1. Mat-F March 7, 2005 Vector Calculus, 10.1-10.5 Åke Nordlund Niels Obers, Sigfus Johnsen Kristoffer Hauskov Andersen Peter Browne Rønne

2. Overview Changes Group 4a, Wednesday 10-12, RF085  D315 (ØL) Sections 10.1-10.5 10.1 Differentiation of vectors 10.2 Integration of vectors 10.3 Space curves 10.4 Vector functions of several arguments 10.5 Surfaces

3. 10: Vector analysis Why? Because most laws of physics expressed this way equations of motion conservation laws How? Derivatives and integrals of vectors Lots of examples on the black board!

4. Examples on the black board 10.1 Derivatives of vectors circular motion, moving unit vectors 10.2 Integral of vectors solutions of equations of motion 10.3 Space curves chain rule 10.4 Vector functions of several variables differentials of vector fields 10.5 Surfaces tangent planes, parametric surfaces (e.g. in Maple)

5. Examples on the black board 10.1 Derivatives of vectors circular motion, moving unit vectors 10.2 Integral of vectors solutions of equations of motion 10.3 Space curves chain rule 10.4 Vector functions of several variables differentials of vector fields 10.5 Surfaces tangent planes, parametric surfaces (e.g. in Maple)

6. Examples on the black board 10.1 Derivatives of vectors circular motion, moving unit vectors 10.2 Integral of vectors solutions of equations of motion 10.3 Space curves chain rule 10.4 Vector functions of several variables differentials of vector fields 10.5 Surfaces tangent planes, parametric surfaces (e.g. in Maple)

7. Examples on the black board 10.1 Derivatives of vectors circular motion, moving unit vectors 10.2 Integral of vectors solutions of equations of motion 10.3 Space curves chain rule 10.4 Vector functions of several variables differentials of vector fields 10.5 Surfaces tangent planes, parametric surfaces (e.g. in Maple)

8. Examples on the black board 10.1 Derivatives of vectors circular motion, moving unit vectors 10.2 Integral of vectors solutions of equations of motion 10.3 Space curves chain rule 10.4 Vector functions of several variables differentials of vector fields 10.5 Surfaces tangent planes, parametric surfaces (e.g. in Maple)

9. Enough for today! Good luck with the Exercises!