Introduction to Real Analysis

This book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. This book is intended for those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.

Analysis Mathematics

Tác giả: William F. Trench
Nhà xuất bản: Trinity University
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 40 mục

01: The Real Numbers
1.00: The Real Number System
1.02: Mathematical Induction
1.03: The Real Line
02: Differential Calculus of Functions of One Variable
2.00: Functions and Limits
2.02: Continuity
2.03: Differentiable Functions of One Variable
2.04: L’Hospital’s Rule
2.05: Taylor’s Theorem
03: Integral Calculus of Functions of One Variable
3.00: Definition of the Integral
3.02: Existence of the Integral
3.03: Properties of the Integral
3.04: Improper Integrals
3.05: A More Advanced Look at the Existence of the Proper Riemann Integral
04: Infinite Sequences and Series
4.00: Sequences of Real Numbers
4.02: Earlier Topics Revisited With Sequences
4.03: Infinite Series of Constants
4.04: Sequences and Series of Functions
4.05: Power Series
05: Real-Valued Functions of Several Variables
5.00: Structure of Rn
5.02: Continuous Real-Valued Function of n Variables
5.03: Partial Derivatives and the Differential
5.04: The Chain Rule and Taylor’s Theorem
06: Vector-Valued Functions of Several Variables
6.00: Linear Transformations and Matrices
6.02: Continuity and Differentiability of Transformations
6.03: The Inverse Function Theorem
6.04: The Implicit Function Theorem
07: Integrals of Functions of Several Variables
7.00: Definition and Existence of the Multiple Integral
7.02: Iterated Integrals and Multiple Integrals
7.03: Change of Variables in Multiple Integrals
08: Metric Spaces
8.00: Introduction to Metric Spaces
8.02: Compact Sets in a Metric Space
8.03: Continuous Functions on Metric Spaces