Transcription of Lectures on Vector Calculus - CSUSB
{{id}} {{{paragraph}}}
Example: confidence
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 .. Determinants and Epsilon Symbols .. Vector Algebra III: Tensor Product .. Problems .. 312 Vector Calculus Fields .. The Gradient .. Lagrange Multipliers .. The Divergence .. The Laplacian .. The Curl .. Vector Calculus with Indices .. Problems.
way of writing the nine equations (1.1) and (1.2). For example, if we choose i= 2 and j= 3 in (1.3), we get ^e 2 ^e 3 = 0; (1.8) (because 23 = 0 by de nition of the Kronecker delta). This is just one of the equations in (1.1). Letting iand jrun from 1 to 3, we get all the nine orthornormality conditions on the basis vectors e^ 1, e^ 2 and e^ 3 ...
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: