vec_calc - Vector Calculus Electromagnetic Waves and Optics...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Vector Calculus Electromagnetic Waves and Optics 1 Vector Calculus and Conservation Laws • uses “del” or “nabla” operator – components are derivatives – simplifies many expressions • boundary theorems (Stokes, Gauss) – convert integral eqs. to differential eqs. – particularly helpful for conservation laws • reference: “Div, Grad, Curl, and All That”, H. M. Schey, (Norton, New York), 1997. z k y j x i ∂ ∂ + ∂ ∂ + ∂ ∂ = ∇ ˆ ˆ ˆ r Vector Calculus Electromagnetic Waves and Optics 2 Vector Calculus ( ) ( ) ( ) , , 2 2 2 2 2 2 2 2 = ∇ × ∇ = × ∇ ⋅ ∇ ∇ − ⋅ ∇ ∇ = × ∇ × ∇ ∂ ∂ + ∂ ∂ + ∂ ∂ = ∇ = ∇ ⋅ ∇ f F F F F z f y f x f f z y x f r r r r r r r r r r r r r r • gradient • curl • divergence • double derivatives: ( ) z F y F x F F y F x F k x F z F j z F y F i F z f k y f j x f i z y x f z y x x y z x y z ∂ ∂ + ∂ ∂ + ∂ ∂ = ⋅ ∇ ∂ ∂ − ∂ ∂ + ∂ ∂ − ∂ ∂ + ∂ ∂ − ∂ ∂ = × ∇ ∂ ∂ + ∂ ∂ + ∂ ∂ = ∇ r r r r r ˆ ˆ ˆ ˆ ˆ ˆ , , Vector Calculus...
View Full Document

This note was uploaded on 08/26/2008 for the course PHYSICS 603 taught by Professor Sage during the Summer '06 term at Northwestern.

Page1 / 7

vec_calc - Vector Calculus Electromagnetic Waves and Optics...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online