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Classical Methods in Ordinary Differential Equations: With Applications to Boundary Value Problems
 
Stuart P. Hastings University of Pittsburgh, Pittsburgh, PA
J. Bryce McLeod Oxford University, Oxford, England and University of Pittsburgh, Pittsburgh, PA
Classical Methods in Ordinary Differential Equations
Hardcover ISBN:  978-0-8218-4694-0
Product Code:  GSM/129
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Sale Price: $64.35
eBook ISBN:  978-0-8218-8485-0
Product Code:  GSM/129.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Hardcover ISBN:  978-0-8218-4694-0
eBook: ISBN:  978-0-8218-8485-0
Product Code:  GSM/129.B
List Price: $184.00 $141.50
MAA Member Price: $165.60 $127.35
AMS Member Price: $147.20 $113.20
Sale Price: $119.60 $91.98
Classical Methods in Ordinary Differential Equations
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Classical Methods in Ordinary Differential Equations: With Applications to Boundary Value Problems
Stuart P. Hastings University of Pittsburgh, Pittsburgh, PA
J. Bryce McLeod Oxford University, Oxford, England and University of Pittsburgh, Pittsburgh, PA
Hardcover ISBN:  978-0-8218-4694-0
Product Code:  GSM/129
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Sale Price: $64.35
eBook ISBN:  978-0-8218-8485-0
Product Code:  GSM/129.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Hardcover ISBN:  978-0-8218-4694-0
eBook ISBN:  978-0-8218-8485-0
Product Code:  GSM/129.B
List Price: $184.00 $141.50
MAA Member Price: $165.60 $127.35
AMS Member Price: $147.20 $113.20
Sale Price: $119.60 $91.98
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1292012; 373 pp
    MSC: Primary 34; 35; 37;

    This text emphasizes rigorous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behavior of solutions with respect to either the independent variable or some parameter. These equations may give special solutions of important PDEs, such as steady state or traveling wave solutions. Often two, or even three, approaches to the same problem are described. The advantages and disadvantages of different methods are discussed.

    The book gives complete classical proofs, while also emphasizing the importance of modern methods, especially when extensions to infinite dimensional settings are needed. There are some new results as well as new and improved proofs of known theorems. The final chapter presents three unsolved problems which have received much attention over the years.

    Both graduate students and more experienced researchers will be interested in the power of classical methods for problems which have also been studied with more abstract techniques. The presentation should be more accessible to mathematically inclined researchers from other areas of science and engineering than most graduate texts in mathematics.

    Readership

    Graduate students and research mathematicians interested in ODEs and PDEs.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Introduction
    • Chapter 2. An introduction to shooting methods
    • Chapter 3. Some boundary value problems for the Painlevé transcendents
    • Chapter 4. Periodic solutions of a higher order system
    • Chapter 5. A linear example
    • Chapter 6. Homoclinic orbits of the FitzHugh-Nagumo equations
    • Chapter 7. Singular perturbation problems—rigorous matching
    • Chapter 8. Asymptotics beyond all orders
    • Chapter 9. Some solutions of the Falkner-Skan equation
    • Chapter 10. Poiseuille flow: Perturbation and decay
    • Chapter 11. Bending of a tapered rod; variational methods and shooting
    • Chapter 12. Uniqueness and multiplicity
    • Chapter 13. Shooting with more parameters
    • Chapter 14. Some problems of A. C. Lazer
    • Chapter 15. Chaotic motion of a pendulum
    • Chapter 16. Layers and spikes in reaction-diffusion equations, I
    • Chapter 17. Uniform expansions for a class of second order problems
    • Chapter 18. Layers and spikes in reaction-diffusion equations, II
    • Chapter 19. Three unsolved problems
  • Reviews
     
     
    • This book brings a new and innovative look to several areas of the theory of ordinary differential equations. It is certainly a very refreshing addition to the existing literature. Students of mathematics who have avoided (for various reasons) differential equations need this volume as an antidote. ...a most informative, stimulating, and refreshing book!

      MAA Reviews
    • This well-conceived and well-presented monograph uniquely provides us an opportunity to learn how these experts analyze a wide variety of boundary value problems of current interest and how they interpret and utilize the relevant recent literature. The skills they display are potent, and they're not found in other textbooks.

      Robert E. O'Malley, SIAM Book Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1292012; 373 pp
MSC: Primary 34; 35; 37;

This text emphasizes rigorous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behavior of solutions with respect to either the independent variable or some parameter. These equations may give special solutions of important PDEs, such as steady state or traveling wave solutions. Often two, or even three, approaches to the same problem are described. The advantages and disadvantages of different methods are discussed.

The book gives complete classical proofs, while also emphasizing the importance of modern methods, especially when extensions to infinite dimensional settings are needed. There are some new results as well as new and improved proofs of known theorems. The final chapter presents three unsolved problems which have received much attention over the years.

Both graduate students and more experienced researchers will be interested in the power of classical methods for problems which have also been studied with more abstract techniques. The presentation should be more accessible to mathematically inclined researchers from other areas of science and engineering than most graduate texts in mathematics.

Readership

Graduate students and research mathematicians interested in ODEs and PDEs.

  • Chapters
  • Chapter 1. Introduction
  • Chapter 2. An introduction to shooting methods
  • Chapter 3. Some boundary value problems for the Painlevé transcendents
  • Chapter 4. Periodic solutions of a higher order system
  • Chapter 5. A linear example
  • Chapter 6. Homoclinic orbits of the FitzHugh-Nagumo equations
  • Chapter 7. Singular perturbation problems—rigorous matching
  • Chapter 8. Asymptotics beyond all orders
  • Chapter 9. Some solutions of the Falkner-Skan equation
  • Chapter 10. Poiseuille flow: Perturbation and decay
  • Chapter 11. Bending of a tapered rod; variational methods and shooting
  • Chapter 12. Uniqueness and multiplicity
  • Chapter 13. Shooting with more parameters
  • Chapter 14. Some problems of A. C. Lazer
  • Chapter 15. Chaotic motion of a pendulum
  • Chapter 16. Layers and spikes in reaction-diffusion equations, I
  • Chapter 17. Uniform expansions for a class of second order problems
  • Chapter 18. Layers and spikes in reaction-diffusion equations, II
  • Chapter 19. Three unsolved problems
  • This book brings a new and innovative look to several areas of the theory of ordinary differential equations. It is certainly a very refreshing addition to the existing literature. Students of mathematics who have avoided (for various reasons) differential equations need this volume as an antidote. ...a most informative, stimulating, and refreshing book!

    MAA Reviews
  • This well-conceived and well-presented monograph uniquely provides us an opportunity to learn how these experts analyze a wide variety of boundary value problems of current interest and how they interpret and utilize the relevant recent literature. The skills they display are potent, and they're not found in other textbooks.

    Robert E. O'Malley, SIAM Book Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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