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Lectures on Vector Calculus - CSUSB

Lectures on Vector CalculusPaul RentelnDepartment of PhysicsCalifornia State UniversitySan Bernardino, CA 92407 March, 2009; Revised March, 2011c Paul Renteln, 2009, 2011iiContents1 Vector Algebra and Index Orthonormality and the Kronecker Delta .. Vector Components and Dummy Indices .. Vector Algebra I: Dot Product .. The Einstein Summation Convention .. Dot Products and Lengths .. Dot Products and Angles .. Angles, Rotations, and Matrices .. Vector Algebra II: Cross Products and the Levi Civita Symbol Products of Epsilon Symbols.

1.2 Vector Components and Dummy Indices Let Abe a vector in R3. As the set fe^ igforms a basis for R3, the vector A may be written as a linear combination of the e^ i: A= A 1e^ 1 + A 2e^ 2 + A 3e^ 3: (1.13) The three numbers A i, i= 1;2;3, are called the (Cartesian) components of the vector A. We may rewrite Equation (1.13) using indices as ...

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