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Informationen zum Autor Stephen A. Wirkus is an associate professor of mathematics at Arizona State University, where he has been a recipient of the Professor of the Year Award and NSF AGEP Mentor of the Year Award. He has published over 30 papers and technical reports. He completed his Ph.D. at Cornell University under the direction of Richard Rand. Randall J. Swift is a professor of mathematics and statistics at California State Polytechnic University, Pomona, where he has been a recipient of the Ralph W. Ames Distinguished Research Award. He has authored more than 80 journal articles, three research monographs, and three textbooks. He completed his Ph.D. at the University of California, Riverside under the direction of M.M. Rao. Klappentext the Geometry of Differential Equations Existence and Uniqueness for First-Order Equations First-Order Autonomous Equatio Zusammenfassung A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author's successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student's field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged. The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra. Most significantly, computer labs are given in MATLAB®, Mathematica®, and Maple™. The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included. Features MATLAB®, Mathematica®, and Maple™ are incorporated at the end of each chapter All three software packages have parallel code and exercises There are numerous problems of varying difficulty for both the applied and pure math major, as well as problems for engineering, physical science and other students. An appendix that gives the reader a "crash course" in the three software packages Chapter reviews at the end of each chapter to help the students review Projects at the end of each chapter that go into detail about certain topics and introduce new topics that the students are now ready to see Answers to most of the odd problems in the back of the book Inhaltsverzeichnis Traditional First-Order Differential Equations Introduction to First-Order EquationsSeparable Differential Equations Linear Equations Some Physical Models Arising as Separable Equations Exact Equations Special Integrating Factors and Substitution Methods Bernoulli Equation Homogeneous Equations of the Form g(y=x) Geometrical and Numerical Methods for First-Order Equations Direction Fields ...
Autorentext
Stephen A. Wirkus is an associate professor of mathematics at Arizona State University, where he has been a recipient of the Professor of the Year Award and NSF AGEP Mentor of the Year Award. He has published over 30 papers and technical reports. He completed his Ph.D. at Cornell University under the direction of Richard Rand.
Randall J. Swift is a professor of mathematics and statistics at California State Polytechnic University, Pomona, where he has been a recipient of the Ralph W. Ames Distinguished Research Award. He has authored more than 80 journal articles, three research monographs, and three textbooks. He completed his Ph.D. at the University of California, Riverside under the direction of M.M. Rao.
Klappentext
A 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(TM). This second edition reflects the feedback of students and professors who used the first edition in the classroom. Thiis version adds two new chapters to the current text.
Zusammenfassung
A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author's successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded.
The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student's field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged.
The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra.
Most significantly, computer labs are given in MATLAB®, Mathematica®, and Maple™. The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included.
Features
Inhalt
Traditional First-Order Differential Equations
Introduction to First-Order Equations
Separable Differential Equations
Linear Equations
Some Physical Models Arising as Separable Equations
Exact Equations
Special Integrating Factors and Substitution Methods
Bernoulli Equation
Homogeneous Equations of the Form g(y=x)
Geometrical and Numerical Methods for First-Order Equations
Direction Fields|the Geometry of Differential Equations
Existence and Uniqueness for First-Order Equations
First-Order Autonomous Equations|Geometrical Insight
Graphing Factored Polynomials
Bifurcations of Equilibria
Modeling in Population Biology
Nondimensionalization
Numerical Approximation: Euler and Runge-Kutta Methods
An Introduction to Autonomous Second-Order Equations
Elements of Higher-Order Linear Equations
Introduction to Higher-Order Equations
Operator Notation
Linear Independence and the Wronskian
Reduction of Order|the Case n = 2
Numerical Considerations for nth-Order Equations
Essential Topics from Complex Variables
Homogeneous Equations with Constant Coecients
Mechanical and Electrical Vibrations
Techniques of Nonhomogeneous Higher-Order Linear Equations
Nonhomogeneous Equations
Method of Undetermined Coecients via Superposition
Method of Undetermined Coecients via Annihilation
Exponential Response and Complex Replacement
Variation of Parameters
Cauchy-Euler (Equidimensional) Equation
Forced Vibrations
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