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Differential Equations

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Analysis for Computer Scientists

Part of the book series: Undergraduate Topics in Computer Science ((UTICS))

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Abstract

In this chapter we discuss the theory of initial value problems for ordinary differential equations. We limit ourselves to scalar equations here; systems will be discussed in the next chapter.

After presenting the general definition of a differential equation and the geometric significance of its direction field, we start with a detailed discussion of first- order linear equations. As important applications we discuss the modelling of growth and decay processes. Subsequently, we investigate questions of existence and (local) uniqueness of the solution of general differential equations and discuss the method of power series. Finally, we study the qualitative behaviour of solutions close to an equilibrium point.

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Notes

  1. 1.

    T.R. Malthus, 1766–1834.

  2. 2.

    G. Peano, 1858–1932.

  3. 3.

    R. Lipschitz, 1832–1903.

  4. 4.

    J.F. Riccati, 1676–1754.

References

Textbooks

  1. S. Lang: Undergraduate Analysis. Springer, New York 1983.

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Further Reading

  1. E. Hairer, S.P. Nørsett, G. Wanner: Solving Ordinary Differential Equations I. Nonstiff Problems. Springer, Berlin 1993 (2nd edition).

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Author information

Authors and Affiliations

  1. Institute of Basic Sciences in Civil Eng, University of Innsbruck, Technikerstrasse 13, Innsbruck, 6020, Austria

    Michael Oberguggenberger

  2. Department of Mathematics, University of Innsbruck, Technikerstrasse 13/7, Innsbruck, 6020, Austria

    Alexander Ostermann

Authors
  1. Michael Oberguggenberger
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  2. Alexander Ostermann
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Corresponding author

Correspondence to Michael Oberguggenberger .

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© 2011 Springer-Verlag London Limited

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Oberguggenberger, M., Ostermann, A. (2011). Differential Equations. In: Analysis for Computer Scientists. Undergraduate Topics in Computer Science. Springer, London. https://doi.org/10.1007/978-0-85729-446-3_19

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  • DOI: https://doi.org/10.1007/978-0-85729-446-3_19

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-445-6

  • Online ISBN: 978-0-85729-446-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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