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86233181
Advanced Mathematical Analysis: Periodic Functions and Distributions, Complex Analysis, Laplace Transform and Applications (Graduate Texts in
Item #:
86233181
STD 1245000
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It is time to reconcile the separation of advanced mathematics for science and engineering from that for mathematicians.
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What Stands Out
Comprehensive Coverage
This text meticulously covers advanced mathematical concepts, including periodic functions and complex analysis, making it an essential resource for graduate students and professionals seeking in-depth knowledge.
Practical Applications
It provides real-world applications of Laplace transforms, linking theory to practice, thereby addressing practical challenges faced by students in engineering and applied sciences.
Expert Authors
Authored by leading mathematicians, the book delivers high-quality content that ensures readers gain authoritative insights into complex topics, enhancing both understanding and academic performance.
Product Details
- Once upon a time students of mathematics and students of science or engineering took the same courses in mathematical analysis beyond calculus. Now it is common to separate advanced mathematics for science and engi neering from what might be called advanced mathematical analysis for mathematicians. It seems to me both useful and timely to attempt a reconciliation. The separation between kinds of courses has unhealthy effects. Mathe matics students reverse the historical development of analysis, learning the unifying abstractions first and the examples later (if ever). Science students learn the examples as taught generations ago, missing modern insights. A choice between encountering Fourier series as a minor instance of the repre sentation theory of Banach algebras, and encountering Fourier series in isolation and developed in an ad hoc manner, is no choice at all. It is easy to recognize these problems, but less easy to counter the legiti mate pressures which have led to a separation. Modern mathematics has broadened our perspectives by abstraction and bold generalization, while developing techniques which can treat classical theories in a definitive way. On the other hand, the applier of mathematics has continued to need a variety of definite tools and has not had the time to acquire the broadest and most definitive grasp-to learn necessary and sufficient conditions when simple sufficient conditions will serve, or to learn the general framework encompass ing different examples.
| Publisher | Springer |
| Publication date | December 26, 1973 |
| Edition | 1st ed. 1973. Corr. 2nd printing 1973 |
| Language | English |
| Print length | 246 pages |
| ISBN-10 | 0387900659 |
| ISBN-13 | 978-0387900650 |
| Item Weight | 1.16 pounds (530 grams) |
| Dimensions | 6.14 x 0.63 x 9.21 inches (15.6 x 1.6 x 23.4 cm) |
Who Should Buy?
-
Graduate Students
Ideal for graduate students focusing on mathematical analysis and requiring in-depth understanding of complex analysis and transforms.
-
Mathematicians
Professionals seeking a comprehensive reference for advanced topics including periodic functions and distribution theory.
-
Researchers
Useful for researchers needing detailed methodologies in Laplace transforms and their applications in various fields.
-
Undergraduate Students
Not suitable for undergraduates as it covers advanced topics that may be beyond their current curriculum.
-
Casual Learners
Not recommended for those casually interested in mathematics, as this book demands focused and rigorous study.
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Basic Mathematicians
Beginners in mathematics may find the content too challenging without prior foundational knowledge in advanced concepts.
Product Description
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Customer Questions & Answers
-
Question:
What topics are covered in Advanced Mathematical Analysis?
Answer: Advanced Mathematical Analysis delves into several core areas, including periodic functions, distributions, complex analysis, and the Laplace transform along with its applications. The book provides a thorough exploration of how these mathematical concepts interconnect and their real-world applications. For example, complex analysis is essential for understanding fluid dynamics and electromagnetic fields, while the Laplace transform is pivotal in engineering for solving differential equations related to systems and control theory. -
Question:
Who is the target audience for this book?
Answer: This graduate-level text is specifically designed for advanced students in mathematics, engineering, and physics. It serves as an essential resource for those pursuing higher studies, enabling a deep understanding of mathematical analysis and its applications. Ideal candidates include graduate students preparing for exams or research, professors seeking comprehensive material for courses, and professionals looking to refresh their knowledge in mathematical theory. -
Question:
Can this book help in practical applications?
Answer: Absolutely! Advanced Mathematical Analysis boasts numerous practical applications across various fields. The rigorous examination of complex functions helps in engineering problems related to signal processing and circuit design. Furthermore, the thorough discussion on the Laplace transform equips readers with techniques to approach real-time problems in control systems and differential equations encountered in engineering solutions. -
Question:
Is this book suitable for self-study?
Answer: Yes, this book is well-suited for self-study due to its comprehensive explanations and structured approach to complex topics. The author presents theoretical concepts followed by practical examples, which aid in understanding. Additionally, its clear organization makes it easy for independent learners to navigate and grasp the material at their own pace, supplementing academic learning with practical insights. -
Question:
What kind of prerequisites should a reader have?
Answer: Readers should possess a solid foundation in undergraduate-level calculus and linear algebra. Familiarity with basic differential equations and introductory complex analysis is beneficial, as these topics are expanded upon in this text. A good understanding of mathematical proof techniques will also facilitate smoother comprehension of the presented theories and applications. -
Question:
Does the book include problem sets or exercises?
Answer: Yes, Advanced Mathematical Analysis includes a variety of exercises and problem sets designed to reinforce learning and application of the concepts discussed. These exercises range from theoretical questions to practical applications, allowing readers to test their understanding and apply what they have learned in realistic scenarios, which is crucial for mastering advanced mathematical topics. -
Question:
Who is the author of this book?
Answer: The author of Advanced Mathematical Analysis is a recognized expert in the field, often holding advanced degrees and academic positions that contribute to their authoritative voice. Their background ensures a blend of theoretical knowledge and practical expertise, allowing for insightful analyses and clear explanations. Readers often find the author's approach engaging, fostering a deep appreciation of the subject matter. -
Question:
How does this book compare to other mathematical analysis texts?
Answer: This book distinguishes itself through its focused depth on specific advanced topics like periodic functions and distributions compared to broader mathematical analyses that only touch upon these subjects peripherally. Its detailed methodologies and applications provide additional insights that are often lacking in more introductory texts. Consequently, it’s an excellent choice for graduate students and professionals who desire an in-depth study of complex mathematical tools. -
Question:
What are some common applications of the Laplace transform discussed in the book?
Answer: The Laplace transform is a powerful tool covered in the book, with applications in systems engineering, control theory, and signal processing. Readers will learn how this transform simplifies the analysis of linear time-invariant systems, making it easier to solve ordinary differential equations. For instance, engineers utilize Laplace transforms in designing electronic circuits, ensuring stability and functionality in real-world applications. -
Question:
Where can I buy the book Advanced Mathematical Analysis in São Tomé and Príncipe?
Answer: You can buy Advanced Mathematical Analysis: Periodic Functions and Distributions, Complex Analysis, Laplace Transform and Applications on Ubuy. Ubuy offers a reliable platform for acquiring this graduate text and often provides various options for purchasing, making it accessible for buyers across São Tomé and Príncipe.
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Features & Benefits
- Addresses the separation of advanced mathematics courses.
- Encourages a reconciliation of math for scientists and mathematicians.
- Highlights the historical evolution of mathematical analysis.
- Offers modern insights into classical theories.
- Focuses on the necessity of both unifying abstractions and practical examples.
- Provides definitive techniques alongside essential tools for application.