7. Approximations_for_partial_derivatives_c

7. Approximations_for_partial_derivatives_c - 2.3...

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

View Full Document Right Arrow Icon
2.3 Approximations for Partial Derivatives Extension of the ideas developed in section 2.2 for partial derivatives is straightforward. Just keep in mind the physical/geometrical meaning of partial derivatives. Consider a function of two variables: ) , ( y x f z = Discrete representation: - set up a grid of ) , ( i i y x values in the ) , ( y x plane - i x values, x Δ apart and j y values, y Δ apart - x Δ and y Δ spacing can be the same or can be different - choose spacing to resolve the shape of the ) , ( y x f surface Recall notation for values of the dependent variable at each (x,y) grid point: . ) , ( ) , ( ) , ( 1 , 1 , 1 1 , etc f y x f f y x f f y x f j i j i j i j i j i j i + + + + = = = The physical interpretation of the partial derivative: x) fixed a for (i.e., given x a for y with y) f(x, of Change of Rate y) fixed a for (i.e., y given a for with x y) f(x, of Change of Rate = = y f x f The geometrical interpretation of the partial derivative: y of direction
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/16/2011 for the course ME 303 taught by Professor Serhiyyarusevych during the Spring '10 term at Waterloo.

Page1 / 3

7. Approximations_for_partial_derivatives_c - 2.3...

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