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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

  • Answers to Selected Exercises

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