Calculus Volume 3 · 免费预览
微分方程的幂级数解
当闭式解无法奏效时，幂级数解法把级数展开代入方程，系数由递推关系确定，收敛半径划定解的有效范围，由此产生贝塞尔函数与勒让德函数这些具名函数。
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.