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Euler's Method definitions

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  • Euler's Method
    An iterative technique using multiple short tangent lines to approximate function values more accurately than a single tangent line.
  • Step Size
    A fixed increment added to the x-value at each iteration, controlling the accuracy and number of steps in the approximation.
  • Tangent Line
    A straight line that locally touches a curve at a point, matching the curve's slope at that location.
  • Initial Condition
    A starting point for x and y values, providing the base for iterative calculations in approximation methods.
  • Differential Equation
    An equation involving a function and its derivative, used to describe the relationship between variables in the method.
  • Linear Approximation
    A method using a single tangent line to estimate a function's value near a known point.
  • Derivative
    A measure of how a function changes as its input changes, used to determine the slope for tangent lines.
  • Iteration
    A repeated process of updating x and y values using previous results and the method's formula.
  • Approximation
    An estimated value of a function at a specific point, obtained through a numerical method.
  • Table
    An organized arrangement of x and y values at each step, aiding in tracking the iterative process.
  • Function Value
    The output of a function for a given input, often the target of the approximation process.
  • Slope
    A numerical value representing the steepness of a tangent line, determined by the derivative at a point.
  • Point
    A specific location on a graph defined by x and y coordinates, marking each step in the method.
  • Accuracy
    The closeness of an approximation to the actual function value, improved by smaller step sizes.
  • Graph
    A visual representation of points and lines showing the progression of approximations alongside the actual curve.