A Primer of Real Analysis

(1 review)

Dan Sloughter, Furman University

Publisher: Dan Sloughter

Language: English

CC BY-NC-SA

Reviews

Reviewed by Seonguk Kim, Assistant of Professor of Mathematics, DePauw University on 9/20/19

This book consists of all essential sections that students should know in the class, Analysis or Introduction of Real Analysis. First, in chapter 1, it has crucial prerequisite contents. Second, from chapter 2 to 8, the order of sections is... read more

1 Fundamentals

• 1.1 Sets and relations
• 1.2 Functions
• 1.3 Rational numbers
• 1.4 Real Numbers

2 Sequences and Series

• 2.1 Sequences
• 2.2 Infinite series

3 Cardinality

• 3.1 Binary representations
• 3.2 Countable and uncountable sets
• 3.3 Power sets

4 Topology of the Real Line

• 4.1 Intervals
• 4.2 Open sets
• 4.3 Closed sets
• 4.4 Compact Sets

5 Limits and Continuity

• 5.1 Limits
• 5.2 Monotonic functions
• 5.3 Limits to infinity and infinite limits
• 5.4 Continuous Functions

6 Derivatives

• 6.1 Best linear approximations
• 6.2 Derivatives
• 6.3 Mean Value Theorem
• 6.4 Discontinuities of derivatives
• 6.5 l'Hˆopital's rule
• 6.6 Taylor's Theorem

7 Integrals

• 7.1 Upper and lower integrals
• 7.2 Integrals
• 7.3 Integrability conditions
• 7.4 Properties of integrals
• 7.5 The Fundamental Theorem of Calculus
• 7.6 Taylor's theorem revisited
• 7.7 An improper integral

8 More Functions

• 8.1 The arctangent function
• 8.2 The tangent function
• 8.3 The sine and cosine Functions
• 8.4 The logarithm function
• 8.5 The exponential function

Index

Ancillary Material

• Submit ancillary resource