Applied Partial Differential Equations

J. David Logan is Willa Cather Professor of Mathematics at the University of Nebraska Lincoln. He received his PhD from The Ohio State University and has served on the faculties at the University of Arizona, Kansas State University, and Rensselaer Polytechnic Institute. For many years he served as a visiting scientist at Los Alamos and Lawrence Livermore National Laboratories. He has published widely in differential equations, mathematical physics, fluid and gas dynamics, hydrogeology, and mathematical biology. Dr. Logan has authored 7 books, among them A First Course in Differential Equations, 2nd ed., published by Springer.

"The aim of this book is to provide the reader with basic ideas encountered in partial differential equations. ... The mathematical content is highly motivated by physical problems and the emphasis is on motivation, methods, concepts and interpretation rather than formal theory. The textbook is a valuable material for undergraduate science and engineering students." (Marius Ghergu, zbMATH 1310.35001, 2015)

• Preface to the Third Edition.- To the Students.- 1: The Physical Origins of Partial Differential Equations.- 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.- 2. Partial Differential Equations on Unbounded Domains.- 2.1 Cauchy Problem for the Heat Equation.- 2.2 Cauchy Problem for the Wave Equation.- 2.3 Well-Posed Problems.- 2.4 Semi-Infinite Domains.- 2.5 Sources and Duhamel’s Principle.- 2.6 Laplace Transforms.- 2.7 Fourier Transforms.- 3. Orthogonal Expansions.- 3.1 The Fourier Method.- 3.2 Orthogonal Expansions.- 3.3 Classical Fourier Series.-4. Partial Differential Equations on Bounded Domains.- 4.1 Overview of Separation of Variables.- 4.2 Sturm–Liouville Problems - 4.3 Generalization and Singular Problems.- 4.4 Laplace's Equation.- 4.5 Cooling of a Sphere.- 4.6 Diffusion inb a Disk.- 4.7 Sources on Bounded Domains.- 4.8 Poisson's Equation*.-5. Applications in the Life Sciences.-5.1 Age-Structured Models.- 5.2 Traveling Waves Fronts.- 5.3 Equilibria and Stability.- References.- Appendix A. Ordinary Differential Equations.- Index.