lec_week4

# lec_week4 - MIT OpenCourseWare http/ocw.mit.edu 18.02...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
18.02 Lecture 8. Tue, Sept 25, 2007 Functions of several variables. Recall: for a function of 1 variable, we can plot its graph, and the derivative is the slope of the tangent line to the graph. Plotting graphs of functions of 2 variables: examples z = y , z = 1 x 2 y 2 , using slices by the coordinate planes. (derived carefully). Contour plot: level curves f ( x, y ) = c . Amounts to slicing the graph by horizontal planes z = c . Showed 2 examples from “real life”: a topographical map, and a temperature map, then did the examples z = y and z = 1 x 2 y 2 . Showed more examples of computer plots ( z = x 2 + y 2 , z = y 2 x 2 , and another one). Contour plot gives some qualitative info about how f varies when we change x, y . (shown an example where increasing x leads f to increase). Partial derivatives. f x = ∂f = lim f ( x 0 + Δ x, y 0 ) f ( x 0 , y 0 ) ; same for f y . ∂x Δ x 0 Δ x Geometric interpretation: f x , f y are slopes of tangent lines of vertical slices of the graph of f (Fxing y = y 0 ; Fxing x = x 0 ). How to compute: treat x as variable, y as constant. Example:
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/04/2011 for the course MATH 18.02 taught by Professor Auroux during the Spring '08 term at MIT.

### Page1 / 4

lec_week4 - MIT OpenCourseWare http/ocw.mit.edu 18.02...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online