• date post

01-Jan-2016
• Category

## Documents

• view

59

2

Embed Size (px)

description

1.2 Differential Calculus. 1.2.1 The Gradient. points in the direction of maximum increase of T. It is perpendicular to the surface T=const. gives the slope (rate of increase) along this direction. T(x,y)=const. θ. y. x. gradient:. Example: Multiplication by a scalar-the gradient. - PowerPoint PPT Presentation

### Transcript of 1.2 Differential Calculus

• 1.2 Differential Calculus

• 1.2.3 The del Operator The del is similar to a vector, but it is an operator.It acts on (takes the partial derivatives of)everything to its right.

• 1.2.4 The Divergencedivergence of a vector field

• no divergence

• large divergence

• F(x,y) = (2*x,-y). F(x,y) = (2*x,-y)-(6,-1).

• 1.2.5 The CurlCurl of the a vector field Keep track of the order in evaluating the determinant!

• G(x,y) - G(x0,y0) (-y-3,x-3) (-y+3,x+3)

• (x-y,x+y).

• Turbulent motion of air around a vibrating cylinder in a wind tunnel.

• 1.2.6 Product RulesApply del to all factors.Keep track of the type of multiplication (dot vs. cross, how connected).Arrange in standard form (gradient, curl, divergence).Most important products are listed in the book.

• 1.2.7 Second derivatives