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Résumés les plus vendus pour Understanding Analysis
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Algebraic Limit Theorem and Order Limit Theorem
- Notes de cours • 3 pages • 2023 Très apprécié
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Explain and provide proof for the algebraic limit theorem and the order limit theorem. Use proof by contradiction for the assumption and conclusion of the two sequences.
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Compact Sets
- Notes de cours • 4 pages • 2023 Très apprécié
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Introduce and provide proof for compact sets, that is a set that is both bounded and closed, hence the Heine-Borel theorem. Then introduce the perfect set, the connected/disconnected sets, and lastly the canter set, write proofs for all three.
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Sequences
- Notes de cours • 2 pages • 2023 Très apprécié
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Introduce sequences and its epsilon proof. Define the convergence of an to a and how to prove it with a backwards proof by first identifying the candidate for the limit and prove that that is the candidate, then prove convergence. Then introduce some theorems about sequences, namely the algebraic limit theorem and the order limit theorem.
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Consequences of Axiom of Completeness
- Notes de cours • 1 pages • 2023 Très apprécié
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Explain the proof for the nested interval property, and also the proofs for the Archimedean Property, which is split into two parts.
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Limit of Sequence
- Notes de cours • 2 pages • 2023 Très apprécié
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Give an epsilon proof for the limit of a sequence, where in more detail the partial sum of a series and its convergence is explained and tested with the p-series test. Then, introduce the Cauchy sequence and the monotone convergence theorem.
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Sequences
- Notes de cours • 3 pages • 2023 Très apprécié
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Disponible en pack
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- 9,24 €
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Introduce sequences and its epsilon proof. Then explain sequences with the algebraic limit theorem and the order limit theorem. Write proof for the theorem that a sequence converges if and only if that sequence is a Cauchy sequence.
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Consequences from Axiom of Completeness Continued.
- Notes de cours • 3 pages • 2023 Très apprécié
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Explain and prove more consequences from the axiom of completeness. First, the density of rational numbers in real numbers using Archimedean principle 1 and axiom of completeness. Then prove the existence of the square root of 2 with contradiction. Lastly, the sequences argument with the algebraic limit theorem and order limit theorem.
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Sequences and Topology of R
- Notes de cours • 4 pages • 2023 Très apprécié
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Disponible en pack
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Finish the lecture on sequences and the convergence of Cauchy. Then introduce the topology of R and in it the epsilon neighborhood of a in R. Define open sets, limit points, isolated points, and closed subsets.
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Axiom of Completeness and Consequences
- Notes de cours • 3 pages • 2023 Très apprécié
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Introduce Axiom of Completeness, the bed rock of advanced calculus, where every nonempty bounded above subset of R has a lower upper bound (supremum), and every nonempty bounded below subset of R has a greatest lower bound (infimum). Introduce the consequences of the Axiom of Completeness, with the Nested Interval Property and the Archimedean Property.
Derniers résumés de Understanding Analysis
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Sequences and Topology of R
- Notes de cours • 4 pages • 2023 Nouveau
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Disponible en pack
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- 9,24 €
- + en savoir plus
Finish the lecture on sequences and the convergence of Cauchy. Then introduce the topology of R and in it the epsilon neighborhood of a in R. Define open sets, limit points, isolated points, and closed subsets.
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Compact Sets
- Notes de cours • 4 pages • 2023 Nouveau
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Disponible en pack
-
- 9,24 €
- + en savoir plus
Introduce and provide proof for compact sets, that is a set that is both bounded and closed, hence the Heine-Borel theorem. Then introduce the perfect set, the connected/disconnected sets, and lastly the canter set, write proofs for all three.
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Consequences from Axiom of Completeness Continued.
- Notes de cours • 3 pages • 2023 Nouveau
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Disponible en pack
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- 9,24 €
- + en savoir plus
Explain and prove more consequences from the axiom of completeness. First, the density of rational numbers in real numbers using Archimedean principle 1 and axiom of completeness. Then prove the existence of the square root of 2 with contradiction. Lastly, the sequences argument with the algebraic limit theorem and order limit theorem.
Est-ce que vous écrivez vous-même des résumés ? Mettez-les ensuite en vente et gagnez de l'argent à chaque achat de vos documents.
-
Axiom of Completeness and Consequences
- Notes de cours • 3 pages • 2023 Nouveau
-
Disponible en pack
-
- 9,24 €
- + en savoir plus
Introduce Axiom of Completeness, the bed rock of advanced calculus, where every nonempty bounded above subset of R has a lower upper bound (supremum), and every nonempty bounded below subset of R has a greatest lower bound (infimum). Introduce the consequences of the Axiom of Completeness, with the Nested Interval Property and the Archimedean Property.
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Sequences
- Notes de cours • 3 pages • 2023 Nouveau
-
Disponible en pack
-
- 9,24 €
- + en savoir plus
Introduce sequences and its epsilon proof. Then explain sequences with the algebraic limit theorem and the order limit theorem. Write proof for the theorem that a sequence converges if and only if that sequence is a Cauchy sequence.
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Algebraic Limit Theorem and Order Limit Theorem
- Notes de cours • 3 pages • 2023 Nouveau
-
Disponible en pack
-
- 9,24 €
- + en savoir plus
Explain and provide proof for the algebraic limit theorem and the order limit theorem. Use proof by contradiction for the assumption and conclusion of the two sequences.
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Sequences
- Notes de cours • 2 pages • 2023 Nouveau
-
Disponible en pack
-
- 9,24 €
- + en savoir plus
Introduce sequences and its epsilon proof. Define the convergence of an to a and how to prove it with a backwards proof by first identifying the candidate for the limit and prove that that is the candidate, then prove convergence. Then introduce some theorems about sequences, namely the algebraic limit theorem and the order limit theorem.
-
Limit of Sequence
- Notes de cours • 2 pages • 2023 Nouveau
-
Disponible en pack
-
- 9,24 €
- + en savoir plus
Give an epsilon proof for the limit of a sequence, where in more detail the partial sum of a series and its convergence is explained and tested with the p-series test. Then, introduce the Cauchy sequence and the monotone convergence theorem.
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Consequences of Axiom of Completeness
- Notes de cours • 1 pages • 2023 Nouveau
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Disponible en pack
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- 9,24 €
- + en savoir plus
Explain the proof for the nested interval property, and also the proofs for the Archimedean Property, which is split into two parts.
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