A good differential equations book

In summary: Fuller's "Theory and Application of the Laplace Transform" is a comprehensive text that covers both theory and practical applications of Laplace transforms. "In summary, there are several good options for a differential equations book that covers topics such as Bessel's functions, Legendre polynomials, Hermite polynomials, special functions, orthogonality relations, Green's functions, Laplace transforms, and Fourier transforms. Some recommended options include Riley, Hobson and Bence's "Mathematical Methods for Physics and Engineering", M.L Boas' "Mathematical Methods in the Physical Sciences", the 1970 edition of G Arfken's "Mathematical Methods for Physicists", and Gordon Fuller's "Theory and Application of
  • #1
captain
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is there any good differential book that has everything about differential equations in it. i am primarily looking for a book that is good for self teaching the subjects of: bessel's functions, legendre polynomial, hermite polynomials, and the other special functions alson with their orthogonality relations, green's functions, laplace transforms, Fourier transforms, and if possible some section on how to apply some of these methods of solving differential equations practically. i am not to picky on whether this is one or two volumes of books that cover all these materials, but i do want some or all of the answers in the back of the book so that i can check my work and go on the right track. i know this is a really long criterion of what i am looking for, but i don't know any good differential equation book(s) that cover all these topics. can anyone recommend any
text(s) that cover all these materials. thanks in advance.
 
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  • #2
Riley, Hobson and Bence "Mathematical Methods for Physics and Engineering", is a good start.

Mathematical Methods in the Physical Sciences by M.L Boas is also worth a look.

Finally the 1970 edition of Mathematical Methods for Physicists, G Arfken, proved good for me and my classmates last year.

Gordon
 
  • #3


I can understand your desire to find a comprehensive book on differential equations. I would recommend checking out "Differential Equations with Applications and Historical Notes" by George F. Simmons. This book covers all the topics you mentioned, including Bessel's functions, Legendre polynomials, Hermite polynomials, and other special functions, as well as Green's functions, Laplace transforms, and Fourier transforms. It also includes exercises and answers at the end of each chapter, allowing for self-teaching and practice. Additionally, the book provides historical context and real-world applications, which may be helpful in understanding the practical use of these methods. I hope this recommendation helps in your search for a good differential equations book.
 

1. What are the key topics covered in a good differential equations book?

A good differential equations book should cover topics such as first-order differential equations, higher-order differential equations, systems of differential equations, and applications of differential equations in various fields such as physics, engineering, and economics.

2. What makes a differential equations book "good"?

A good differential equations book should have a clear and organized presentation of concepts, a variety of examples and exercises to reinforce learning, and a balance between theory and application. It should also have a comprehensive index and appendices for quick reference.

3. Is prior knowledge of calculus required to understand a differential equations book?

Yes, a solid understanding of calculus is necessary to comprehend a differential equations book. Differential equations build upon the concepts of calculus, such as derivatives and integrals, and use them to model real-world phenomena.

4. Are there any recommended supplemental materials for a differential equations book?

Some recommended supplemental materials for a differential equations book include online resources such as interactive tutorials, practice problems, and lecture notes. Other helpful resources may include study guides, solution manuals, and video lectures.

5. What are some popular and highly recommended differential equations books?

Some popular and highly recommended differential equations books include "Elementary Differential Equations" by Boyce and DiPrima, "Differential Equations with Boundary-Value Problems" by Zill and Cullen, and "Ordinary Differential Equations" by Tenenbaum and Pollard. It is best to do some research and read reviews to find a book that best fits your learning style and level.

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