Engineering Applications

Numerical Analysis · Axiom Academy

REAL WORLD Engineering Applications How root-finding methods solve real engineering problems Finding the natural frequencies of bridges and buildings requires solving the characteristic equation: The roots give vibration frequencies. Engineers avoid designs where these match earthquake frequencies! Transistor operating points come from solving nonlinear I-V equations: Newton's method is used in SPICE circuit simulators to find bias points. Kepler's equation relates time and position on an elliptical orbit: Solved billions of times for spacecraft navigation using Newton's method. The Internal Rate of Return (IRR) requires finding r where: Every spreadsheet uses root-finding to compute IRR and bond yields. Interactive Demo: Internal Rate of Return Calculate the IRR for an investment with annual cash flows: Interactive Demo: Kepler's Equation Given mean anomaly M and eccentricity e, find eccentric anomaly E: Verification: M - (E - e·sin(E)) =

This is the written version of the interactive lesson above. See the full Numerical Analysis course.