L29_A
5.7 The contraction mapping principle(cont.)
5.7 The contraction mapping principle(cont.)
(1)Fredhdm equation
L29_B
5.7 The contraction mapping principle(cont.)
5.7 The contraction mapping principle(cont.)
(1)Theorem for Fredhdm equation
(2)Definition of Volterra equation
L29_C
5.7 The contraction mapping principle(cont.)
5.7 The contraction mapping principle(cont.)
(1)Definition of Volterra equation(cont.)
(2)Q:Does Φ has a unique fixed point?
(3)Theorem of Volterra equation
L29_D
5.8 The Stone-Weierstrass Thm
(1)Definition:Let A be a subset of a metric space M.A
is said to be dense in M,if cl(A)=M
(2)Question:the set P of all polynomials in C([a,b],R)
是否open? 是否closed?
(3)Weierstrass Thm
(4)Remark:
a.定理成立的理由可用機率論解釋
b.f is analytic
10610高等微積分練習題_1(暫).jpg
