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Ordinary Differential Equations

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Karl Gustav Andersson Lars-Christer Böiers Ordinary Differential Equations This is a translation of a book that has been used for many years in Sweden in courses on ordinary differential equations for advanced undergraduate and beginning graduate students. It gives a careful and thorough introduction to the main areas of the field and should also be useful for engineers and applied mathematicians. Topics covered are existence, uniqueness and approximation of solutions, linear system...

Karl Gustav Andersson Lars-Christer Böiers Ordinary Differential Equations This is a translation of a book that has been used for many years in Sweden in courses on ordinary differential equations for advanced undergraduate and beginning graduate students. It gives a careful and thorough introduction to the main areas of the field and should also be useful for engineers and applied mathematicians. Topics covered are existence, uniqueness and approximation of solutions, linear systems with constant coefficients, power series solutions, eigenfunction expansions and qualitative methods for non-linear systems. The book contains many illustrative examples and almost three hundred exercises.

      • 0
        1
         Terminology and introductory examples
        • 0.1
          1
           Terminology
        • 0.2
          2
           Differential equations of first order
        • 0.3
          10
           Linear differential equations
        • 0.4
          20
           Systems of differential equations
        • 0.5
          28
           Initial value problems and boundary value problems
        • 0.6
          29
           Integral equations
      • 1
        31
         General theorems on existence and uniqueness
        • 1.1
          31
           Existence and uniqueness
        • 1.2
          46
           Linear systems
        • 1.3
          57
           Differential inequalities
        • 1.4
          59
           Approximate solutions
        • 1.5
          65
           Construction of solutions
        • 1.6
          71
           An orientation on numerical methods for solving differential equations
        • 1.7
          84
           Some historical notes
      • 2
        87
         Linear systems with constant coefficients
        • 2.1
          87
           The exponential function etA
        • 2.2
          102
           Homogeneous systems
        • 2.3
          108
           Inhomogeneous systems
        • 2.4
          115
           Decomposition into invariant subspaces
        • 2.5
          122
           Variable coefficients
        • 2.6
          123
           Systems of second order
        • 2.7
          127
           Some historical notes
      • 3
        131
         Differential equations with singular points
        • 3.1
          131
           Linear systems with analytic coefficients
        • 3.2
          135
           Singular points
        • 3.3
          148
           Frobenius’ method
        • 3.4
          160
           Some classical differential equations
        • 3.5
          167
           Some historical notes
      • 4
        171
         Boundary value problems Eigenfunction expansions
        • 4.1
          171
           Introductory example Separation of variables
        • 4.2
          177
           Boundary value problems
        • 4.3
          188
           Eigenvalues and eigenfunctions The spectral theorem
        • 4.4
          200
           Sturm-Liouville theory
        • 4.5
          215
           Convergence of eigenfunction expansions
        • 4.6
          224
           A general proof of the spectral theorem
        • 4.7
          235
           Some examples of singular Sturm-Liouville problems
        • 4.8
          245
           Some historical notes
      • 5
        253
         Autonomous systems
        • 5.1
          253
           Phase portraits
        • 5.2
          264
           Linear systems in the plane
        • 5.3
          268
           Liapunov’s method
        • 5.4
          280
           Investigation of stability via linearization
        • 5.5
          286
           Periodic solutions
        • 5.6
          303
           Systems of higher order
        • 5.7
          310
           Some historical notes
    • 317
      A The spaces Rn and Cn
    • 323
      B Bolzano-Weierstrass’ theorem
    • 327
      C Cauchy’s convergence principle
    • 331
      D Functions operating on matrices
    • 339
      Bibliography
    • 341
      Answers to the exercises
    • 363
      Index

Information

Författare:
Karl Gustav Andersson Lars-Christer Böiers
Språk:
Engelska
ISBN:
9789144134956
Utgivningsår:
2019
Artikelnummer:
40453-01
Upplaga:
Första
Sidantal:
374

Köp- och leveransvillkor

Författare

Karl Gustav Andersson

Karl Gustav Andersson är universitetslektor i matematik vid Lunds universitet.

Lars-Christer Böiers

Lars-Christer Böiers är universitetslektor i matematik och har mångårig erfarenhet av undervisning vid Lunds Tekniska Högskola.

Förlagskontakt

Jens Fredholm

Förläggare Teknik
Teknik, matematik och statistik
046-31 21 58 E-post

Fritjof Janson

Förlagskoordinator Kurslitteratur och Kompetensutveckling
046-31 22 57 E-post
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