gain more insight into real-world problems.
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Along with covering traditional topics, the text describes a number of modern topics, such as direction fields, phase lines, the Runge-Kutta method, and epidemiological and ecological models. It also explains concepts from linear algebra so that students acquire a thorough understanding of differential equations.(back to top)
Typos and Errata