DIFFERENTIATION Finding the acceleration of a rocket from its velocity. How quickly does the slick spread? Stress Concentration Around a Hole (extended version coming soon) Detecting edges of images Avoiding arcing in switches Reliability of manufactured parts over time How does the thermal expansion coefficient vary at different temperatures? NONLINEAR EQUATIONS How much of the float is submerged? A scale to measure oil in a tank A sagging bookshelves! Divide unit missing in a supercomputer? Checking calibration curve of a thermistor Mom and Pop shop wants to break even Trunnion cool down for a shrink fit SIMULTANEOUS LINEAR EQUATIONS Finding the velocity profile of a rocket Liquid-Liquid extraction How much pressure can a compounded cylinder take? To infer the surface shape from images. Finding the unbalance in a 3-phase load system. Maximizing the production schedule. Find constants of a regression model for coefficient of thermal expansion vs temperature. INTERPOLATION Predict velocity of a rocket Tea time: time needed to boil the water Tips on bass fishing Short and smoothest path for a robot Measuring temperature by a thermistor Profiling a cam Calculating the shrinkage of a trunnion correctly REGRESSION Finding the best mousetrap for a mousetrap car Infrared spectroscopy Finding the longitudinal Young's moduli of a composite materials? Extraction of road networks in images by function fitting Finding the appropriate value for the resistance of a resistor. When should the machine be stopped? Finding a regression model for calculating the contraction of a trunnion immersed in liquid nitrogen? INTEGRATION Distance covered by a rocket Time required for oxygen to be consumed in the fuel cell Is the toxicity level of benzene dangerous? To infer the surfaces from vector fields Confidence in acceptable circuit behavior with variation in components? Are there as many plies of tissue paper in a roll? Finding the shrinkage of a trunnion? ORDINARY DIFFERENTIAL EQUATIONS How much time will it take the ball to cool down? Controlling sodium chloride waste while making soap. When is it safe to go back into the lake? Sizing a rectifier-based power supply (orginal problem coming soon) Sizing a rectifier-based power supply. Controlling the speed of a DC motor Contracting a cylinder to shrink fit in to a hub. Text Link

NONLINEAR EQUATIONS Cubic equations solution Newton Raphson Galois INTERPOLATION History of Interpolation Extrapolation is dangerous! Higher order interpolation is a bad idea! Comparison of spline and polynomial interpolation Choice of points affects polynomial interpolation Shortest path of a robot Runge Taylor REGRESSION On adequacy of regression models Multivariate regression INTEGRATION What is integration? A primer on integration Integrating discrete functions Integrating improper integrals Cotes Gauss Simpson Text Link

Introduction to Numerical Methods Measuring Errors Sources of Error Binary Representation Floating Point Representation Propagation of Errors Taylor Series Revisited Differentiation: Background Differentiation: Continuous Functions Differentiation: Discrete Functions Nonlinear Equations Background Nonlinear Equations Bisection Method Nonlinear Equations Newton-Raphson Method Nonlinear Equations Secant Method Background of Simultaneous Linear Equations Simultaneous Linear Equations Gaussian Elimination Simultaneous Linear Equations LU Decomposition Method Simultaneous Linear Equations Gauss-Seidal Method Interpolation Background Interpolation Direct Method Interpolation Newton Divided Difference Method Interpolation Lagrange Method Interpolation Spline Method Regression Background Regression Linear Regression Nonlinear Integration Background Integration Trapezoidal Rule Integration Simpson 1/3 Rule Integration Romberg Integration Gauss Quadrature ODE Background ODE Euler's Method ODE Runge-Kutta 2nd Order Method ODE Runge-Kutta 4th Order Method ODE Finite Difference Method ODE Shooting Method Text Link