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Trigonometric Functions

  • Kenneth Eriksson
  • Donald Estep
  • Claes Johnson
Chapter

Abstract

In this chapter, we shall study the following initial value problem for a second order differential equation: Find a function u(x) defined for x ≥ 0 satisfying
$$u''\left( x \right) = - u\left( x \right)\;for\,x > 0,\quad u\left( 0 \right) = {u_0},\,u'\left( 0 \right) = {u_1},$$
(32.1)
where u 0 and u 1 are given initial data. We here require two initial conditions because the problem involves a second order derivative. We may compare with the first order initial value problem: u′(x) = −u(x) for x > 0, u(0) = u 0, with the solution u(x) = exp(−x), which we studied in the previous chapter.

Keywords

Unit Circle Trigonometric Function Order Differential Equation Spring Force Small Positive Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Kenneth Eriksson
    • 1
  • Donald Estep
    • 2
  • Claes Johnson
    • 1
  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden
  2. 2.Department of MathematicsColorado State UniversityFort CollinsUSA

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