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Euler's Method

Definition

Euler's Method is a numerical approximation technique used to estimate the value of a function at certain points when its derivative is known. It involves using small steps and linear approximations based on the slope at each point.

Analogy

Imagine you're hiking up a mountain but there is no trail. You can estimate your position at certain points by taking small steps in the direction you think leads higher. Euler's Method works similarly by taking small steps along the curve of a function based on its slope at each point.

Related terms

Differential Equation: A differential equation relates an unknown function with its derivatives. Euler's Method can be used to approximate solutions for differential equations.

Slope Field: A graphical representation that shows how the slope (derivative) changes at different points on a plane. It helps visualize how Euler's Method works.

Taylor Series Expansion: A mathematical series that represents a function as an infinite sum of terms derived from its derivatives. Euler's Method can be seen as an approximation using only the first-order term of a Taylor series.