The primary textbook you are looking for is Numerical Methods for Scientific and Engineering Computation
While it has practical aspects, some readers find the math a bit dense, making it more of a theoretical book than a practical "how-to" guide. Language Usage:
If you're looking for a downloadable PDF of the book, here are some possible sources:
- Balanced mix of theory and practical algorithms suitable for engineering students.
- Numerous worked examples and exercises that build computational intuition.
- Accessible mathematical rigor — proofs when useful, but emphasis on method implementation and error behavior.
- Good for course use, self-study, and as a reference for implementing classic algorithms.