Processing math: 100%
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

5: Eigenvalue problems

( \newcommand{\kernel}{\mathrm{null}\,}\)

  • 5.1: Sturm-Liouville problems
    A classical ??????Sturm-Liouville equation??????, is a real second-order linear differential equation. In the simplest of cases all coefficients are continuous on the finite closed interval [a, b], and p(x) has continuous derivative.
  • 5.2: Application of Eigenfunction Series
    The eigenfunction series can arise even from higher order equations.
  • 5.3: Steady Periodic Solutions
    The page discusses the problem of forced vibrations on a guitar string, accounting for an external force such as noise. The system is modeled using wave equations, incorporating boundary and initial conditions. Solutions include both a general solution for free vibrations and a particular solution for forced vibrations. Resonance, the condition of amplified oscillations when the frequency matches a natural frequency, is examined.
  • 5.E: Eigenvalue Problems (Exercises)
    These are homework exercises to accompany Libl's "Differential Equations for Engineering" Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.


This page titled 5: Eigenvalue problems is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Jiří Lebl via source content that was edited to the style and standards of the LibreTexts platform.

Support Center

How can we help?