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This textbook is intended to introduce advanced undergraduate and
early-career graduate students to the field of numerical analysis.
This field pertains to the design, analysis, and implementation of
algorithms for the approximate solution of mathematical problems
that arise in applications spanning science and engineering, and
are not practical to solve using analytical techniques such as
those taught in courses in calculus, linear algebra or differential
equations. Topics covered include computer arithmetic, error
analysis, solution of systems of linear equations, least squares
problems, eigenvalue problems, nonlinear equations, optimization,
polynomial interpolation and approximation, numerical
differentiation and integration, ordinary differential equations,
and partial differential equations. For each problem considered,
the presentation includes the derivation of solution techniques,
analysis of their efficiency, accuracy and robustness, and details
of their implementation, illustrated through the Python programming
language. This text is suitable for a year-long sequence in
numerical analysis, and can also be used for a one-semester course
in numerical linear algebra.
This textbook is intended to introduce advanced undergraduate and
early-career graduate students to the field of numerical analysis.
This field pertains to the design, analysis, and implementation of
algorithms for the approximate solution of mathematical problems
that arise in applications spanning science and engineering, and
are not practical to solve using analytical techniques such as
those taught in courses in calculus, linear algebra or differential
equations.Topics covered include computer arithmetic, error
analysis, solution of systems of linear equations, least squares
problems, eigenvalue problems, nonlinear equations, optimization,
polynomial interpolation and approximation, numerical
differentiation and integration, ordinary differential equations,
and partial differential equations. For each problem considered,
the presentation includes the derivation of solution techniques,
analysis of their efficiency, accuracy and robustness, and details
of their implementation, illustrated through the Python programming
language.This text is suitable for a year-long sequence in
numerical analysis, and can also be used for a one-semester course
in numerical linear algebra.
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