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Variational Calculus on Time Scales [Hardback]

  • Formāts: Hardback, 310 pages, height x width: 254x178 mm, weight: 542 g
  • Izdošanas datums: 12-Oct-2018
  • Izdevniecība: Nova Science Publishers Inc
  • ISBN-10: 1536143235
  • ISBN-13: 9781536143232
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  • Cena: 320,00 €
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Variational Calculus on Time ScalesPalielināt
  • Formāts: Hardback, 310 pages, height x width: 254x178 mm, weight: 542 g
  • Izdošanas datums: 12-Oct-2018
  • Izdevniecība: Nova Science Publishers Inc
  • ISBN-10: 1536143235
  • ISBN-13: 9781536143232
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781536143232.html
Keywords:
Preface ix
1 Elements of the Time Scale Calculus
1(78)
1.1 Forward and Backward Jump Operators, Graininess Function
1(4)
1.2 Differentiation
5(7)
1.3 Integration
12(7)
1.4 The Exponential Function
19(10)
1.5 Hyperbolic and Trigonometric Functions
29(1)
1.6 The Multidimensional Time Scale Calculus
30(36)
1.7 Line Integrals
66(6)
1.8 Green's Formula
72(3)
1.9 Advanced Practical Problems
75(4)
2 Dynamic Systems on Time Scales
79(52)
2.1 Structure of Dynamic Systems on Time Scales
79(36)
2.2 Constant Coefficients
115(12)
2.3 Advanced Practical Problems
127(4)
3 Functionals
131(26)
3.1 Definition for Functionals
131(2)
3.2 Self-Adjoint Second Order Matrix Equations
133(11)
3.3 Jacobi's Condition
144(9)
3.4 Sturmian Theory
153(4)
4 Linear Hamiltonian Dynamic Systems
157(62)
4.1 Linear Symplectic Dynamic Systems
157(6)
4.2 Hamiltonian Systems
163(3)
4.3 Conjoined Bases
166(11)
4.4 Riccati Equations
177(5)
4.5 Picone's Identity
182(16)
4.6 "Big" Linear Hamiltonian Systems
198(13)
4.7 Positivity of Quadratic Functionals
211(8)
5 The First Variation
219(32)
5.1 The Dubois-Reymond Lemma
219(6)
5.2 The Variational Problem
225(8)
5.3 The Euler-Lagrange Equation
233(8)
5.4 Legendre's Condition
241(4)
5.5 Jacobi's Condition
245(3)
5.6 Advanced Practical Problems
248(3)
6 Higher Order Calculus of Variations
251(10)
6.1 Statement of the Variational Problem
251(3)
6.2 Euler's Equation
254(6)
6.3 Advanced Practical Problems
260(1)
7 Double Integral Calculus of Variations
261(14)
7.1 Statement of the Variational Problem
262(1)
7.2 First and Second Variation
263(5)
7.3 Euler's Condition
268(4)
7.4 Advanced Practical Problems
272(3)
8 Noether's Second Theorem
275(16)
8.1 Invariance under Transformations
275(4)
8.2 Noether's Second Theorem without Transformations of Time
279(2)
8.3 Noether's Second Theorem with Transformations of Time
281(4)
8.4 Noether's Second Theorem-Double Delta Integral Case
285(6)
References 291(2)
Author Contact Information 293(2)
Index 295