Differential Equations: Theory, Technique, and Practice with Boundary Value Problems

ISBN-13: 9781498735018 / Angielski / Twarda / 2015 / 464 str.

Steven G. Krantz

Opis

Differential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge techniques for a contemporary, undergraduate-level, one- or two-semester course on ordinary differential equations. Authored by a widely respected researcher and teacher, the text covers standard topics such as partial differential equations (PDEs), boundary value problems, numerical methods, and dynamical systems. Lively historical notes and mathematical nuggets of information enrich the reading experience by offering perspective on the lives of significant contributors to the discipline. "Anatomy of an Application" sections highlight applications from engineering, physics, and applied science. Problems for review and discovery provide students with open-ended material for further exploration and learning. Streamlined for the interests of engineers, this version:

• Includes new coverage of Sturm-Liouville theory and problems
• Discusses PDEs, boundary value problems, and dynamical systems
• Features an appendix that provides a linear algebra review
• Augments the substantial and valuable exercise sets
• Enhances numerous examples to ensure clarity

A solutions manual is available with qualifying course adoption. Differential Equations: Theory, Technique, and Practice with Boundary Value Problems delivers a stimulating exposition of modeling and computing, preparing students for higher-level mathematical and analytical thinking.

Spis treści

What Is a Differential Equation? Second-Order Linear Equations. Power Series Solutions and Special Functions. Numerical Methods. Fourier Series: Basic Concepts. Sturm–Liouville Problems and Boundary Value Problems. Partial Differential Equations and Boundary Value Problems. Laplace Transforms. Systems of First-Order Equations. The Nonlinear Theory. Appendix: Review of Linear Algebra.

O autorze

Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has written more than 175 scholarly papers and more than 65 books, including the following books published by CRC Press: Foundations of Analysis (2014), Convex Analysis (2014), Real Analysis and Foundations, Third Edition (2013), and Elements of Advanced Mathematics, Third Edition (2012). An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D from Princeton University.