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Lecture 19, 10/5/2022. This page is for Section 1 only.
ACMS 20550: Applied Mathematics Method I
Instructor: Bei Hu, b1hu@nd.edu, Hurley 174A
Chapter 5. Multiple integrals.
- Review of some integration formulas.
- Substitution: For functions like $\exp\;$
$\mm\rule{0ex}{2ex}$
,
$\ln\;$ $\mm\rule{0ex}{2ex}$
,
$\sin\;$ $\mm\rule{0ex}{2ex}$
, $\cos\;$ $\mm\rule{0ex}{2ex}$
, $\cdots$;
use $u= \;$ $\mm\rule{0ex}{2ex}$
,
- Integration by parts: Try to differentiate the following after integration by parts,
(a) $\ln\;$
$\mm\rule{0ex}{2ex}$
, (b) polynomials,
(c) $\cdots$;
- Partial fraction: decompose into
(a) $\frac{A}{x+a}+\frac{B}{x+b}+\cdots$, where $a\neq b$; $\cdots$,
(b) $\frac{Ax+B}{(x+a)^2+b^2}+\cdots$,
(c) $\cdots$;
- Double and tripple integrals.
- Draw a picture;
- Determine the order of integration;
- Determine the upper and lower limit.