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This textbook gives an introduction to Partial Differential
Equations (PDEs), for any reader wishing to learn and understand
the basic concepts, theory, and solution techniques of elementary
PDEs. The only prerequisite is an undergraduate course in Ordinary
Differential Equations. This work contains a comprehensive
treatment of the standard second-order linear PDEs, the heat
equation, wave equation, and Laplace's equation. First-order and
some common nonlinear PDEs arising in the physical and life
sciences, with their solutions, are also covered.This textbook
includes an introduction to Fourier series and their properties, an
introduction to regular Sturm-Liouville boundary value problems,
special functions of mathematical physics, a treatment of
nonhomogeneous equations and boundary conditions using methods such
as Duhamel's principle, and an introduction to the finite
difference technique for the numerical approximation of solutions.
All results have been rigorously justified or precise references to
justifications in more advanced sources have been cited. Appendices
providing a background in complex analysis and linear algebra are
also included for readers with limited prior exposure to those
subjects.The textbook includes material from which instructors
could create a one- or two-semester course in PDEs. Students may
also study this material in preparation for a graduate school
(masters or doctoral) course in PDEs.
This textbook gives an introduction to Partial Differential
Equations (PDEs), for any reader wishing to learn and understand
the basic concepts, theory, and solution techniques of elementary
PDEs. The only prerequisite is an undergraduate course in Ordinary
Differential Equations. This work contains a comprehensive
treatment of the standard second-order linear PDEs, the heat
equation, wave equation, and Laplace's equation. First-order and
some common nonlinear PDEs arising in the physical and life
sciences, with their solutions, are also covered.This textbook
includes an introduction to Fourier series and their properties, an
introduction to regular Sturm-Liouville boundary value problems,
special functions of mathematical physics, a treatment of
nonhomogeneous equations and boundary conditions using methods such
as Duhamel's principle, and an introduction to the finite
difference technique for the numerical approximation of solutions.
All results have been rigorously justified or precise references to
justifications in more advanced sources have been cited. Appendices
providing a background in complex analysis and linear algebra are
also included for readers with limited prior exposure to those
subjects.The textbook includes material from which instructors
could create a one- or two-semester course in PDEs. Students may
also study this material in preparation for a graduate school
(masters or doctoral) course in PDEs.
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