APM346--2020S > Chapter 3

Section3.2

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christine:
When solving the IBVP questions in section3.2 (e.g. problem3.8 ), I know the way to first write $u=\frac{1} {\sqrt{4kt\pi}} \int_{0}^{\infty}( e^{-\frac{(x-y)^2}{4kt}}-e^{-\frac{(x+y)^2}{4kt}}) g(y) dy$, and solve the integrals by completing the squares. When I solve it I normally need 20-30 minutes to write out the whole thing, however, during tutorial we only have 10 minutes to finish these kinds of questions, are there any simpler ways to solve them?

Victor Ivrii:
Sometimes, for some functions there are shortcuts, but generally not