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ε-δ Perspective on Derivatives
Establishing convergence of secant lines
Jul 12
•
Howard Heaton
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ε-δ Perspective on Derivatives
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Relating ε-δ Continuity to Open Inverses
A proof of one direction of the equivalence
Jul 5
•
Howard Heaton
1
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Relating ε-δ Continuity to Open Inverses
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June 2024
Positivity and Continuity
Picking ε in the definition of continuity
Jun 21
•
Howard Heaton
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Positivity and Continuity
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Pointwise Convergence with Rounded Tents
Fixing x and then taking a limit over n.
Jun 14
•
Howard Heaton
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Pointwise Convergence with Rounded Tents
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Composition of Continuous Functions in 2D
A visual proof sketch
Jun 7
•
Howard Heaton
1
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Composition of Continuous Functions in 2D
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1
May 2024
Banach Fixed Point Theorem via Cosine
Iteratively solving x = cos(x)
May 29
•
Howard Heaton
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Banach Fixed Point Theorem via Cosine
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Uniformly Continuous Function
Same δ for all points in the domain
May 22
•
Howard Heaton
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Uniformly Continuous Function
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Proof for Limit of Quadratic Function
Picking δ as the minimum of two numbers
May 13
•
Howard Heaton
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Proof for Limit of Quadratic Function
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Alternating Harmonic Series
Insight into a peculiar series that approximates an integral
May 1
•
Howard Heaton
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Alternating Harmonic Series
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April 2024
Bolzano-Weierstrass Theorem
Bounded sequences have convergent subsequences
Apr 21
•
Howard Heaton
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Bolzano-Weierstrass Theorem
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