1. Mat-F March 14, 2005 Line-, surface-, and volume-integrals 11.1-11.9 Åke Nordlund Niels Obers, Sigfus Johnsen Kristoffer Hauskov Andersen Peter Browne Rønne

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

3. 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

4. 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)

5. Chapter 11 Black Board Line integrals (11.1-11.4) 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)

6. Chapter 11 Black Board Line integrals Green’s theorem in a plane Conservative fields & potentials Surface & volume integrals (11.5-11.9) Gauss’ theorem (divergence) Stokes’ theorem (curl) Integral form of grad, div, and curl Revisit (cf. last week’s lecture)

7. 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)

8. End of lecture! Over to the Exercises!