Abstract
Our treatment of differential equations, with the exception of SOLDEs with constant coefficients, did not consider inhomogeneous equations. At this point, however, we can put into use one of the most elegant pieces of machinery in higher mathematics, Green’s functions, to solve inhomogeneous differential equations.
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- 1.
Here and elsewhere in this chapter, a prime over a GF indicates differentiation with respect to its first argument.
- 2.
The boundary conditions on v ∗ should not depend on the choice of u.
- 3.
The lemma applies to all linear DOs, not just second order ones.
References
Birkhoff, G., Rota, G.-C.: Ordinary Differential Equations, 3rd edn. Wiley, New York (1978)
Stakgold, I.: Green’s Functions and Boundary Value Problems. Wiley, New York (1979)
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Hassani, S. (2013). Green’s Functions in One Dimension. In: Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-01195-0_20
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DOI: https://doi.org/10.1007/978-3-319-01195-0_20
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