Systems of differential equations

  • Martin Braun
Part of the Applied Mathematical Sciences book series (AMS, volume 15)


In this chapter we will consider simultaneous first-order differential equations in several variables, that is, equations of the form
$$ \begin{array}{*{20}{c}} {\frac{{d{x_{1}}}}{{dt}} = {f_{1}}\left( {t,\,{x_{1}},...,\,{x_{n}}} \right),} \\ {\frac{{d{x_{2}}}}{{dt}} = {f_{2}}\left( {t,\,{x_{1}},...,\,{x_{n}}} \right),} \\ \begin{gathered} \;\; \vdots \hfill \\ \frac{{d{x_{n}}}}{{dt}} = {f_{n}}\left( {t,\,{x_{1}},...,\,{x_{n}}} \right). \hfill \\ \end{gathered} \\ \end{array} $$


Linear Transformation Scalar Multiplication Independent Solution Nonzero Vector Independent Vector 
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Copyright information

© Springer-Verlag New York, Inc. 1983

Authors and Affiliations

  • Martin Braun
    • 1
  1. 1.Department of Mathematics, Queens CollegeCity University of New YorkFlushingUSA

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