Lecture notes have been around for centuries, either informally, as handwritten notes, or formally as textbooks. Recently improvements in typesetting have made it easier to produce \personalised" printed notes as here, but there has been no fundamental change. Experience shows that very few people are able to use lecture notes as a substitute for lectures; if it were otherwise, lecturing, as a profession would have died out by now. | Department of Mathematical Sciences Advanced Calculus and Analysis MA1002 Ian Craw ii April 13 2000 Version Copyright 2000 by Ian Craw and the University of Aberdeen All rights reserved. Additional copies may be obtained from Department of Mathematical Sciences University of Aberdeen Aberdeen AB9 2TY DSN mth200-101982-8 Foreword These Notes The notes contain the material that I use when preparing lectures for a course I gave from the mid 1980 s until 1994 in that sense they are my lecture notes. Lectures were once useful but now when all can read and books are so numerous lectures are unnecessary. Samuel Johnson 1799. Lecture notes have been around for centuries either informally as handwritten notes or formally as textbooks. Recently improvements in typesetting have made it easier to produce personalised printed notes as here but there has been no fundamental change. Experience shows that very few people are able to use lecture notes as a substitute for lectures if it were otherwise lecturing as a profession would have died out by now. These notes have a long history a first course in analysis rather like this has been given within the Mathematics Department for at least 30 years. During that time many people have taught the course and all have left their mark on it clarifying points that have proved difficult selecting the right examples and so on. I certainly benefited from the notes that Dr Stuart Dagger had written when I took over the course from him and this version builds on that foundation itslef heavily influenced by Spivak 1967 which was the recommended textbook for most of the time these notes were used. The notes are written in LATEX which allows a higher level view of the text and simplifies the preparation of such things as the index on page 101 and numbered equations. You will find that most equations are not numbered or are numbered symbolically. However sometimes I want to refer back to an equation and in that case it is numbered within the .
