LECTURE NOTES OF WILLIAM CHEN

 

FIRST YEAR CALCULUS

This set of notes has been compiled over a period of more than 30 years. Some chapters were used in various forms and on many occasions between 1981 and 1990 by the author at Imperial College, University of London. The remaining chapters were written in Sydney.

The material has been organized in such a way to create a single volume suitable for use as an introduction to elementary calculus.

To read the notes, click the links below for connection to the appropriate PDF files.

The material is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, the documents may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible to any individuals other than its owners.

Chapter 1 : THE NUMBER SYSTEM >>

Chapter 2 : FUNCTIONS >>

Chapter 3 : INTRODUCTION TO DERIVATIVES >>

Chapter 4 : SOME SPECIAL FUNCTIONS >>

Chapter 5 : APPLICATIONS OF DERIVATIVES >>

Chapter 6 : LIMITS OF FUNCTIONS >>

Chapter 7 : CONTINUITY >>

Chapter 8 : DIFFERENTIATION >>

Chapter 9 : THE DEFINITE INTEGRAL >>

Chapter 10 : TECHNIQUES OF INTEGRATION >>

Chapter 11 : NUMERICAL INTEGRATION >>

Chapter 12 : APPLICATIONS OF INTEGRATION >>

Chapter 13 : IMPROPER INTEGRALS >>

Chapter 14 : ORDINARY DIFFERENTIAL EQUATIONS >>

Chapter 15 : FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS >>

Chapter 16 : SECOND ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS >>

Chapter 17 : FUNCTIONS OF TWO VARIABLES >>

Chapter 18 : INTERPOLATION AND APPROXIMATION >>

Chapter 19 : SEQUENCES >>

Chapter 20 : SERIES >>

Chapter 21 : POWER SERIES >>

Chapter 22 : THE BINOMIAL THEOREM >>