It is amusing to realize how much the basic concept of integration by parts is fruitful in mathematics and in mathematical physics. Here are some instances:
- Abel transformation
- Schwinger-Dyson equation
- Malliavin calculus
- Schwartz-Sobolev distributions
- Wick calculus
- Stockes' theorem and Green's theorem
- Chen-Stein method
- Helffer-Sjöstrand formula
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