Computational science is fundamentally changing how
technological questions are addressed. The design of aircraft,
automobiles, and even racing sailboats is now done by computational
simulation. The mathematical foundation of this new approach is
numerical analysis, which studies algorithms for computing
expressions defined with real numbers. Emphasizing the theory
behind the computation, this book provides a rigorous and
self-contained introduction to numerical analysis and presents the
advanced mathematics that underpin industrial software, including
complete details that are missing from most textbooks.
Using an inquiry-based learning approach, "Numerical Analysis"
is written in a narrative style, provides historical background,
and includes many of the proofs and technical details in exercises.
Students will be able to go beyond an elementary understanding of
numerical simulation and develop deep insights into the foundations
of the subject. They will no longer have to accept the mathematical
gaps that exist in current textbooks. For example, both necessary
and sufficient conditions for convergence of basic iterative
methods are covered, and proofs are given in full generality, not
just based on special cases.
The book is accessible to undergraduate mathematics majors as
well as computational scientists wanting to learn the foundations
of the subject.Presents the mathematical foundations of numerical
analysis Explains the mathematical details behind simulation
software Introduces many advanced concepts in modern analysis
Self-contained and mathematically rigorous Contains problems and
solutions in each chapter Excellent follow-up course to Principles
of Mathematical Analysis by Rudin
General
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