Course MA2321

This is a one-semester course on functions of several real variables, to be given in Michaelmas term 2014 (first given in Michaelmas term 2009 ).

It will be followed in Hilary term 2015 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 course MA2321 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.

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

I expect you to know and understand the definitions, to know and understand and be able to give proofs of the theorems, and show that you are able to apply the theory.

The course will be examined at the end of the academic year in April or May.

The course is not based on any specific books. The following webnotes from earlier courses 211 and 221 are strongly recommended for background reading.

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.

Books for background reading are:

Calculus on manifolds by Michael Spivak

Foundations of Modern Analysis by Jean Dieudonne

Advanced calculus of several variables by Charles Henry Edwards

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

PDF file for Exercises 1 .

PDF file for Exercises 2 .

PDF file for Exercises 3 .

PDF file for Exercises 4 .

PDF file for Exercises 5 .

PDF file for Exercises 6 .

My email address is and my postal address is School of Mathematics
Trinity College
Dublin 2

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

Updated 12 December 2014