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 . . . . . . . . . . . . . . . . . . . . . Angles, Rotations, and Matrices . . . . . . . . . . . . . . . . . Vector Algebra II: Cross Products and the Levi Civita Symbol Products of Epsilon Symbols . . . . . . . . . . . . . . . . . . . Determinants and Epsilon Symbols.

Lectures on Vector Calculus Paul Renteln Department of Physics California State University San Bernardino, CA 92407 March, 2009; Revised March, 2011

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