title: Introductory Applications of Partial Differential Equations: With Emphasis on Wave Propagation and Diffusion
author: G. L. Lamb Jr.
description: Designed to provide students with the ability to translate physical situations into mathematical terms. Offers them the opportunity to synthesize their scattered exposure to partial differential equations and to realize the usefulness of various topics within this area. One-dimensional problems, Laplace Transform method, Green's functions, spherical geometry and first order equations are among the subjects discussed.
zlib_text: © Springer International Publishing Switzerland 2015
  
  J. David LoganApplied Partial Differential EquationsUndergraduate Texts in
  Mathematics10.1007/978-3-319-12493-3_1
  
  # 1\. The Physical Origins of Partial Differential Equations
  
  J. David Logan1
  
  (1)
  
  Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska,
  USA
  
  J. David Logan
  
  Email: [dlogan@math.unl.edu](mailto:dlogan@math.unl.edu)
  
  1.1 PDE Models
  
  1.2 Conservation Laws
  
  1.3 Diffusion
  
  1.4 Diffusion and Randomness
  
  1.5 Vibrations and Acoustics
  
  1.6 Quantum Mechanics*
  
  1.7 Heat Conduction in Higher Dimensions
  
  1.8 Laplace’s Equation
  
  1.9 Classification of PDEs
  
  Many important ideas in mathematics are developed within the framework of
  physical science, and mathematical equations, especially partial differential
  equations, provides the language to formulate these ideas. In reverse,
  advances in mathematics provides the stimulus for new advancements in science.
  Over the years mathematicians and scientists extended th