Mathematical Analysis I For Engineers And Beginning Mathematicians by Sever Angel Popescu

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Mathematical Analysis I For Engineers And Beginning Mathematicians written by Sever Angel Popescu
This is an other great mathematics book cover the following topics.

The real line. 1
The real line. Sequences of real numbers, Sequences of complex numbers, Problems 29

Series of numbers Series with nonnegative real numbers, Series with arbitrary terms, Approximate computations, Problems

Sequences and series of functions Continuous and di§erentiable functions, Sequences and series of functions, Problems

Taylor series Taylor formula, Taylor series, Problems 93

Power series Power series on the real line, Complex power series and Euler formulas, Problems 107

The normed space Rm: Distance properties in Rm, Continuous functions of several variables, Continuous functions on compact sets, Continuous functions on connected sets, The Riemannís sphere, Problems

Taylorís formula for several variables. Higher partial derivatives. Di§erentials of order k, Chain rules in two variables, Taylorís formula for several variables, Problems 185

Contractions and Öxed points Banachís Öxed point theorem, Problems 191

Local extremum points Local extremum points for many variables, Problems

Implicitly deÖned functions Local Inversion Theorem, Implicit functions, Functional dependence, Conditional extremum points, Change of variables, The Laplacian in polar coordinates, A proof for the Local Inversion Theorem, The derivative of a function of a complex variable, Problems