Abstract
In this chapter we shall present a systematic study of the solutions of linear ordinary differential equations. Such equations continue to play an important role in many branches of the natural sciences and other fields, e.g., economics, so that they may be treated here in their own right. On the other hand, we should not forget that our main objective is to study nonlinear equations, and in the construction of their solutions the solutions of linear equations come in at several instances.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Groups and Invariance
E. C. G. Sudarshan, M. Mukunda: Classical Dynamics: A Modern Perspective (Wiley, New York 1974)
R. D. Richtmyer: Principles of Advanced Mathematical Physics II (Springer, Berlin, Heidelberg, New York 1981)
Pathways to Self-Organization
Self-Organization Through Change of Control Parameters
H. Haken: Synergetics, Springer Ser. Synergetics, Vol. 1, 3rd. ed. (Springer, Berlin, Heidelberg, New York 1983)
Self-Organization Through Change of Number of Components
H. Haken: Prog. Theor. Phys. Suppl. 69, 30 (1980)
H. Haken: Unpublished material
O. Duffing: Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre technische Bedeutung (Vieweg, Braunschweig 1918)
C. Hayashi: Nonlinear Oscillations in Physical Systems (McGraw-Hill, New York 1964) compare Sect. 2.1.1 also
R. Bellman, K. L. Cooke: Introduction to Matrix Analysis (McGraw-Hill, New York 1960)
N. Dunford, J. T. Schwartz: Linear Operators, Pure and Applied Mathematics, Vol. VII, Parts I-III (Wiley, Interscience, New York 1957)
Theorem on vanishing Lyapunov exponents: H. Haken: Phys. Lett. 94A, 71 (1983)
E. A. Coddington, N. Levinson: Theory of Ordinary Differential Equations (McGraw-Hill, New York 1955)
G. Floquet: Sur les équations différentielles linéaires à coefficients périodiques. Ann. École Norm. Ser. 2 12, 47 (1883)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Haken, H. (1983). Linear Ordinary Differential Equations. In: Advanced Synergetics. Springer Series in Synergetics, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45553-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-45553-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45555-1
Online ISBN: 978-3-642-45553-7
eBook Packages: Springer Book Archive