09-23-2026, 05:13 PM
Fundamentals of Numerical Computation, by Tobin A. Driscoll and Richard J. Braun, is an advanced undergraduate introduction to numerical analysis and scientific computing. The book develops the central idea that computers transform continuous mathematical problems into finite, approximate ones, and therefore numerical computation requires understanding roundoff error, conditioning, stability, discretization, and convergence.
It begins with numerical representations of numbers and algorithms, then develops linear algebra, including solving square and overdetermined systems, nonlinear equations, interpolation, and calculus. The authors emphasize linear algebra as the language of scientific computing and use more than 200 MATLAB functions and examples to connect mathematical concepts with actual computation.
The second half moves toward more sophisticated and computationally demanding problems: matrix analysis and eigenvalue/singular-value decompositions, Krylov methods, global function approximation, ordinary differential equations, boundary-value problems, and partial differential equations, including two-dimensional problems.
A recurring theme is that when a problem becomes too large or complicated for direct methods, one must choose appropriate approximations and algorithms while carefully assessing accuracy and convergence. Rather than being merely a collection of programming recipes, the book aims to teach students how to formulate mathematical problems computationally, understand the trade-offs between numerical methods, and judge whether a computed result can be trusted.
BOOK
It begins with numerical representations of numbers and algorithms, then develops linear algebra, including solving square and overdetermined systems, nonlinear equations, interpolation, and calculus. The authors emphasize linear algebra as the language of scientific computing and use more than 200 MATLAB functions and examples to connect mathematical concepts with actual computation.
The second half moves toward more sophisticated and computationally demanding problems: matrix analysis and eigenvalue/singular-value decompositions, Krylov methods, global function approximation, ordinary differential equations, boundary-value problems, and partial differential equations, including two-dimensional problems.
A recurring theme is that when a problem becomes too large or complicated for direct methods, one must choose appropriate approximations and algorithms while carefully assessing accuracy and convergence. Rather than being merely a collection of programming recipes, the book aims to teach students how to formulate mathematical problems computationally, understand the trade-offs between numerical methods, and judge whether a computed result can be trusted.
BOOK
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