Introduction to Analysis

A master teacher authored the third edition of this widely popular textbook, which provides a mathematically rigorous introduction to analysis of real-valued functions of one variable. It is written in a manner that will help to ease the transition from primarily computational to primarily theoretical mathematics, and includes examples to develop intuition and highlight the need for hypothesis in a theorem. The text also covers the topology of the real number system, continuous functions, differentiation, integration, series of real numbers, sequences and series of functions, Fourier series, and more.

Format: Hardback
Length: 324 pages
Publication date: 16 August 2021
Publisher: Taylor & Francis Ltd

This extensively well-liked textbook has been authored by a highly skilled teacher. This comprehensive guide offers a mathematically rigorous exploration of the analysis of real-valued functions of a single variable. This user-friendly text is crafted in a manner that facilitates a seamless transition from a computational to a theoretical mathematical approach, making it accessible and engaging for students. The content is presented in a clear and intuitive manner, while upholding rigorous mathematical principles. The author provides the foundational ideas of proofs, leaving the detailed write-up as an exercise for the reader. Additionally, the text elucidates the rationale behind each step in a proof and highlights recurring techniques.

While examples cannot replace proofs, they serve as valuable tools in fostering intuition and play a significant role in this text. Examples can serve as a poignant reminder that our assumptions may not always hold true.

The Third Edition of this textbook offers several notable features:

It begins with a discussion of the axioms of the real number system, providing a solid foundation for the subsequent chapters.

The concept of the limit is introduced through sequences, making it more accessible and intuitive for students.

Examples serve as motivating factors, highlighting the importance of hypotheses in theorems and bringing abstract concepts to life.

A new section on the Cantor set and the Cantor function is included, expanding the coverage of complex mathematical topics.

Additional material on connectedness is provided, enhancing the understanding of mathematical relationships.

The exercise range spans from routine problems that help students get their feet wet to moderately challenging ones that encourage deeper understanding.

Topology of the real number system is developed to establish the familiar properties of continuous functions.

Some exercises are dedicated to constructing counterexamples, fostering critical thinking and deepening the student's grasp of the subject.

The author's primary goal is to present the material in a manner that is accessible and captivating to individuals embarking on their study of abstract mathematics.

A comprehensive table of contents provides an overview of the book's contents, facilitating easy navigation and reference.

Weight: 636g
Dimension: 162 x 242 x 25 (mm)
ISBN-13: 9780367702359
Edition number: 3 New edition