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Supplementary GeoGebra files for a Real Analysis course, in relation to NSF-funded project ULTRA: Upgrading Learning for Teachers in Real Analysis (DUE-1524681, DUE-1524739, DUE-1524619).
The files can be used by an instructor as a supplement to a class lecture, but were designed to allow students to interact with them also (e.g., alter the givens, etc.).

Table of Contents

Introductory Aspects of Real Numbers

Max Min Supremum Infimum of Sets

Sequences and Series

Sequences

Series: Associativity?

Examples of Convergent and Bounded

Proof of Convergence for Sequences

Example of Proof of Convergence for Sequences: Exact vs Approximate error-bound

Approximating sqrt(7)

Proof of if Convergent, then Bounded

Proof of Algebraic (Scalar) Limit Theorem for Sequences

Proof of Algebraic (Sum) Limit Theorem for Sequences

Proof of Algebraic (Product) Limit Theorem for Sequences

Proof of Algebraic (Reciprocal) Limit Theorem for Sequences

Examples of Sequence Monotonicity

Subsequences

Proof of Bolzano-Weierstrass Theorem

Cauchy Sequence

Functional Limits and Continuity

Examples of Continuity of Functions

Proof of Continuity of Functions

Proof of Limits of Functions

Proof of Intermediate Value Theorem

Function Monotonicity (Increasing)

The Derivative

Function Differentiability

Examples of Function Differentiability

Proof of Interior Extremum Theorem

Proof of Darboux's Theorem

Examples of Darboux's Theorem

Proof of Mean Value Theorem (and Rolle's Theorem)

Proof of Generalized Mean Value Theorem

Example of Continuous Nowhere-Differentiable Function

Sequences and Series of Functions

Definition of Convergence of Sequence of Functions

Examples of Convergence of Sequence of Functions

Examples of Power Series Convergence

The Riemann Integral

Equi-Partition (and Refinement) for Riemann Sums

General Partition (and Refinement) for Riemann Sums

Difficulties with "cut-reassemble" transformation - preparing for Cavalieri's Principle

Integration and Cavalieri's Principle

Cavalieri "segment-skewing" transformation for area-preservation