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Lectures on Vector Calculus - CSUSB

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Lectures on Vector CalculusPaul RentelnDepartment of PhysicsCalifornia State UniversitySan Bernardino, CA 92407March, 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.

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 ...

  Vector, Calculus, Vector calculus

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