CENG 101A BRIEF MATH REVIEW D. MILLER 9/24/09 You are expected to know the following differential and vector operations. Please review your math if you are not able to obtain the answers below readily. (vectors in bold type) Given the following cartesian vectors : A = 2x i + 3xy j and B = 2 i + x j Given the cartesian “nabla” or “del” vector operator : ∇ = ∂/∂x i + ∂/∂y j + ∂/∂z k Given the scalar function : P(x,y) = 2 + x 2 + 3xy Then some results are (make certain you can work these out!) : A•B = 4x + 3x 2 y (result is a scalar called the dot product) ∇ • A = 2 + 3x (result is a scalar called the `divergence’ of vector) ∇ •P is not defined ; dot product must be between two vectors note : i • i = 1 ; j • k = 0 AxB = (2x 2 – 6xy) k (result is a vector called the cross product which is perpendicular ∇ xA = 3y k (result is a vector called the `curl’ of the vector – to plane of vectors A and B ) perpendicular Ax P is not defined ; cross product must be between two vectors
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This note was uploaded on 10/22/2009 for the course CENG 101A taught by Professor Krashinov during the Spring '07 term at UCSD.