1549901369-Elements_of_Real_Analysis__Denlinger_

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3.4 *The Cantor Set.

Limits of Functions

4.1 Definition of Limit for Functions.

4.2 Algebra of Limits of Functions

4.3 One-Sided Limits

4.4 *Infinity in Limits.

Continuous Functions

5.1 Continuity of a Function at a Point

5.2 Discontinuities and Monotone Functions

5.3 Continuity on Compact Sets and Intervals

5.

5.

5.

5.

Uniform Continuity.. ..........

*Monotonicity, Continuity, and Inverses.

*Exponentials, Powers, and Logarithms.

*sets of Points of Discontinuity (Project)

Differentiable Functions

6.1 The Derivative and Differentiability

6.2 Rules for Differentiation ......

6.

6.

6.

6.

Local Extrema and Monotone Functions

Mean-Value Type Theorems

Taylor's Theorem

*L'Hopital's Rule

The Riemann Integral

7.1 Refresher on Suprema, Infima , and the Forcing Principle

7.2 The Riemann Integral Defined .......

7.3 The Integral as a Limit of Riemann Sums.

7.

7.

7.

7.

7.

7.

Basic Existence and Additivity Theorems.

Algebraic Properties of the Integral..

The Fundamental Theorem of Calculus

*Elementary Transcendental Functions

*Improper Riemann Integrals.....

*Lebesgue's Criterion for Riemann Integrability

Infinite Series of Real Numbers

8.1 Basic Concepts and Examples

8.

8.

8.

Nonnegative Series.. .... ......

Series with Positive and N~gative Terms

The Cauchy Product of Series.....

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