Successful for over 40 years, Boundary Value Problems and Partial Differential Equations 7th 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, the work 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. NEW TO THIS EDITION: 35% new or revised compared to the 2009 edition reflects a decade of advances Discusses all-new modelling techniques with derivations - often critically important in engineering Chapter-length coverage of elasticity problems, focusing particularly on Euler beam theory All-new coverage of 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 Accompanied by Instructor's Manual and Student Solutions Manual.