Title
Generalized Functions And Partial Differential Equations (Dover Books On Mathematics)
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This Selfcontained Treatment Develops The Theory Of Generalized Functions And The Theory Of Distributions, And It Systematically Applies Them To Solving A Variety Of Problems In Partial Differential Equations. A Major Portion Of The Text Is Based On Material Included In The Books Of L. Schwartz, Who Developed The Theory Of Distributions, And In The Books Of Gelfand And Shilov, Who Deal With Generalized Functions Of Any Class And Their Use In Solving The Cauchy Problem. In Addition, The Author Provides Applications Developed Through His Own Research.Geared Toward Upperlevel Undergraduates And Graduate Students, The Text Assumes A Sound Knowledge Of Both Real And Complex Variables. Familiarity With The Basic Theory Of Functional Analysis, Especially Normed Spaces, Is Helpful But Not Necessary. An Introductory Chapter Features Helpful Background On Topological Spaces. Applications To Partial Differential Equations Include A Treatment Of The Cauchy Problem, The Goursat Problem, Fundamental Solutions, Existence And Differentiality Of Solutions Of Equations With Constants, Coefficients, And Related Topics. Supplementary Materials Include Endofchapter Problems, Bibliographical Remarks, And A Bibliography.
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- Q: What is the page count of this book? A: The book contains three hundred sixty-eight pages. It provides a comprehensive exploration of generalized functions and partial differential equations.
- Q: What are the dimensions of this book? A: The book measures five point five nine inches in length, zero point seven one inches in width, and eight point five inches in height. These dimensions make it easy to handle and store.
- Q: What binding type does this book have? A: This book is available in paperback binding. This type of binding is lightweight and flexible, making it suitable for students.
- Q: What level of mathematics knowledge is required for this book? A: A sound knowledge of real and complex variables is required. It is geared towards upper-level undergraduates and graduate students.
- Q: Is this book suitable for beginners in mathematics? A: No, this book is not suitable for beginners. It is intended for those with prior knowledge of advanced mathematics concepts.
- Q: How does one apply the concepts from this book? A: The concepts can be applied by solving various problems in partial differential equations. The text provides methods and examples for practical applications.
- Q: Are there exercises included in this book? A: Yes, the book includes end-of-chapter problems. These exercises help reinforce the material and enhance understanding.
- Q: What mathematical topics are covered in this book? A: The book covers generalized functions, distributions, and partial differential equations. It also addresses the Cauchy problem and fundamental solutions.
- Q: What should I do if I have trouble understanding the material? A: You can refer to the supplementary materials, including bibliographical remarks and a bibliography for additional resources. These can aid in comprehension.
- Q: What is the author's name for this book? A: The book is authored by Avner Friedman. He is known for his contributions to the field of mathematics.
- Q: Is this book appropriate for self-study? A: Yes, this book is appropriate for self-study. It provides thorough explanations and exercises for independent learners.
- Q: What is the publisher of this book? A: The book is published by Dover Publications. They are known for their quality educational materials.
- Q: Can this book help in preparing for exams on differential equations? A: Yes, this book can help in exam preparation. It covers essential topics and provides practice problems relevant to the subject.
- Q: Does this book include applications from the author's research? A: Yes, the author includes applications developed through his own research. These provide real-world context to the theoretical concepts.
- Q: Is this book part of a series? A: No, this book is not part of a series. It stands alone as a comprehensive text on its subject matter.