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

Sine Verse 

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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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