The Resource Dynamic Equations on Time Scales : An Introduction with Applications, by Martin Bohner, Allan Peterson, (electronic resource)

Dynamic Equations on Time Scales : An Introduction with Applications, by Martin Bohner, Allan Peterson, (electronic resource)

Label
Dynamic Equations on Time Scales : An Introduction with Applications
Title
Dynamic Equations on Time Scales
Title remainder
An Introduction with Applications
Statement of responsibility
by Martin Bohner, Allan Peterson
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
On becoming familiar with difference equations and their close re­ lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro­ duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa­ tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals
http://library.link/vocab/creatorName
Bohner, Martin
Dewey number
  • 510
  • 515
  • 515.3
  • 515.352
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • CL5zIEi3xrs
  • HYD7oZw5M0c
Language note
English
LC call number
QA299.6-433
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Peterson, Allan.
http://library.link/vocab/subjectName
  • Global analysis (Mathematics)
  • Differential Equations
  • Mathematics
  • Systems theory
  • Computer science
  • Analysis
  • Ordinary Differential Equations
  • Applications of Mathematics
  • Systems Theory, Control
  • Computational Mathematics and Numerical Analysis
Label
Dynamic Equations on Time Scales : An Introduction with Applications, by Martin Bohner, Allan Peterson, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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
Dimensions
unknown
Edition
1st ed. 2001.
Extent
1 online resource (364 p.)
Form of item
online
Isbn
9781461202011
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-0201-1
Specific material designation
remote
System control number
  • (CKB)3400000000089034
  • (EBL)1246663
  • (SSID)ssj0001296473
  • (PQKBManifestationID)11886455
  • (PQKBTitleCode)TC0001296473
  • (PQKBWorkID)11347982
  • (PQKB)10161232
  • (DE-He213)978-1-4612-0201-1
  • (EXLCZ)993400000000089034
Label
Dynamic Equations on Time Scales : An Introduction with Applications, by Martin Bohner, Allan Peterson, (electronic resource)
Publication
Note
Description based upon print version of record
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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
Dimensions
unknown
Edition
1st ed. 2001.
Extent
1 online resource (364 p.)
Form of item
online
Isbn
9781461202011
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-0201-1
Specific material designation
remote
System control number
  • (CKB)3400000000089034
  • (EBL)1246663
  • (SSID)ssj0001296473
  • (PQKBManifestationID)11886455
  • (PQKBTitleCode)TC0001296473
  • (PQKBWorkID)11347982
  • (PQKB)10161232
  • (DE-He213)978-1-4612-0201-1
  • (EXLCZ)993400000000089034

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