Boundary Value Problems and Partial Differential Equations

For over fifty years, Boundary Value Problems and Partial Differential Equations, Seventh Edition has provided advanced students an accessible and practical introduction to deriving, solving, and interpreting explicit solutions involving partial differential equations with boundary and initial conditions. Fully revised and now in its Seventh Edition, this valued text aims to be comprehensive without affecting the accessibility and convenience of the original. The resource’s main tool is Fourier analysis, but the work covers other techniques, including Laplace transform, Fourier transform, numerical methods, characteristics, and separation of variables, as well, to provide well-rounded coverage. Mathematical modeling techniques are illustrated in derivations, which are widely used in engineering and science. In particular, this includes the modeling of heat distribution, a vibrating string or beam under various boundary conditions and constraints. New to this edition, the text also now uniquely discusses the beam equation. Throughout the text, examples and exercises have been included, pulled from the literature based on popular problems from engineering and science. These include some "outside-the-box" exercises at the end of each chapter, which provide challenging and thought-provoking practice that can also be used to promote classroom discussion. Chapters also include Projects, problems that synthesize or dig more deeply into the material that are slightly more involved than standard book exercises, and which are intended to support team solutions. Additional materials, exercises, animations, and more are also accessible to students via links and in-text QR codes to support practice and subject mastery.

Table of Contents:
1. Ordinary Differential Equations 2. Fourier Series and Integrals 3. The Heat Equation 4. The Wave Equation 5. The Potential Equation 6. Higher Dimensions and Other Coordinates 7. Transform Methods 8. Numerical Methods

About the Author :
David Powers has taught applied mathematics for over 40 years. His research includes matrix theory, graph theory and applications to biochemistry and engineering. Matthew Beauregard is a professor of mathematics at Stephen F. Austin State University (SFA). His research interests are in applied mathematics, particularly mathematical modeling and scientific computing. In this decade, he has mentored over 50 undergraduate students in undergraduate interdisciplinary research activities in applied mathematics. Lynn Greenleaf has worked as a Mission Control engineer on the early missions of NASA’s Space Shuttle, supported multiple space and ground simulation projects, and worked as a senior scientist on ballistic missile defense, including live tests in the Pacific. She recently retired from the Department of Mathematics at Stephen F. Austin State University in Nacogdoches, Texas. Her most recent research interests include mathematical simulation with a special focus on modeling violent storms such as tornadoes and hurricanes. She now lives in northern Colorado. Jonathan Mitchell is an associate professor of mathematics at Stephen F. Austin State University (SFA). His research interests include nonlinear oscillators, epidemiological models, and delay differential equations. Dr Mitchell has facilitated dozens of undergraduate research projects in mathematics and mentored future educators.