Euler's Method Demonstration

Uttryck 13:

Uttryck 14: "u" left parenthesis, "x" , right parenthesis equals left parenthesis, "g" left parenthesis, "p" , right parenthesis , right parenthesis left parenthesis, "x" minus left parenthesis, "p" plus "w" , right parenthesis , right parenthesis plus "h" left brace, "m" Subscript, "i" "n" , Baseline left parenthesis, "p" , "p" plus "w" , right parenthesis less than or equal to "x" less than or equal to "m" Subscript, "a" "x" , Baseline left parenthesis, "p" , "p" plus "w" , right parenthesis , right brace

Extra equations

t(x) draws tangent lines of our function, which are used to draw u(x).

Uttryck 17: "t" left parenthesis, "x" , right parenthesis equals left parenthesis, "g" left parenthesis, "p" , right parenthesis , right parenthesis left parenthesis, "x" minus "p" , right parenthesis plus "f" left parenthesis, "p" , right parenthesis left brace, "p" minus StartFraction, "w" Over 4 , EndFraction less than or equal to "x" less than or equal to "p" plus StartFraction, "w" Over 4 , EndFraction , right brace

h calculates a list of total change in height after l approximations, where l ranges from 1 to n.

Uttryck 19: "h" equals "f" left parenthesis, "a" , right parenthesis plus Start sum from "i" equals 1 to "l" , end sum, "w" left parenthesis, "g" left parenthesis, "p" , right parenthesis left bracket, "i" , right bracket , right parenthesis

equals

0.1 3 1 7 9 5 0 5 2 3 6 7

0.1 5 4 8 7 7 7 3 5 6 2 7

0.1 8 2 2 6 4 7 2 4 2 1 6

0.2 1 4 7 3 7 9 2 3 3 9 2

0.2 5 3 2 1 2 7 9 7 6 4 8

0.2 9 8 7 5 7 7 1 8 2 9 3

0.3 5 2 6 1 4 6 6 9 3 1 9

0.4 1 6 2 2 0 7 3 8 3 5 1

0.4 9 1 2 2 9 4 5 0 0 1

0.5 7 9 5 3 0 5 0 2 0 0 5

0.6 8 3 2 6 5 8 1 9 6 1 9

0.8 0 4 8 3 9 0 4 2 6 0 8

0.9 4 6 9 1 4 6 1 3 5 5 4

1.1 1 2 4 0 1 6 0 2 5

1.3 0 4 4 1 6 3 9 7 7 6

Lista med 16 element

Minimum and maximum functions that work without creating additional tables.

Uttryck 21: "m" Subscript, "i" "n" , Baseline left parenthesis, "x" , "y" , right parenthesis equals StartFraction, left parenthesis, sign left parenthesis, "x" minus "y" , right parenthesis plus 1 , right parenthesis Over 2 , EndFraction times "y" plus StartFraction, left parenthesis, sign left parenthesis, "y" minus "x" , right parenthesis plus 1 , right parenthesis Over 2 , EndFraction times "x"

Uttryck 22: "m" Subscript, "a" "x" , Baseline left parenthesis, "x" , "y" , right parenthesis equals StartFraction, left parenthesis, sign left parenthesis, "x" minus "y" , right parenthesis plus 1 , right parenthesis Over 2 , EndFraction times "x" plus StartFraction, left parenthesis, sign left parenthesis, "y" minus "x" , right parenthesis plus 1 , right parenthesis Over 2 , EndFraction times "y"

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