Abstract
This chapter deals with linear systems of ordinary differential equations (ODEs), both homogeneous and nonhomogeneous equations. Linear systems are extremely useful for analyzing nonlinear systems. The main emphasis is given for finding solutions of linear systems with constant coefficients so that the solution methods could be extended to higher-dimensional systems easily. The eigenvalue-eigenvector method and the fundamental matrix method have been described.
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References
Friedberg S.H., Insel A.J., Spence L.E.: Linear Algebra. Prentice Hall (2003)
Hoffman, K., Kunze, R.: Linear Algebra. Prentice Hall (1971)
Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Springer, New York (2001)
Jordan, D.W., Smith, P.: Non-linear Ordinary Differential Equations. Oxford University Press, Oxford (2007)
Hirsch, M.W., Smale, S.: Differential Equations. Dynamical Systems and Linear Algebra. Academic Press, London (1974)
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© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
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Layek, G.C. (2024). Linear Systems. In: An Introduction to Dynamical Systems and Chaos. University Texts in the Mathematical Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-99-7695-9_2
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DOI: https://doi.org/10.1007/978-981-99-7695-9_2
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