開放式課程>>自然科學學群>>高等微積分(一)>>第32講 Chapter 6:Differentiable mappings

第32講 Chapter 6:Differentiable mappings

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.)
         (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.)
         (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,
              denoted by Df(x),s.t. f(x+h)-f(x)=Df(x)h+o(R)  

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