Core Python Codes for Numerical Applications

You do not really understand a numerical method until you have watched yours diverge.

This book has you write each algorithm yourself in clear Python, measure its error, then compare it with the library routine you will use at work. You will implement bisection and Newton-Raphson and see their convergence orders in a table, factorise matrices with pivoting and learn what a condition number costs you, fit and interpolate data without falling into the Runge trap, integrate with Simpson, Romberg and Gauss quadrature, and solve initial value, boundary value and partial differential problems including stiff systems. Closing case studies cover heat exchangers, beam deflection, reaction kinetics and circuit transients.

For engineers, scientists and students who want working code and honest error analysis together.

What you will learn:

• Implement bisection, Newton-Raphson and other root-finding methods, and verify their convergence orders
• Solve systems of linear equations with pivoting and understand the impact of condition numbers
• Apply iterative solvers and eigenvalue algorithms for large-scale problems
• Fit and interpolate data using regression, splines and polynomial interpolation without Runge oscillations
• Differentiate and integrate numerically with finite differences, Simpson, Romberg and Gauss quadrature
• Solve initial value problems, including stiff systems, with explicit and implicit methods
• Tackle boundary value and partial differential problems using finite differences
• Optimise functions and apply numerical methods to engineering case studies

This book is for engineers, scientists and students who want to write their own numerical code, understand the errors involved, and compare their implementations with standard library routines. Whether you are a practising professional or a student, you will gain practical skills to solve real-world problems with confidence.