Synopses & Reviews
This book is designed to be an easily readable, intimidation-free guide to advanced calculus. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first book to cover both single and multivariable analysis in such a clear, reader-friendly setting. Chapter topics cover sequences, limits of functions, continuity, differentiation, integration, infinite series, sequences and series of functions, vector calculus, functions of two variables, and multiple integration. For individuals seeking math fun at a higher level.
Synopsis
Designed to be readable and intimidation-free, this advanced calculus book presents material that flows logically allowing readers to grasp concepts and proofs. Providing in-depth discussion of topics, the book also features common errors to encourage caution and easy recall of errors. It also presents many proofs in great detail and those which should not provide difficulty are either short or simply outlined. Throughout the book, there are a number of important and useful features, such as cross-referenced functions, expressions, and ideas; footnotes which place mathematical development in historical perspective; an index of symbols; and definitions and theorems which are clearly stated and well marked. An important reference for every professional who uses advanced math.
Table of Contents
1. Introduction.
2. Sequences.
3. Limits of Functions.
4. Continuity.
5. Differentiation.
6. Integration.
7. Infinite Series.
8. Sequences and Series of Functions.
9. Vector Calculus.
10. Functions of Two Variables.
11. Multiple Integration.
Hints and Solutions to Selected Exercises.
Index of Symbols.
Index.