hw2 - CALIFORNIA INSTITUTE OF TECHNOLOGY Control and...

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: CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems CDS 202 R. Murray Winter 2004 Problem Set #2 Issued: 21 Jan 04 Due: 26 Jan 04 Reading: Boothby, Chapter I and Sections III.1III.3 Note: Most of the problems are taken from the exercises in Guillemin and Pollack. If you read Guillemin and Pollack, be warned that they treat manifolds slightly differently, using parameterizations instead of coordinate charts. Problems: 1. [Guillemin and Pollack, page 5, #3] Let M , N , and P be smooth manifolds and let f : M N and g : N P be smooth maps. (a) Show that the composite map g f : M P is smooth. (b) Show that if f and g are diffeomorphisms, so is g f . (You may use the fact that the composition of smooth functions between open subsets of Euclidian spaces are smooth.) 2. [Boothby II.1.2] Using stereographic projection from the north pole N (0 , , +1) of all of the standard unit sphere in R 3 except (0 , , +1) determine a coordinate neighborhood U N , N . In....
View Full Document

This note was uploaded on 03/06/2010 for the course CDS 202 taught by Professor Marsden,j during the Spring '08 term at Caltech.

Page1 / 2

hw2 - CALIFORNIA INSTITUTE OF TECHNOLOGY Control and...

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