6.1--Slope Fields
Find a general solution to the differential equation:
1)
2)
dy/dx = sec2x
dy/dx =
x3
1 + x4
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6.1--Slope Fields
Find a general solution to the differential equation:
3)
4)
dy/dx =
x
1 + x4
Using the differential equation, construct a
slope field through the 9 points shown:
dy/dx =
2x + y
y
2
6.1--Slope Fields
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What is Euler's Method and why is it useful?
Euler's Method is a numerical approach to finding an unknown
point on a curve, provided that you have a starting point and
that you know the curve's derivative.
f(x)
dy/dx = x + y
(2.6,???)
(2,1)
1
3
2
6.1--Euler's Method
Use Euler's Method with increments of ∆x = 0.2 to approximate f(2.6):
1)
dy/dx = x + y,
(x, y)
(2, 1)
dy/dx
f(2) = 1
∆x
∆y = (dy/dx) ∆x
(x+∆x, y+∆y)
0.2
0.2
0.2
4
6.1--Euler's Method
Use Euler's Method with equal increments of ∆x to approximate f(1.5):
2)
dy/dx = 2x - y,
(x, y)
dy/dx
f(2) = 3
∆x
∆y = (dy/dx) ∆x
(x+∆x, y+∆y)
(2, 3)
View the Excel spreadsheet next...
(Tonight's assignment is Worksheet 6.1)
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6.1--Euler's Method
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