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.