Title
Elementary Real And Complex Analysis (Dover Books On Mathematics)
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In this book the renowned Russian mathematician Georgi E. Shilov brings his unique perspective to real and complex analysis, an area of perennial interest in mathematics. Although there are many books available on the topic, the present work is specially designed for undergraduates in mathematics, science and engineering. A high level of mathematical sophistication is not required.The book begins with a systematic study of real numbers, understood to be a set of objects satisfying certain definite axioms. The concepts of a mathematical structure and an isomorphism are introduced in Chapter 2, after a brief digression on set theory, and a proof of the uniqueness of the structure of real numbers is given as an illustration. Two other structures are then introduced, namely ndimensional space and the field of complex numbers.After a detailed treatment of metric spaces in Chapter 3, a general theory of limits is developed in Chapter 4. Chapter 5 treats some theorems on continuous numerical functions on the real line, and then considers the use of functional equations to introduce the logarithm and the trigonometric functions. Chapter 6 is on infinite series, dealing not only with numerical series but also with series whose terms are vectors and functions (including power series). Chapters 7 and 8 treat differential calculus proper, with Taylor's series leading to a natural extension of real analysis into the complex domain. Chapter 9 presents the general theory of Riemann integration, together with a number of its applications. Analytic functions are covered in Chapter 10, while Chapter 11 is devoted to improper integrals, and makes full use of the technique of analytic functions.Each chapter includes a set of problems, with selected hints and answers at the end of the book. A wealth of examples and applications can be found throughout the text. Over 340 theorems are fully proved.
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- Q: How many pages are in this book? A: This book has five hundred forty-four pages. It provides a comprehensive exploration of real and complex analysis.
- Q: What type of binding does this book have? A: This book is available in paperback binding. This makes it lightweight and easy to handle.
- Q: Who is the author of this book? A: The author is Georgi E. Shilov, a renowned Russian mathematician. His expertise enriches the content of this analysis book.
- Q: What topics does this book cover? A: This book covers real numbers, metric spaces, limits, and analytic functions. It is designed for undergraduates in mathematics and related fields.
- Q: Is this book suitable for beginners? A: Yes, this book is designed for undergraduates and does not require a high level of mathematical sophistication. It is accessible for beginners.
- Q: How do I use this book for study? A: You can use this book as a textbook for courses in mathematics, science, or engineering. Each chapter includes problems to enhance understanding.
- Q: Are there exercises included in this book? A: Yes, each chapter includes a set of problems with selected hints and answers. This helps reinforce the concepts presented.
- Q: What is the recommended reading level for this book? A: This book is suitable for undergraduate students. It is ideal for those studying mathematics, science, and engineering.
- Q: How should I store this book? A: Store this book in a cool, dry place, away from direct sunlight. This will help preserve its quality over time.
- Q: Can I clean the book cover? A: Yes, you can gently wipe the cover with a damp cloth to remove dust. Avoid using harsh chemicals that may damage the material.
- Q: Is this book safe for all age groups? A: Yes, this book is suitable for anyone interested in real and complex analysis. It is appropriate for high school students and above.
- Q: What if the book arrives damaged? A: If the book arrives damaged, you should contact the seller for a return or exchange. Most sellers provide policies for such issues.
- Q: Where can I buy this book? A: You can purchase this book from various online retailers, including major bookstores and educational websites. It's widely available.
- Q: Does this book include real-world applications? A: Yes, the book includes numerous examples and applications throughout the text. This enhances the practical understanding of concepts.
- Q: Is there a glossary in this book? A: No, this book does not specifically mention a glossary. However, terms are explained within the context of the chapters.