Definition of functions of several variables
We will be studying functions of several variables, say . It is often convenient to organize this list of input variables into a vector x . When n is two or three, we usually dispense with the subscripts and write x = or x = .
For example, consider the function f from to defined by
.
With x = , we can write this as
.
As we shall see, sometimes it is very helpful to think of the input variables as united into a single vector variable x, while other times it is helpful to think of them individually and separately.
We will also be considering functions from to . These take vector variables as input, and return vector variables as output. For example, consider the function F from to given by
.
Introducing the functions and , and with f(x; y) defined as in , we can rewrite as
.
Often, the questions we ask about F(x) can be answered by considering the functions f, g and h one at a time. 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | Поиск по сайту:
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