Introduction To Real Analysis by William F. Trench

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Introduction To Real Analysis written by William F. Trench
. This is an other book of mathematics cover the following topics.

The Real Numbers The Real Number System, Mathematical Induction, The Real Line

Differential Calculus of Functions of One Variable Functions and Limits, Continuity, Differentiable Functions of One Variable, L’Hospital’s Rule, Taylor’s Theorem

Integral Calculus of Functions of One Variable Definition of the Integral, Existence of the Integral, Properties of the Integral, Improper Integrals, A More Advanced Look at the Existence of the Proper Riemann Integral

Infinite Sequences and Series Sequences of Real Numbers, Earlier Topics Revisited With Sequences, Infinite Series of Constants, Sequences and Series of Functions, Power Series

Real-Valued Functions of Several Variables Structure of Rn, Continuous Real-Valued Function of n Variables, Partial Derivatives and the Differential, The Chain Rule and Taylor’s Theorem

Vector-Valued Functions of Several Variables Linear Transformations and Matrices, Continuity and Differentiability of Transformations, The Inverse Function Theorem, The Implicit Function Theorem

Integrals of Functions of Several Variables Definition and Existence of the Multiple Integral, Iterated Integrals and Multiple Integrals, Change of Variables in Multiple Integrals

Metric Space Introduction to Metric Spaces, Compact Sets in a Metric Space, Continuous Functions on Metric Spaces