Abstract
In this chapter we study some classes of partial differential equations, including the heat equation, the Laplace equation, and the wave equation. In particular, based on the study of Fourier series, we find solutions for several equations and several types of boundary conditions. We mainly use the method of separation of variables. In contrast to what happens in all former chapters, here not everything is proved since this would require additional techniques. One notable exception is the proof of existence and uniqueness of solutions for the heat equation under certain assumptions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag London
About this chapter
Cite this chapter
Barreira, L., Valls, C. (2012). Partial Differential Equations. In: Complex Analysis and Differential Equations. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-4008-5_8
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4008-5_8
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4007-8
Online ISBN: 978-1-4471-4008-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)