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.
- Provides students with more thorough treatments of existing material in a clearer, more readable, and student-friendly format.
- Expanded use of geometry and illustrations. Enhances the visual appeal of the text and students' understanding and visualization.
- Enhances the visual appeal of the text and students' understanding and visualization.
- Unique coverage of both single and multivariable calculus. Encompasses the teaching of methods of proof with theory.
- Encompasses the teaching of methods of proof with theory.
- In-depth discussions of topics. Improves students' understanding of present and past material. Allows instructors to see how to bring material together in an orderly fashion.
- Improves students' understanding of present and past material. Allows instructors to see how to bring material together in an orderly fashion.
- Projects. Teaches students independence and the usefulness of math in related areas.
- Teaches students independence and the usefulness of math in related areas.
- Focus on common errors made by students. Alerts students to be cautious in specific areas that often cause confusion.
- Alerts students to be cautious in specific areas that often cause confusion.
- Numerous proofs—Which prove challenging to students are presented in great detail, while proofs which should not provide difficulty are either short or outlined with details left as exercises. Enables students to overcome a lack of skill and feeling of intimidation.
- Enables students to overcome a lack of skill and feeling of intimidation.
- 3,000 quality exercises—Of varied difficulty, ranging from routine to creative and innovative, mixing theory and applications. Stimulates creativity, introduces new material, interrelates ideas, and checks students' knowledge of concepts and skills.
- Stimulates creativity, introduces new material, interrelates ideas, and checks students' knowledge of concepts and skills.
- Thorough review sections—Features problems of a true/false nature. Gives students a deeper understanding of concepts and the opportunity to check that understanding before moving on.
- Gives students a deeper understanding of concepts and the opportunity to check that understanding before moving on.
- Cross-referencing throughout. Makes it easy for students and instructors to locate similar functions, expressions, and ideas in other places of the text.
- Makes it easy for students and instructors to locate similar functions, expressions, and ideas in other places of the text.
- Historical notes—In footnotes. Places mathematical development in historical perspective.
- Places mathematical development in historical perspective.
- Hints and solutions for selected exercises. Provides students with a means to check answers and get ideas on how to complete exercises.
- Provides students with a means to check answers and get ideas on how to complete exercises.
- Index of symbols. Saves valuable student and instructor time by making the symbols convenient and easy to locate.
- Saves valuable student and instructor time by making the symbols convenient and easy to locate.
- Revised and reorganized content—Hundreds of small improvements enhance the presentation of material throughout the text. Provides students with more thorough treatments of existing material in a clearer, more readable, and student-friendly format.
- Provides students with more thorough treatments of existing material in a clearer, more readable, and student-friendly format.
- Added examples and explanations.
- Reworded exercises. Further enhances the precision of the instructions, making it easier for students to follow.
- Further enhances the precision of the instructions, making it easier for students to follow.
- Expanded use of geometry and illustrations. Enhances the visual appeal of the text and students' understanding and visualization.
- Enhances the visual appeal of the text and students' understanding and visualization.
- Author website with additional topics. The chapter on Fourier Analysis is, for example, available now in this form.
- The chapter on Fourier Analysis is, for example, available now in this form.
- Provides students with more thorough treatments of existing material in a clearer, more readable, and student-friendly format.
- Expanded use of geometry and illustrations. Enhances the visual appeal of the text and students' understanding and visualization.
- Enhances the visual appeal of the text and students' understanding and visualization.
- Unique coverage of both single and multivariable calculus. Encompasses the teaching of methods of proof with theory.
- Encompasses the teaching of methods of proof with theory.
- In-depth discussions of topics. Improves students' understanding of present and past material. Allows instructors to see how to bring material together in an orderly fashion.
- Improves students' understanding of present and past material. Allows instructors to see how to bring material together in an orderly fashion.
- Projects. Teaches students independence and the usefulness of math in related areas.
- Teaches students independence and the usefulness of math in related areas.
- Focus on common errors made by students. Alerts students to be cautious in specific areas that often cause confusion.
- Alerts students to be cautious in specific areas that often cause confusion.
- Numerous proofs—Which prove challenging to students are presented in great detail, while proofs which should not provide difficulty are either short or outlined with details left as exercises. Enables students to overcome a lack of skill and feeling of intimidation.
- Enables students to overcome a lack of skill and feeling of intimidation.
- 3,000 quality exercises—Of varied difficulty, ranging from routine to creative and innovative, mixing theory and applications. Stimulates creativity, introduces new material, interrelates ideas, and checks students' knowledge of concepts and skills.
- Stimulates creativity, introduces new material, interrelates ideas, and checks students' knowledge of concepts and skills.
- Thorough review sections—Features problems of a true/false nature. Gives students a deeper understanding of concepts and the opportunity to check that understanding before moving on.
- Gives students a deeper understanding of concepts and the opportunity to check that understanding before moving on.
- Cross-referencing throughout. Makes it easy for students and instructors to locate similar functions, expressions, and ideas in other places of the text.
- Makes it easy for students and instructors to locate similar functions, expressions, and ideas in other places of the text.
- Historical notes—In footnotes. Places mathematical development in historical perspective.
- Places mathematical development in historical perspective.
- Hints and solutions for selected exercises. Provides students with a means to check answers and get ideas on how to complete exercises.
- Provides students with a means to check answers and get ideas on how to complete exercises.
- Index of symbols. Saves valuable student and instructor time by making the symbols convenient and easy to locate.
- Saves valuable student and instructor time by making the symbols convenient and easy to locate.
- Revised and reorganized content—Hundreds of small improvements enhance the presentation of material throughout the text. Provides students with more thorough treatments of existing material in a clearer, more readable, and student-friendly format.
- Provides students with more thorough treatments of existing material in a clearer, more readable, and student-friendly format.
- Added examples and explanations.
- Reworded exercises. Further enhances the precision of the instructions, making it easier for students to follow.
- Further enhances the precision of the instructions, making it easier for students to follow.
- Expanded use of geometry and illustrations. Enhances the visual appeal of the text and students' understanding and visualization.
- Enhances the visual appeal of the text and students' understanding and visualization.
- Author website with additional topics. The chapter on Fourier Analysis is, for example, available now in this form.
- The chapter on Fourier Analysis is, for example, available now in this form.
