Scientific computing¶

Five ranked references. Rank 1 is the default spine, not a requirement to read all five.

1 | Numerical Linear Algebra¶

Lloyd N. Trefethen, David Bau III | Primary spine | Upper undergraduate / graduate

Short, deep, and essential: conditioning, stability, QR, eigenproblems, Krylov methods, and the numerical meaning of linear algebra.

Amazon search | No legal full text located

2 | Accuracy and Stability of Numerical Algorithms¶

Nicholas J. Higham | Numerical reliability | Graduate

The definitive mindset for rounding error, conditioning, backward error, and why mathematically correct algorithms fail numerically.

Amazon search | No legal full text located

3 | Scientific Computing: An Introductory Survey¶

Michael T. Heath | Broad reference | Upper undergraduate

Wide-ranging treatment of numerical algebra, interpolation, integration, ODEs, PDEs, optimization, and computational tradeoffs.

Amazon search | No legal full text located

4 | Numerical Analysis¶

Timothy Sauer | Methods / practice | Undergraduate

Accessible and comprehensive numerical methods with strong computational orientation.

Amazon search | No legal full text located

5 | Fundamentals of Numerical Computation¶

Tobin A. Driscoll, Richard J. Braun | Open computational spine | Undergraduate

Excellent interactive open text spanning conditioning, linear systems, approximation, integration, ODEs, BVPs, and PDEs.

Amazon search | Full open web text

Strongest legal free/open path¶

• Fundamentals of Numerical Computation: Full open web text: open