Numerical Methods in EXCEL/VBA PROGRAMING

Compare forward, backward, and centered finite difference methods in VBA for the first derivative of f(x) = log x + x^2, and analyze how step size affects accuracy.

Discover Simpson's 1/3 rule for numerical integration, using second-order polynomials and Newton interpolation to accurately compute the area under the curve, and compare it with the trapezoidal rule.

Explore Heun's, Midpoint, and Ralston methods for solving differential equations, using start-to-end averages, Midpoint derivatives, and weighted averages to improve accuracy.

Compare the secant method and Newton-Raphson as open methods, using backward finite difference and Taylor series to approximate derivatives and evaluate iteration accuracy.

Explore optimization fundamentals: identify minima, maxima, saddles, and local versus global optima, apply the second derivative test and contour lines, and graph 2-D functions in Excel.

Apply Newton-Raphson to turn optimization into root finding, solve f'(x)=0 to locate optima, and use the second derivative test to classify minima or maxima.

Explore how gradient descent turns 2-D optimization into 1-D line searches along a gradient direction, incorporating Newton-Raphson ideas, then convert back to x,y until reaching the valley bottom.

Explore solving linear systems with the Gauss-Jordan method by forward elimination, backward elimination, and normalization to convert the augmented matrix to an identity matrix, yielding the solution on the right.

Apply linearization to fit power, exponential, and saturation growth trends by transforming them into linear forms and performing regression; extract A and B and assess with R-squared.

Explore cubic spline interpolation to fit a separate cubic on each interval between data points, using second derivatives and a tri-diagonal system solved by the Thomas algorithm.