Boundary Value Problems and Partial Differential Equations, Seventh Edition, remains the preeminent resource for upper division undergraduate and graduate students seeking to derive, solve and interpret explicit solutions involving partial differential equations with boundary and initial conditions. Fully revised to reflect advances since the 2009 edition, this book aims to be comprehensive without affecting the accessibility and convenience of the original. The main tool is Fourier analysis, but other techniques including Laplace transform, numerical methods, and separation of variables are introduced as well. Examples and exercises are carefully selected from the literature based on popular problems from engineering and science.
Features 35% new or revised content compared to the 2009 edition, reflecting a decade of advances. The book discusses all-new modeling techniques with derivations, which are often critically important in engineering. Includes coverage of elasticity problems, focusing particularly on Euler beam theory, as well as all new content on vibrating beams in wave equations.
- Introduces students to mathematical modeling leading to explicit solutions for ordinary and partial differential equations
- Provides a palette of methods including separation of variables, Laplace transforms, and numerical methods
- Contains 1000+ exercises and numerous examples and case studies drawn from the literature
- Includes an Instructor's Manual and Student Solutions Manual
1. Ordinary Differential Equations2. Fourier Series and Integrals3. The Heat Equation4. The Wave Equation5. The Potential Equation6. Euler Beam (NEW)7. Higher Dimensions and Other Coordinates8. Laplace Transform9. Numerical Methods
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.
