From 593d9f6d4d1a9d18484ffca3c7e9fe72483baee9 Mon Sep 17 00:00:00 2001 From: Tom Malone Date: Sat, 24 Oct 2015 20:29:00 -0400 Subject: [PATCH] Created an outline of topics I need to learn and practice for Test 2 --- .../Test_2_Study_Outline-checkpoint.ipynb | 172 ++++++++++++++++++ Test_2_Study_Outline.ipynb | 172 ++++++++++++++++++ 2 files changed, 344 insertions(+) create mode 100644 .ipynb_checkpoints/Test_2_Study_Outline-checkpoint.ipynb create mode 100644 Test_2_Study_Outline.ipynb diff --git a/.ipynb_checkpoints/Test_2_Study_Outline-checkpoint.ipynb b/.ipynb_checkpoints/Test_2_Study_Outline-checkpoint.ipynb new file mode 100644 index 0000000..020ab52 --- /dev/null +++ b/.ipynb_checkpoints/Test_2_Study_Outline-checkpoint.ipynb @@ -0,0 +1,172 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Test II \n", + "\n", + "## Study Plan \n", + "\n", + "

This is an outline of all the topics and sub-topics, theorems, concepts, and tests, etc. which I'll need to know in order to pass __Test II__ with a good grade.

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "___\n", + "\n", + "
    \n", + "
  1. \n", + "

    Improper Integrals

    \n", + " 7.8\n", + "
    2. \n", + "
  2. \n", + "

    Sequences

    \n", + " 11.1\n", + "
      \n", + "
    1. Limit of Function/Limit of Sequence Relationship Theorem
      2. \n", + "
    2. Infinite Limit of a Sequence
      3. \n", + "
    3. __Limit Laws for Sequences__
      4. \n", + "
    4. Squeeze Theorem for Sequences
      5. \n", + "
    5. Limit of Absolute Value of a Sequence
      6. \n", + "
    6. __Convergence of Sequences__
      7. \n", + "
    7. Upper Bounds of Sequences
      8. \n", + "
    8. Lower Bounds of Sequences
      9. \n", + "
    9. Monotonic Sequences
      10. \n", + "
    10. Bounded Monotonic Sequences Converge
      11. \n", + "
    \n", + "
    3. \n", + "
  3. \n", + "

    Series

    \n", + " 11.2\n", + "
      \n", + "
    1. Definition of Series Convergence
      2. \n", + "
    2. Definition of Series Divergence
      3. \n", + "
    3. Definition of Partial Sums
      4. \n", + "
        \n", + "
      1. __Nth Partial Sum__
        2. \n", + "
      2. __Sequence of Partial Sums__
        3. \n", + "
      \n", + "
    4. \n", + " Geometric Series\n", + "
        \n", + "
      1. Common Ration
        2. \n", + "
      2. Convergence of Geometric Series ( $|r| < 1$ )
        3. \n", + "
      3. \n", + " Formula for the Sum of a Geometric Series
        \n", + " $\\sum_{n=1}^{\\infty} ar^{n-1} = \\frac{a}{1-r}$\n", + "
        4. \n", + "
      \n", + "
      5. \n", + "
    5. Harmonic Series
      6. \n", + "
    6. \n", + " __Nth Term Test__
      \n", + " $\\sum_{n=1}^{\\infty}a_n$ diverges if $\\lim_{n\\to\\infty}a_n \\ne 0$ or _fails to exist._\n", + "
      7. \n", + "
    7. Adding or Deleting Terms in a Series (doesn't alter convergence/divergence)
      8. \n", + "
    8. Can change __index start value__
      9. \n", + "
    9. __Limit Laws for Series__
      10. \n", + "
    \n", + "
    4. \n", + "
  4. \n", + "

    Integral Test

    \n", + " 11.3\n", + "
      \n", + "
    1. Non-Decreasing Partial Sums
      (only converges if bounded from above)
      2. \n", + "
    2. __Integral Test Theorem__
      3. \n", + "
    3. \n", + " P-Series
      \n", + "
        \n", + "
      1. Difference between _P-Series & Geometric Series_\n", + "
      \n", + "
      4. \n", + "
    4. \n", + " __Estimating Sums of Series__
      \n", + "
        \n", + "
      1. Estimating size of remainder
        2. \n", + "
      2. Bounds for remainder in _Integral Test_
        3. \n", + " \n", + "
      \n", + "
      5. \n", + "
    5. \n", + "
    6. \n", + "
    7. \n", + "
    8. \n", + "
    \n", + "
    5. \n", + "
  5. \n", + "

    Comparison Tests

    \n", + " 11.4\n", + "
      \n", + "
    1. __Comparison Test__
      2. \n", + "
    2. __Limit Comparison Test__
      3. \n", + "
    3. Estimating Sums with the Comparison & Limit Comparison Tests
      4. \n", + "
    \n", + "
    6. \n", + "
  6. \n", + "

    Alternating Series

    \n", + " 11.5\n", + "
      \n", + "
    1. Estimating Sums of Alternating Series
      \n", + "
        \n", + "
      1. Alternating Series Estimation Theorem
        2. \n", + " \n", + "
      \n", + "
      2. \n", + "
    2. __Alternating Series Test__
      3. \n", + "
    \n", + "
    7. \n", + "
  7. \n", + "

    Ratio & Root Tests

    \n", + " 11.6\n", + "
      \n", + "
    1. __Absolute Convergence__
      2. \n", + "
    2. __Conditional Convergence__
      3. \n", + "
    3. __Ratio Test__
      4. \n", + "
    4. _Root Test__
      5. \n", + "
    5. __Rearranging Series__
      6. \n", + "
    \n", + "
    8. \n", + "
  8. \n", + "

    Series Testing Strategy

    \n", + " 11.7\n", + "
      \n", + "
    \n", + "
    9. \n", + "
" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Test_2_Study_Outline.ipynb b/Test_2_Study_Outline.ipynb new file mode 100644 index 0000000..020ab52 --- /dev/null +++ b/Test_2_Study_Outline.ipynb @@ -0,0 +1,172 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Test II \n", + "\n", + "## Study Plan \n", + "\n", + "

This is an outline of all the topics and sub-topics, theorems, concepts, and tests, etc. which I'll need to know in order to pass __Test II__ with a good grade.

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "___\n", + "\n", + "
    \n", + "
  1. \n", + "

    Improper Integrals

    \n", + " 7.8\n", + "
    2. \n", + "
  2. \n", + "

    Sequences

    \n", + " 11.1\n", + "
      \n", + "
    1. Limit of Function/Limit of Sequence Relationship Theorem
      2. \n", + "
    2. Infinite Limit of a Sequence
      3. \n", + "
    3. __Limit Laws for Sequences__
      4. \n", + "
    4. Squeeze Theorem for Sequences
      5. \n", + "
    5. Limit of Absolute Value of a Sequence
      6. \n", + "
    6. __Convergence of Sequences__
      7. \n", + "
    7. Upper Bounds of Sequences
      8. \n", + "
    8. Lower Bounds of Sequences
      9. \n", + "
    9. Monotonic Sequences
      10. \n", + "
    10. Bounded Monotonic Sequences Converge
      11. \n", + "
    \n", + "
    3. \n", + "
  3. \n", + "

    Series

    \n", + " 11.2\n", + "
      \n", + "
    1. Definition of Series Convergence
      2. \n", + "
    2. Definition of Series Divergence
      3. \n", + "
    3. Definition of Partial Sums
      4. \n", + "
        \n", + "
      1. __Nth Partial Sum__
        2. \n", + "
      2. __Sequence of Partial Sums__
        3. \n", + "
      \n", + "
    4. \n", + " Geometric Series\n", + "
        \n", + "
      1. Common Ration
        2. \n", + "
      2. Convergence of Geometric Series ( $|r| < 1$ )
        3. \n", + "
      3. \n", + " Formula for the Sum of a Geometric Series
        \n", + " $\\sum_{n=1}^{\\infty} ar^{n-1} = \\frac{a}{1-r}$\n", + "
        4. \n", + "
      \n", + "
      5. \n", + "
    5. Harmonic Series
      6. \n", + "
    6. \n", + " __Nth Term Test__
      \n", + " $\\sum_{n=1}^{\\infty}a_n$ diverges if $\\lim_{n\\to\\infty}a_n \\ne 0$ or _fails to exist._\n", + "
      7. \n", + "
    7. Adding or Deleting Terms in a Series (doesn't alter convergence/divergence)
      8. \n", + "
    8. Can change __index start value__
      9. \n", + "
    9. __Limit Laws for Series__
      10. \n", + "
    \n", + "
    4. \n", + "
  4. \n", + "

    Integral Test

    \n", + " 11.3\n", + "
      \n", + "
    1. Non-Decreasing Partial Sums
      (only converges if bounded from above)
      2. \n", + "
    2. __Integral Test Theorem__
      3. \n", + "
    3. \n", + " P-Series
      \n", + "
        \n", + "
      1. Difference between _P-Series & Geometric Series_\n", + "
      \n", + "
      4. \n", + "
    4. \n", + " __Estimating Sums of Series__
      \n", + "
        \n", + "
      1. Estimating size of remainder
        2. \n", + "
      2. Bounds for remainder in _Integral Test_
        3. \n", + " \n", + "
      \n", + "
      5. \n", + "
    5. \n", + "
    6. \n", + "
    7. \n", + "
    8. \n", + "
    \n", + "
    5. \n", + "
  5. \n", + "

    Comparison Tests

    \n", + " 11.4\n", + "
      \n", + "
    1. __Comparison Test__
      2. \n", + "
    2. __Limit Comparison Test__
      3. \n", + "
    3. Estimating Sums with the Comparison & Limit Comparison Tests
      4. \n", + "
    \n", + "
    6. \n", + "
  6. \n", + "

    Alternating Series

    \n", + " 11.5\n", + "
      \n", + "
    1. Estimating Sums of Alternating Series
      \n", + "
        \n", + "
      1. Alternating Series Estimation Theorem
        2. \n", + " \n", + "
      \n", + "
      2. \n", + "
    2. __Alternating Series Test__
      3. \n", + "
    \n", + "
    7. \n", + "
  7. \n", + "

    Ratio & Root Tests

    \n", + " 11.6\n", + "
      \n", + "
    1. __Absolute Convergence__
      2. \n", + "
    2. __Conditional Convergence__
      3. \n", + "
    3. __Ratio Test__
      4. \n", + "
    4. _Root Test__
      5. \n", + "
    5. __Rearranging Series__
      6. \n", + "
    \n", + "
    8. \n", + "
  8. \n", + "

    Series Testing Strategy

    \n", + " 11.7\n", + "
      \n", + "
    \n", + "
    9. \n", + "
" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}