Numerical methods turn mathematics into numbers you can trust. Written for the Numerical Methods course at Mahindra University, Hyderabad, this book builds each method from a picture, derives it carefully and works full examples by hand, then asks how fast it converges, how large the error is and when it fails.
Its lectures cover computer arithmetic and errors, nonlinear equations, linear systems, eigenvalues, least squares, interpolation, numerical integration and ordinary differential equations. Every lecture ends with pitfalls, a summary and exercises, and every part with review problems, with answers to every exercise at the back.
For B.Tech, B.Sc. and M.Sc. students and their teachers. A free companion video course is at biswarupbiswas.github.io/numerical-methods.