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Math 310: Elementary Real Analysis
Text: Introduction to Real Analysis by Bartle & Sherbert
Chapter 1: Preliminaries 2
The Algebra of Sets
Functions
Mathematical Induction
Chapter 2: The Real Numbers 5
The Algebraic Properties of R
The Order Properties of R
Absolute Value
The completeness Property of R
Applications of the Supremum Property
Intervals and Decimals
Infinite Sets
Chapter 3: Sequences 8
Sequences and Their Limits
Limit Theorems
Monotone Sequences
Subsequences and the Bolzano-Weierstrass Theorem
The Cauchy Criterion
Properly Divergent Sequences
Chapter 4: Limits 4
Limits of Functions
Limit Theorems
Some Extensions of the limit Concept
Chapter 5: Continuous Functions 6
5.1 Continuous Functions
5.2 combinations of Continuous Functions
5.3 Continuous Functions on Intervals
5.4 Uniform Continuity
5.5 Monotone and Inverse Functions
Chapter 6: Differentiation 6
The Derivative
The Mean Value Theorem
LHospitals Rules
Taylors Theorem
Chapter 7: The Riemann Integral 8
Riemann Integrability
Properties of the Riemann Integral
The Fundamental Theorem of Calculus
The Integral as a Limit
Approximate Integration
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