Calculus Volume 3 · free preview
Series Solutions of Differential Equations
When closed forms fail, power series solutions substitute the expansion into the equation, the coefficients determined recursively, the radius of convergence the validity's extent, Bessel and Legendre the named functions arising.
1. The series method
The series method
2. Airy and the recurrence
Airy and the recurrence
3. Bessel and Legendre
Bessel and Legendre
4. The course's completion
The course's completion
5. Series substitution
The power series method substitutes y equals which form into the differential equation?
6. Recurrence relation
Matching coefficients in the series method produces which relation among the coefficients?
7. Airy equation source
Airy's equation arises in which disciplines?
8. Radius of convergence
The series solution's radius of convergence extends to what?
9. Why series
The series method is needed when the equation has which feature?
10. Airy recurrence denominator
The Airy recurrence has (n + 2)(n + 1) in the denominator. As a product, what two factors? Answer like n plus 2.
11. Bessel source
Bessel functions describe which membrane's vibrations? Answer with one word.
12. Legendre geometry
Legendre polynomials arise on which surface's potential problems? Answer with one word.
13. Series legitimacy
The special functions from series, the Bessel and Legendre, are legitimate because of which fact?
14. Free coefficients count
The series solution's first two coefficients are free. As a number, how many? Answer with a number.
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