Abstract
In this chapter we study topics that form the traditional core of applied mathematics—boundary value problems and orthogonal expansions. These subjects are interrelated in one of the most aesthetic theories in all of mathematics. Topics include Fourier series, Sturm-Liouville problems, and boundary value problems for partial differential equations.
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Notes
- 1.
A formal calculation in mathematics is one done without complete rigor, but can be verified under special assumptions.
- 2.
The integral here is, appropriately, the Lebesgue integral studied in advanced analysis courses rather than the Riemann integral, which is studied in elementary calculus; however, there will be no harm in interpreting the integrals in this text as a Riemann integrals since all of the functions that we examine are Riemann integrable (and therefore Lebesgue integrable).
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© 2015 Springer International Publishing Switzerland
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Logan, J. (2015). Orthogonal Expansions. In: Applied Partial Differential Equations. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-12493-3_3
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DOI: https://doi.org/10.1007/978-3-319-12493-3_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12492-6
Online ISBN: 978-3-319-12493-3
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