DOI link for Transform Methods
Transform Methods book
In Example 1.1.2 we showed that applying a Fourier cosine transform leads to the dual integral equations:
− 2 π
k coth(kh)A(k) cos(kx) dk = 1/h, 0 ≤ x < 1, (4.0.1)
and 2 π
A(k) cos(kx) dk = 0, 1 < x <∞. (4.0.2)
The purpose of this chapter is to illustrate how these dual integral equations are solved. In Sections 4.1 and 4.2 we focus on Fourier-type of integrals while Sections 4.3 and 4.4 treat Fourier-Bessel integrals. Finally Section 4.5 deals with situations where we have a mixture of Fourier series and transforms, Fourier and Fourier-Bessel transforms and Fourier series and Laplace transforms.