Klienditugi: 7440010 (E-R 10-18)

E-raamat: Ordinary Differential Equations and Calculus of Variations [World Scientific e-raamat]

Mikola Vladimirovich Makarets (Kyiv Taras Shevchenko Nat'l Univ, Ukraine), Victor Yu Reshetnyak (Kyiv Taras Shevchenko Nat'l Univ, Ukraine)

Formaat: 384 pages
Ilmumisaeg: 06-Jan-1995
Kirjastus: World Scientific Publishing Co Pte Ltd
ISBN-13: 9789812831118

Teised raamatud teemal:

World Scientific e-raamat
Hind: 165,40 €*
* hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks

Formaat: 384 pages
Ilmumisaeg: 06-Jan-1995
Kirjastus: World Scientific Publishing Co Pte Ltd
ISBN-13: 9789812831118

Teised raamatud teemal:

Rohkem infot World Scientific e-raamatute kohta

Raamatu kodulehekülg: http://www.worldscientific.com/worldscibooks/10.1142/2683#t=toc

This problem book contains exercises for courses in differential equations and calculus of variations at universities and technical institutes. It is designed for non-mathematics students and also for scientists and practicing engineers who feel a need to refresh their knowledge. The book contains more than 260 examples and about 1400 problems to be solved by the students much of which have been composed by the authors themselves. Numerous references are given at the end of the book to furnish sources for detailed theoretical approaches, and expanded treatment of applications.

Preface

First Order Differential Equations

(76)

Separable equations

(8)

Homogeneous equations

(10)

Quasihomogeneous Equations

(3)

Exact equations

(14)

Integrating Factor's

(8)

Linear equations

(19)

Bernoulli's Equation

(3)

Darboux's Equation

(2)

Riccati's Equation

(4)

Bool's Equation

(2)

Nonlinear equations

(12)

Solvable Equations. General Solution

(6)

Solvable Equations. Singular Solution

(3)

Unsolvable Equations

(2)

Applications in physics

(10)

Mechanics

(3)

Hydrodynamics

(1)

Electrical Networks

(1)

Kinetic Theory

(3)

Nuclear Physics

(1)

Optics

(2)

Miscellaneous problems

(3)

N-th Order Differential Equations

(76)

Reduction of order

(10)

Simple Cases

(1)

Homogeneous Equations

(1)

Exact Equations

(2)

Linear Equations

(1)

The Initial Value Problem

(4)

Linear homogeneous equations

(10)

Exponential Solution

(1)

Power Solution

(2)

Transformations of Equation

(2)

The Initial Value Problem

(3)

Linear nonhomogeneous equations

(10)

Method of Variation of Parameters

(2)

Method of Undetermined Coefficients

100

(2)

The Influence Function

102

(1)

The Initial Value Problem

103

(4)

Linear equation with constant coefficients

107

(33)

The Homogeneous Equation with Constant Coefficients

107

(5)

The Complete Equation with Constant Coefficients. Method of Undetermined Coefficients

112

(8)

The Method of Variation of Parameters

120

(3)

Symbolic Methods

123

(8)

Laplace Transform

131

(9)

Equations with polynomial coefficients

140

(13)

Changes of Variable

141

(2)

Substitutions

143

(2)

Substitutions and Changes of Variable

145

(1)

Series Solutions

146

(7)

Linear Second Order Equations

153

(38)

Series solutions

153

(19)

Ordinary Point

153

(4)

Regular Singular Point

157

(9)

Irregular Singular Point

166

(6)

Linear boundary value problem

172

(10)

Homogeneous Problem

173

(2)

Nonhomogeneous Problem

175

(3)

Green's Function

178

(4)

Eigenvalues and eigenfunctions

182

(9)

Self-adjoint Problems

184

(2)

The Sturm-Liouville Problem

186

(2)

Nonhomogeneous Problem

188

(3)

Systems of Differential Equations

191

(46)

Linear systems with constant coefficients

191

(25)

Homogeneous Systems

191

(1)

Homogeneous Systems. Euler's Method

192

(1)

Euler's Method. Different Eigenvalues

192

(1)

Euler's Method. Repeated Eigenvalues

193

(1)

Repeated Eigenvalues. Method of Associated Vectors

194

(4)

Repeated Eigenvalues. Method of Undetermined Coefficients

198

(1)

Homogeneous Systems. Matrix Method

199

(4)

Nonhomogeneous Systems

203

(1)

Method of Variation of Parameters

203

(1)

Method of Undetermined Coefficients

204

(1)

Matrix Method

205

(1)

Initial Value Problem

206

(1)

Laplace Transform

207

(1)

Systems of Higher Order Equations

208

(8)

Linear systems

216

(8)

Solution by Eliminations

216

(3)

Matrix Method

219

(1)

Nonhomogeneous Linear Systems

219

(2)

Initial Value Problem

221

(3)

Nonlinear systems

224

(13)

Method of Eliminations

225

(3)

Method of Integrable Combinations

228

(2)

Systems-of Bernoulli's Form

230

(1)

Method of Complex Variable

231

(1)

Systems of Canonical Form

232

(5)

Partial Equations of the First Order

237

(18)

Linear partial equations

237

(7)

Pfaffian equation

244

(4)

Mayer's Method

246

(2)

Nonlinear partial equations

248

(7)

Lagrange - Charpit's Method

250

(5)

Nonlinear Equations and Stability

255

(24)

Phase plane. Linear systems

257

(9)

Almost linear systems

266

(7)

Liapunov's second method

273

(6)

Calculus of Variations

279

(28)

Euler's equation

279

(5)

Conditional extremum

284

(8)

Isoperimetric Problem

288

(4)

Movable end points

292

(7)

Bolza problem

299

(2)

Euler-Poisson equation

301

(2)

Ostrogradsky equation

303

(4)

Answers to Problems

307

(58)

Separable equations

307

(1)

Homogeneous equations

308

(2)

Exact equations

310

(2)

Linear equations

312

(3)

Nonlinear equations

315

(3)

Applications in physics

318

(3)

Miscellaneous problems

321

(2)

Reduction of order

323

(3)

Linear homogeneous equations

326

(1)

Linear nonhomogeneous equations

327

(3)

Linear equation with constant coefficients

330

(6)

Equations with polynomial coefficients

336

(2)

Series solutions

338

(4)

Linear boundary value problems

342

(2)

Eigenvalues and eigenfunctions

344

(2)

Systems with constant coefficients

346

(4)

Linear systems

350

(1)

Nonlinear systems

351

(3)

Linear partial equations

354

(1)

Pfaffian equation

355

(1)

Nonlinear partial equations

355

(2)

Phase plane. Linear systems

357

(1)

Almost linear systems

358

(1)

Liapunov's second method

359

(1)

Euler's equation

359

(1)

Conditional extremum

360

(1)

Isoperimetric problem

361

(1)

Movable end points

361

(1)

Bolza problem

362

(1)

Euler-Poisson equation

362

(1)

Ostrogradsky equation

363

(2)

Bibliography

365

(4)

Index

369

Püsilink: https://www.kriso.ee/db/9789812831118_pe.html

Märksõnad:

E-raamat: Ordinary Differential Equations and Calculus of Variations [World Scientific e-raamat]

Konto & seaded

Otsing

Otsingu andmebaas

Filtreeri tulemusi

Teemad Kirjastuste teemad

Vali ostukorv