Calculus II pp 369-417 | Cite as

Differential Equations

  • Jerrold Marsden
  • Alan Weinstein
Part of the Undergraduate Texts in Mathematics book series (UTM)


In the first two sections of this chapter, we study two of the simplest and most important differential equations, which, describe oscillations, growth, and decay. A variation of these equations leads to the hyperbolic functions, which are important for integration and other applications. To end the chapter, we study two general classes of differential equations whose solutions can be expressed in terms of integrals. These equations, called separable and linear equations, occur in a number of interesting geometrical and physical examples. We shall continue our study of differential equations in Chapter 12 after we have learned more calculus.


Direction Field Chain Rule Euler Method Hyperbolic Function Radioactive Substance 
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Copyright information

© Springer-Verlag New York Inc. 1985

Authors and Affiliations

  • Jerrold Marsden
    • 1
  • Alan Weinstein
    • 2
  1. 1.Control and Dynamical Systems 107–81California Institute of TechnologyPasadenaUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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