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第32講 Chapter 6:Differentiable mappings
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L32_A
L32_ A
Chapter 6:Differentiable mappings
(1)Thm_1
L32_ B
Chapter 6:Differentiable mappings(cont.)
(1)Definition: Let f:A ⊂ R^n -> R^m be a function O⊂A
(2)Prop: Let f:A ⊂ R^n -> R^m be a function O⊂ A'
(3)Thm:(o(x)的四則運算)
L32_C
Chapter 6:Differentiable mappings(cont.)
Chapter 6:Differentiable mappings(cont.)
(1)Thm:(o(x)的四則運算)
(2)Definition:
Let f:I⊂ R->R be a function.
We sat that f is diff. at x if ∃ a number in R,denoted by
f(x),s.t. f(x＋h)-f(x)=f'(x)h＋o(R)
(3)Definition:
Let f:I⊂ R->R be a function.
We sat that f is diff. at x if ∃ a vector in R,denoted by
∇f(x),s.t. f(x＋h)-f(x)=∇f(x)h＋o(R)
(4)In general,let f:A ⊂ R->R be a function.
Consider f(x＋h)-f(x)=∇h
L32_D
C. Chapter 6:Differentiable mappings(cont.)
C. Chapter 6:Differentiable mappings(cont.)
(1)In general,let f:A ⊂ R->R be a function.
Consider f(x＋h)-f(x)= h
(2)Consider a linear function
(3)Definition:A mapping f:A ⊂ R^n -> R^m is said to be
diff. at x if there is a linear function,
diff. at x if there is a linear function,
denoted by Df(x),s.t. f(x＋h)-f(x)=Df(x)h＋o(R)
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