Page 341 - Schaum's Outline of Differential Equations
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324 EIGENFUNCTION EXPANSIONS [CHAP. 33
Supplementary Problems
33.12. Find a Fourier sine series fotf(x) = 1 on (0, 1).
33.13. Find a Fourier sine series for/(x) = x on (0, 3).
2
33.14. Find a Fourier cosine series for/(x) = x on (0, n).
f
33.15. Find a Fourier cosine series for ( x ) = on (0, 3).
33.16. Find a Fourier cosine series fotf(x) = 1 on (0, 7).
f
33.17. Find a Fourier sine series for ( x ) = on (0, 2).
33.18. Find an expansion for/(x) = 1 in terms of the eigenfunctions of the Sturm-Liouville problem y" + *ky = 0; y'(0) = 0,
y(n) = 0.
33.19. Find an expansion fotf(x) = x in terms of the eigenfunctions of the Sturm-Liouville problem y" + 'ky = 0; y(0) = 0,
y'(n) = 0.
33.20. Determine whether the following functions are piecewise continuous on [—1, 5]:
33.21. Which of the following functions are piecewise smooth on [-2, 3]?
