Applied Mathematics with F#

This book highlights the enormous potential of F#—in comparison to other programming languages—to be used in scientific computing. It presents solutions of diverse real-life problems by using the combination of applied mathematics and F#. The book begins by introducing different generic collections offered by F# and goes on to present their usages in various areas of applied mathematics such as vectors and matrices, descriptive statistics, set theory, probability and calculus. Empowering users to tackle complex computing problems by using succinct yet robust code, F# is very well positioned to be used for applied mathematics; making this book all the more important for interested readers in this area.

The book uses Plotly.NET to create interactive, publication-quality charts and visualizes vector fields, Jacobians, matrices as heatmaps, and probability distributions and KDEs, ordinary differential equations solutions and phase plots. It uses AngouriMath for symbolic differentiation, simplification, and algebra. It also shows how to blend symbolic math with numerical methods like Trapezoidal and Simpson’s rule, Runge–Kutta methods and Gaussian quadrature. The book includes several real-life case studies as examples such as soccer player analytics, housing price analysis, bungee jumper physics simulation, predator–prey ecosystem model and credit score evaluation.