Chapter 6: Slope Fields
Chapter 6: Slope Fields and Initial Value Problems
Slope fields: a geometric solution to a differential equation
Creating a slope field:
dy/dx – slope of the tangent line, so using dy/dx find the slope at each point.
Draw a tiny tangent line at each point with it’s appropriate slope
Using a slope field:
Draw a solution to the differential equation by plotting the initial condition, then using the tiny tangent lines as guides, draw the solution curve. You are not connecting the lines.
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Solving Initial Value problems:
Separate variables
Integrate both sides
Find antiderivatives
Substitute initial condition and solve for C
Write equation using value for C
Solve for y
Recognize initial condition
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