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Resúmenes más vendidos de Understanding Analysis

Compact Sets Compact Sets

  • Notas de lectura

    Compact Sets

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    4
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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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Algebraic Limit Theorem and Order Limit Theorem Algebraic Limit Theorem and Order Limit Theorem

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    Algebraic Limit Theorem and Order Limit Theorem

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    3
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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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Consequences of Axiom of Completeness Consequences of Axiom of Completeness

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    Consequences of Axiom of Completeness

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    1
    junio 2023
    2022/2023
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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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Sequences Sequences

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    Sequences

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    junio 2023
    2022/2023
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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 from Axiom of Completeness Continued. Consequences from Axiom of Completeness Continued.

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    Consequences from Axiom of Completeness Continued.

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    3
    junio 2023
    2022/2023
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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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Axiom of Completeness and Consequences Axiom of Completeness and Consequences

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    Axiom of Completeness and Consequences

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    3
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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 and Topology of R Sequences and Topology of R

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    Sequences and Topology of R

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    4
    junio 2023
    2022/2023
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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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Limit of Sequence Limit of Sequence

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    Limit of Sequence

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    2
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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 Sequences

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    Sequences

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    3
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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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Resúmenes más recientes de Understanding Analysis

Advanced Calculus I (MATH521)

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    Advanced Calculus I (MATH521)

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    11
    junio 2023
  • This package provides the full course class notes, homework answers, and exam questions for the course MATH521 (advanced calculus I) at UNC Chapel hill.
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Compact Sets Compact Sets

  • Notas de lectura

    Compact Sets

  • Disponible en un paquete
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    -
    4
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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.
  • Nuevo
    mierli
    $10.14 Más información
Sequences and Topology of R Sequences and Topology of R

  • Notas de lectura

    Sequences and Topology of R

  • Disponible en un paquete
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    4
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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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    mierli
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Sequences Sequences

  • Notas de lectura

    Sequences

  • Disponible en un paquete
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    -
    -
    3
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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.
  • Nuevo
    mierli
    $10.14 Más información
Consequences from Axiom of Completeness Continued. Consequences from Axiom of Completeness Continued.

  • Notas de lectura

    Consequences from Axiom of Completeness Continued.

  • Disponible en un paquete
    -
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    3
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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.
  • Nuevo
    mierli
    $10.14 Más información
Axiom of Completeness and Consequences Axiom of Completeness and Consequences

  • Notas de lectura

    Axiom of Completeness and Consequences

  • Disponible en un paquete
    -
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    -
    3
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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.
  • Nuevo
    mierli
    $10.14 Más información
Algebraic Limit Theorem and Order Limit Theorem Algebraic Limit Theorem and Order Limit Theorem

  • Notas de lectura

    Algebraic Limit Theorem and Order Limit Theorem

  • Disponible en un paquete
    -
    -
    -
    3
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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.
  • Nuevo
    mierli
    $10.14 Más información
Limit of Sequence Limit of Sequence

  • Notas de lectura

    Limit of Sequence

  • Disponible en un paquete
    -
    -
    -
    2
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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.
  • Nuevo
    mierli
    $10.14 Más información
Sequences Sequences

  • Notas de lectura

    Sequences

  • Disponible en un paquete
    -
    -
    -
    2
    junio 2023
    2022/2023
    Disponible en un paquete
  • 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.
  • Nuevo
    mierli
    $10.14 Más información
Consequences of Axiom of Completeness Consequences of Axiom of Completeness

  • Notas de lectura

    Consequences of Axiom of Completeness

  • Disponible en un paquete
    -
    -
    -
    1
    junio 2023
    2022/2023
    Disponible en un paquete
  • Explain the proof for the nested interval property, and also the proofs for the Archimedean Property, which is split into two parts.
  • Nuevo
    mierli
    $10.14 Más información