Course MA2321

This is a new one-semester course on functions of several real variables, given in Michaelmas term 2009

It will be followed in Hilary term 2010 by course MA2322 on calculus on manifolds. The two courses, MA2321 and MA2322 correspond essentially to the one year long course 224, which was given in 2006-2007, 2007-2008 and 2008-2009.

In this course we extend the methods of the differential calculus to functions of two or more real variables and, more generally, to functions on finite dimensional real vector spaces.

Most of the topics in courses MA2321 and MA2322 are covered in the notes of two earlier one-year courses, 211 and 221, which are available as pdf files at:

PDF file for Course 211 (Linear algebra and Differential Forms).

PDF file for Course 221 (Real and Complex Analysis) .

See in particular sections 3, 4, 5, 6, 7.3, 9, 11 and 12 of course 211

and sections 4, 6 and 7 of course 221.

The objective of this course is to familiarise you with the calculus of functions of several real variables, and the associated geometrical ideas and concepts of multilinear algebra.

The emphasis is on the theory, and the applications are intended to strengthen the grasp of the theory.

The course is not based on any specific books. The webnotes mentioned above may form useful background reading.

The following, however, may be of interest as further background reading:

Advanced calculus of several variables by Charles Henry Edwards

Advanced Calculus: a differential forms approach by Harold M. Edwards

Foundations of Modern Analysis by Jean Dieudonne

PDF file for Exercises 1 .

PDF file for Exercises 2 .

PDF file for Exercises 3 .

PDF file for Exercises 4 .

My email address is simms@maths.tcd.ie and my postal address is School of Mathematics
Trinity College
Dublin 2
Ireland

My office telephone is +353-1-896 1944 and the departmental fax is at +353-1-896 2282