From Calculus to Analysis

This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. __From Calculus to Analysis__ prepares readers for their first analysis course—important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course. This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus.¡The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. Key features: * Contains numerous exercises; * Provides unique examples, such as many ways to estimate the number Pi; * Introduces the basic principles¡of analysis; * Offers a straightforward introduction to the calculus basics such as¡number systems, sequences, and series; * Carefully written book with a thoughtful perspective for students. From Calculus to Analysis prepares readers for their first analysis course--important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. Key features: * Contains numerous exercises; * Provides unique examples, such as many ways to estimate the number Pi; * Introduces the basic principles of analysis; * Offers a straightforward introduction to the calculus basics such as number systems, sequences, and series; * Carefully written book with a thoughtful perspective for students. From Calculus to Analysis prepares readers for their first analysis course--important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. From Calculus to Analysis prepares readers for their first analysis course important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will Front Matter....Pages I-X Number Systems....Pages 1-32 Sequences and Series....Pages 33-63 Power Series and Special Functions....Pages 65-94 Fifty Ways to Estimate the Number π ....Pages 95-135 Continuity, Limits, and Differentiation....Pages 137-176 Riemann Integration....Pages 177-205 Convergence of Functions....Pages 207-219 Decimal Representation of Numbers....Pages 221-233 Countable and Uncountable Sets....Pages 235-244 Back Matter....Pages 245-250 1. Number systems 2. Sequences and series 3. Power series and special functions 4. Fifty ways to estimate the number [pi] 5. Continuity, limits, and differentiation 6. Riemann integration 7. Convergence of functions 8. Decimal representation of numbers 9. Countable and uncountable sets.