Mat-F March 14, 2005 Vector Calculus, 10.6-10.10 Åke Nordlund
Niels Obers, Sigfus Johnsen
Kristoffer Hauskov Andersen
Peter Browne Rønne
Mat-F March 14, 2005 Vector Calculus, 10.6-10.10 Åke Nordlund
Niels Obers, Sigfus Johnsen
Kristoffer Hauskov Andersen
Peter Browne Rønne
10: Vector operators
Why?
Because most laws of physics derived this way
conservation laws
electrodynamics …
How?
Generalization of chain rule for derivatives
Lots of examples
on the black board!
Overview
Sections 10.6-10.10
10.6 Scalar and vector fields
scalar or vector that varies in space
10.7 Vector operators
gradient, divergence, curl
10.8 Vector operator formulae
learn the magic!
10.9 Vector operators in polar coordinates
explains what was used before
10.10 General curvilinear coordinates
generalizes e.g. polars; Einsteins theory of general rel.
Black board
Sections 10.6-10.10
10.6 Scalar and vector fields
scalar or vector that varies in space
10.7 Vector operators
gradient, divergence, curl
10.8 Vector operator formulae
learn the magic!
10.9 Vector operators in polar coordinates
explains what was used before
10.10 General curvilinear coordinates
generalizes e.g. polars; Einsteins theory of general rel.
Black board
Sections 10.6-10.10
10.6 Scalar and vector fields
scalar or vector that varies in space
10.7 Vector operators
gradient, divergence, curl
10.8 Vector operator formulae
learn the magic!
10.9 Vector operators in polar coordinates
explains what was used before
10.10 General curvilinear coordinates
generalizes e.g. polars; Einsteins theory of general rel.
Black board
Sections 10.6-10.10
10.6 Scalar and vector fields
scalar or vector that varies in space
10.7 Vector operators
gradient, divergence, curl
10.8 Vector operator formulae
learn the magic!
10.9 Vector operators in polar coordinates
explains what was used before
10.10 General curvilinear coordinates
generalizes e.g. polars; Einsteins theory of general rel.
Black board
Sections 10.6-10.10
10.6 Scalar and vector fields
scalar or vector that varies in space
10.7 Vector operators
gradient, divergence, curl
10.8 Vector operator formulae
learn the magic!
10.9 Vector operators in polar coordinates
explains what was used before
10.10 General curvilinear coordinates
generalizes e.g. polars; Einsteins theory of general rel.
Black board
Sections 10.6-10.10
10.6 Scalar and vector fields
scalar or vector that varies in space
10.7 Vector operators
gradient, divergence, curl
10.8 Vector operator formulae
learn the magic!
10.9 Vector operators in polar coordinates
explains what was used before
10.10 General curvilinear coordinates
generalizes e.g. polars; Einsteins theory of general rel.
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