Friendly Introduction to Analysis, A

Description

• 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.

• Added examples and explanations.

• Reworded exercises.

  • 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.

• Author website with additional topics.

  • The chapter on Fourier Analysis is, for example, available now in this form.

For two-semester/three-quarter, first undergraduate courses in Advanced Calculus or Real Analysis.

This book is an easy, readable, intimidation-free analysis textbook. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first text to cover both single and multivariable analysis in such a student friendly setting.

For two-semester/three-quarter, first undergraduate courses in Advanced Calculus or Real Analysis.

This book is an easy, readable, intimidation-free analysis textbook. Ideas and methods of proof build upon each other and are explained thoroughly. This text covers both single and multivariable analysis in a student friendly setting.

• 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.

• Unique coverage of both single and multivariable calculus.

  • 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.

• Projects.

  • 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.

• 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.

• 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.

• 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.

• Cross-referencing throughout.

  • 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.

• Hints and solutions for selected 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.

•  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.