Section 6.1: Euler’s Method

Local Linearity and Differential Equations Slope at (2,0): Tangent line at (2,0): Not a good approximation. Consider smaller pieces. Tangent line approximation at x=2.2:

Local Linearity and Differential Equations Slope at (2.2,0.4): “Tangent line” at (2.2,0.4): “Tangent line” approximation at x=2.4:

Local Linearity and Differential Equations Slope at (2.4,0.92): “Tangent line” at (2.4,0.92): “Tangent line” approximation at x=2.6:

Local Linearity and Differential Equations Slope at (2.6,1.584): “Tangent line” at (2.6,1.584): “Tangent line” approximation at x=2.8:

Local Linearity and Differential Equations Slope at (2.8,2.421): “Tangent line” at (2.8,2.421): “Tangent line” approximation at x=3: We can generalize this process. Previous y Derivative Change in x Next y

Euler’s Method Next Approximate Solution Previous Approximate Solution Change in x Value of Differential Equation at Previous Point

Example Euler’s Method