A Concrete Introduction to Real Analysis (Hardcover, 1st)

DISCRETE CALCULUS
Introduction
Proof by Induction
A Calculus of Sums and Differences
Sums of Powers
Problems
SELECTED AREA COMPUTATIONS
Introduction
Areas under Power Function Graphs
The Computation of p
Natural Logarithms
Stirling's Formula
Problems
LIMITS AND TAYLOR'S THEOREM
Introduction
Limits of Infinite Sequences
Series Representations
Taylor Series
Problems
INFINITE SERIES
Introduction
Positive Series
General Series
Grouping and Rearrangement
Problems
A BIT OF LOGIC
Somemathematical Philosophy
Propositional Logic
Predicates and Quantifiers
Proofs
Problems
REAL NUMBERS
Field Axioms
Order Axioms
Completeness Axioms
Subsequences and Compact Intervals
Products and Fractions
Problems
FUNCTIONS
Introduction
Basics
Limits and Continuity
Derivatives
Problems
INTEGRALS
Introduction
Integrable Functions
Properties of Integrals
Numerical Computation of Integrals
Problems
MORE INTEGRALS
Introduction
Improper Integrals
Integrals with Parameters
Problems
REFERENCES
INDEX