Numerical methods

• How to Solve an Equation with Exponential and Polynomial Terms
  Learn when mixed exponential-polynomial equations have exact solutions, how to locate all real roots, and how to approximate them reliably.
• How Do You Compute Irrational Numbers?
  Irrational numbers are computed by algorithms that produce rational approximations to a chosen precision, often with an error bound.
• How to Fit Spherical Harmonics to a 3D Grid
  Fit a 3D grid with spherical harmonics by separating radius from angle, weighting samples correctly, and solving for coefficients by least squares.
• What Is the Approximation Formula for a Higher-Order Derivative?
  Approximate an nth derivative with finite differences, understand the error, and see a worked second-derivative example using a central stencil.
• How to Apply Alpha-Max-Beta-Min to Three Numbers
  The two-input alpha-max-beta-min formula does not directly extend to three values; sort their magnitudes and include the middle value.
• How to Calculate an nth Root on a Simple Calculator
  To find the nth root, raise the number to the reciprocal power. If your calculator has only basic operations, use Newton's iteration and check the result.
• What Is the Steepest Descent Method?
  The steepest descent method minimizes a differentiable function by moving opposite its gradient; learn how to choose a step size and avoid slow convergence.