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Preface

Published online by Cambridge University Press:  05 June 2012

Marcus Pivato
Affiliation:
Trent University, Peterborough, Ontario
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Summary

This is a textbook for an introductory course on linear partial differential equations (PDEs) and initial/boundary value problems (I/BVPs). It also provides a mathematically rigorous introduction to Fourier analysis (Chapters 7, 8, 9, 10, and 19), which is the main tool used to solve linear PDEs in Cartesian coordinates. Finally, it introduces basic functional analysis (Chapter 6) and complex analysis (Chapter 18). The first is necessary to characterize rigorously the convergence of Fourier series, and also to discuss eigenfunctions for linear differential operators. The second provides powerful techniques to transform domains and compute integrals, and also offers additional insight into Fourier series.

This book is not intended to be comprehensive or encyclopaedic. It is designed for a one-semester course (i.e. 36–40 hours of lectures), and it is therefore strictly limited in scope. First, it deals mainly with linear PDEs with constant coefficients. Thus, there is no discussion of characteristics, conservation laws, shocks, variational techniques, or perturbation methods, which would be germane to other types of PDEs. Second, the book focuses mainly on concrete solution methods to specific PDEs (e.g. the Laplace, Poisson, heat, wave, and Schrödinger equations) on specific domains (e.g. line segments, boxes, disks, annuli, spheres), and spends rather little time on qualitative results about entire classes of PDEs (e.g. elliptic, parabolic, hyperbolic) on general domains.

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Publisher: Cambridge University Press
Print publication year: 2010

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  • Preface
  • Marcus Pivato, Trent University, Peterborough, Ontario
  • Book: Linear Partial Differential Equations and Fourier Theory
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511810183.001
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  • Preface
  • Marcus Pivato, Trent University, Peterborough, Ontario
  • Book: Linear Partial Differential Equations and Fourier Theory
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511810183.001
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Preface
  • Marcus Pivato, Trent University, Peterborough, Ontario
  • Book: Linear Partial Differential Equations and Fourier Theory
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511810183.001
Available formats
×