For first undergraduate analysis courses. This book is designed to be an easily readable, intimidation-free advanced calculus textbook. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first text to cover both single and mulitvariable analysis in such a student friendly setting.
Covers both single and multivariable calculus. Presents material logically, which helps students gradually acquire more tools, allowing them to write proofs and reason on their own.
Provides in-depth discussion of topics which helps improve understanding of material.
Includes projects which teach independence and the usefulness of math in related areas. Highlights common errors to encourage caution and easy recall of common errors.
Presents many proofs in great detail.
proofs which should not provide difficulty are either short or outlined with details left as exercises.
Includes a number of important pedagogical features:
3,000 quality exercises
thorough review of concepts
cross-references similar functions, expressions, and ideas throughout the text.
footnotes place mathematical development in historical perspective.
hints and solutions for selected exercises provide a means to check answers to get an idea how to complete an exercise.
index of symbols is convenient and easy to locate.
definitions and theorems are clearly stated and well marked.
remarks clarify the material and illustrations.
3. Limits of Functions.
7. Infinite Series.
8. Sequences and Series of Functions.
9. Fourier Series.
10. Vector Calculus.
11. Functions of Two Variables.
12. Multiple Integration.
Hints and Solutions to Selected Exercises.
Index of Symbols.