This graduate-level textbook is a detailed exposition of key
mathematical tools in analysis aimed at students, researchers, and
practitioners across science and engineering. Every topic covered
has been specifically chosen because it plays a key role outside
the field of pure mathematics. Although the treatment of each topic
is mathematical in nature, and concrete applications are not
delineated, the principles and tools presented are fundamental to
exploring the computational aspects of physics and engineering.
Readers are expected to have a solid understanding of linear
algebra, in Rn and in general vector spaces. Familiarity with the
basic concepts of calculus and real analysis, including Riemann
integrals and infinite series of real or complex numbers, is also
required.
General
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