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In this video, we dive into Euler's Method, one of the most fundamental numerical techniques for solving Ordinary Differential Equations (ODEs). We solve the initial value problem: dy/dx = x² + y, with y(0) = 1 and a step size of h = 0.1. What you will learn: How to apply the Euler formula: y_{n+1} = y_n + h × f(x_n, y_n) How to keep an ...
1K views2 months ago
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Euler's method ✏️ for approximating DE solutions 😵‍💫😵‍💫 #apcalculus #apcalc #unit7 We look at Euler's method from Topic 7.5 of AP Calc BC, which approximates solutions to differential equations. The accuracy of Euler's method decreases with each step taken away from the starting point because each subsequent approximation relies on the previous one, so the error compounds with each additional step. This iterative process inherently involves basing one approximation on another, resulting in l
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