Buy Dynamic Equations on Time Scales by Martin Bohner
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Differential calculus and equations > Dynamic Equations on Time Scales: An Introduction with Applications
36%
Dynamic Equations on Time Scales: An Introduction with Applications

Dynamic Equations on Time Scales: An Introduction with Applications


     0     
5
4
3
2
1



Available


X
About the Book

The study of dynamic equations on a measure chain (time scale) goes back to its founder S. Hilger (1988), and is a new area of still fairly theoretical exploration in mathematics. Motivating the subject is the notion that dynamic equations on measure chains can build bridges between continuous and discrete mathematics. Further, the study of measure chain theory has led to several important applications, e.g., in the study of insect population models, neural networks, heat transfer, and epidemic models. Key features of the book: * Introduction to measure chain theory; discussion of its usefulness in allowing for the simultaneous development of differential equations and difference equations without having to repeat analogous proofs * Many classical formulas or procedures for differential and difference equations cast in a new light * New analogues of many of the "special functions" studied * Examination of the properties of the "exponential function" on time scales, which can be defined and investigated using a particularly simple linear equation * Additional topics covered: self-adjoint equations, linear systems, higher order equations, dynamic inequalities, and symplectic dynamic systems * Clear, motivated exposition, beginning with preliminaries and progressing to more sophisticated text * Ample examples and exercises throughout the book * Solutions to selected problems Requiring only a first semester of calculus and linear algebra, Dynamic Equations on Time Scales may be considered as an interesting approach to differential equations via exposure to continuous and discrete analysis. This approach provides an early encounter with many applications in such areas as biology, physics, and engineering. Parts of the book may be used in a special topics seminar at the senior undergraduate or beginning graduate levels. Finally, the work may

Table of Contents:
1. The Time Scales Calculus.- 1.1. Basic Definitions.- 1.2. Differentiation.- 1.3. Examples and Applications.- 1.4. Integration.- 1.5. Chain Rules.- 1.6. Polynomials.- 1.7. Further Basic Results.- 1.8. Notes and References.- 2. First Order Linear Equations.- 2.1. Hilger's Complex Plane.- 2.2. The Exponential Function.- 2.3. Examples of Exponential Functions.- 2.4. Initial Value Problems.- 2.5. Notes and References.- 3. Second Order Linear Equations.- 3.1. Wronskians.- 3.2. Hyperbolic and Trigonometric Functions.- 3.3. Reduction of Order.- 3.4. Method of Factoring.- 3.5. Nonconstant Coefficients.- 3.6. Hyperbolic and Trigonometric Functions II.- 3.7. Euler-Cauchy Equations.- 3.8. Variation of Parameters.- 3.9. Annihilator Method.- 3.10. Laplace Transform.- 3.11. Notes and References.- 4. Self-Adjoint Equations.- 4.1. Preliminaries and Examples.- 4.2. The Riccati Equation.- 4.3. Disconjugacy.- 4.4. Boundary Value Problems and Green's Function.- 4.5. Eigenvalue Problems.- 4.6. Notes and References.- 5. Linear Systems and Higher Order Equations.- 5.1. Regressive Matrices.- 5.2. Constant Coefficients.- 5.3. Self-Adjoint Matrix Equations.- 5.4. Asymptotic Behavior of Solutions.- 5.5. Higher Order Linear Dynamic Equations.- 5.6. Notes and References.- 6. Dynamic Inequalities.- 6.1. Gronwall's Inequality.- 6.2. Holder's and Minkowski's Inequalities.- 6.3. Jensen's Inequality.- 6.4. Opial Inequalities.- 6.5. Lyapunov Inequalities.- 6.6. Upper and Lower Solutions.- 6.7. Notes and References.- 7. Linear Symplectic Dynamic Systems.- 7.1. Symplectic Systems and Special Cases.- 7.2. Conjoined Bases.- 7.3. Transformation Theory and Trigonometric Systems.- 7.4. Notes and References.- 8. Extensions.- 8.1. Measure Chains.- 8.2. Nonlinear Theory.- 8.3. Alpha Derivatives.- 8.4. Nabla Derivatives.- 8.5. Notes and References.- Solutions to Selected Problems.

Review :
"This would be an excellent book to use in a topics course on dynamic equations on time scales at the advanced undergraduate level and/or beginning graduate level." --Zentralblatt Math "The monograph under review comes at an excellent time in the rapid development of dynamic equations on time scales. Both authors are authorities in this field of study and they have produced an excellent introduction to it. Much of the material is accessible to upper-level undergraduate mathematics majors, and yet, the results and the techniques are pertinent to active researchers in the area." --Mathematical Reviews


Best Sellers


Product Details
  • ISBN-13: 9780817642259
  • Publisher: Birkhauser Boston
  • Publisher Imprint: Birkhauser Boston
  • Height: 254 mm
  • No of Pages: 358
  • Returnable: Y
  • Width: 178 mm
  • ISBN-10: 0817642250
  • Publisher Date: 15 Jun 2001
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Sub Title: An Introduction with Applications


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Dynamic Equations on Time Scales: An Introduction with Applications
Birkhauser Boston -
Dynamic Equations on Time Scales: An Introduction with Applications
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Dynamic Equations on Time Scales: An Introduction with Applications

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    Fresh on the Shelf


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!