Mat-F March 14, 2005 Line-, surface-, and volume-integrals Åke Nordlund Niels Obers, Sigfus Johnsen Kristoffer Hauskov Andersen Peter Browne Rønne

News on the web Course summary what’s most important Trial examination examples so far two sets

11: Line-, surface-, and volume-integrals Why? Because most laws of physics need these conservation laws electrodynamics … How? Three gentlemen’s theorems Green, Gauss, Stokes Derivations on the black board

Chapter 11 Overview Line integrals Green’s theorem in a plane Conservative fields & potentials Surface & volume integrals Gauss’ theorem (divergence) Stokes’ theorem (curl) Integral form of grad, div, and curl Revisit (cf. last week’s lecture)

Chapter 11 Black Board Line integrals ( ) Green’s theorem in a plane Conservative fields & potentials Surface & volume integrals Gauss’ theorem (divergence) Stokes’ theorem (curl) Integral form of grad, div, and curl Revisit (cf. last week’s lecture)

Chapter 11 Black Board Line integrals Green’s theorem in a plane Conservative fields & potentials Surface & volume integrals ( ) Gauss’ theorem (divergence) Stokes’ theorem (curl) Integral form of grad, div, and curl Revisit (cf. last week’s lecture)

Chapter 11 Black Board Line integrals Green’s theorem in a plane Conservative fields & potentials Surface & volume integrals Gauss’ theorem (divergence) Stokes’ theorem (curl) Integral form of grad, div, and curl (11.7) Revisit (cf. last week’s lecture)

End of lecture! Over to the Exercises!