While partial differential equations (PDEs) are fundamental in
mathematics and throughout the sciences, most undergraduate
students are only exposed to PDEs through the method of separation
of variations. This text is written for undergraduate students from
different cohorts with one sole purpose: to facilitate a
proficiency in many core concepts in PDEs while enhancing the
intuition and appreciation of the subject. For mathematics students
this will in turn provide a solid foundation for graduate study. A
recurring theme is the role of concentration as captured by Dirac's
delta function. This both guides the student into the structure of
the solution to the diffusion equation and PDEs involving the
Laplacian and invites them to develop a cognizance for the theory
of distributions. Both distributions and the Fourier transform are
given full treatment. The book is rich with physical motivations
and interpretations, and it takes special care to clearly explain
all the technical mathematical arguments, often with
pre-motivations and post-reflections. Through these arguments the
reader will develop a deeper proficiency and understanding of
advanced calculus. While the text is comprehensive, the material is
divided into short sections, allowing particular issues/topics to
be addressed in a concise fashion. Sections which are more
fundamental to the text are highlighted, allowing the instructor
several alternative learning paths. The author's unique pedagogical
style also makes the text ideal for self-learning.
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