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 . . . . . . . . . . . . . . Dot Products and Lengths . . . . . . . . . . . . . . . . . . . . Dot Products and Angles.

instead. (They are called ‘indices’ because they index something, and they are called ‘dummy’ because the exact letter used is irrelevant.) In index notation, then, I claim that the conditions (1.1) and (1.2) may be written e^ i^e j = ij: (1.3) How are we to understand this equation? Well, for starters, this equation

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