Introductory Excel for Scientists and Engineers

Explore evaluating Euler's method in Excel by plotting simulated versus analytical solutions, measuring errors, and refining with smaller step sizes to improve accuracy.

Analyze how step size affects accuracy in Euler's method in Excel and how residuals indicate issues. Examine how Taylor series expansions offer faster convergence at the cost of added complexity.

Derive a second-order finite difference model of a mass on a spring with damping or driving forces and build an algorithm updating x with m, c, k, and h.

Solve a second-order simple harmonic oscillator with initial conditions using time-step finite difference, converting to a system of first-order equations in Excel with m, c, k.

Factor constants into A and B and tabulate them to simplify complex formulas. Apply finite difference methods to propagate X with clear initial conditions for easier debugging in Excel.

Explore solving differential equations in Excel using a simple finite-difference approach, visualize damping, amplitude, and frequency, and assess accuracy against analytical predictions.

Use the relaxation method in a square heat-conduction domain in Excel to compute interior temperatures from fixed boundary conditions via a four-neighbor average.

Build Taylor series based models in Excel by inputting derivatives, using e^x, and locking references with dollar signs to drag formulas, then compare to the analytical solution.

Explore Taylor series modelling in excel by inputting and dragging formulas, defining a safe x-domain, and checking numerical results against experiment and the analytical solution.

Explore convergence analysis by comparing absolute and relative errors against analytical solutions across different spacings, and identify how order of accuracy and derivative terms affect the results.

Demonstrates how to perform a convergence study to detect errors in a tailor series method for a differential equation, using error comparisons and convergence rate.

Understand why Runge-Kutta methods offer greater accuracy than naive finite spacing or Taylor series approaches in solving differential equations, especially for higher dimensions, with controllable error and practical computer costs.

Learn to implement the Runge-Kutta 4 method in Excel, using k1-k4 and the RK4 update y_x+h = y_x + (k1+2k2+2k3+k4)/6, with f(x,y) = (1+y^2) sin x.

Explore implicit, explicit, and Crank-Nicholson methods for solving differential problems, comparing accuracy, stability, and reliability, and learn when averaging explicit and implicit terms improves results.

Explore predictor correct methods that blend explicit guesses with implicit refinements to improve accuracy. Prime implicit steps with explicit results using trapezoid or crank Nicholson approaches for iterative refinement.

Plot a normal distribution using the mean and standard deviation, compare it to cumulative frequencies with the probability distribution function and cumulative distribution function, and normalize for overlay.

Apply the student t test to compare sample means from treated and untreated data, testing null versus alternative hypotheses to decide if a treatment changes hardness beyond random chance.

Source gaussian distributed random numbers from the internet, using random.org, and import the data into Excel by copying and pasting with a normal distribution setup (mean 5, std dev 5.6).