Skip to content

Commit

Permalink
Created an outline of topics I need to learn and practice for Test 2
Browse files Browse the repository at this point in the history
  • Loading branch information
Tom Malone committed Oct 25, 2015
1 parent 260cdad commit 593d9f6
Show file tree
Hide file tree
Showing 2 changed files with 344 additions and 0 deletions.
172 changes: 172 additions & 0 deletions .ipynb_checkpoints/Test_2_Study_Outline-checkpoint.ipynb
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,172 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Test II \n",
"\n",
"## Study Plan \n",
"\n",
"<p class='lead'>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.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"___\n",
"\n",
"<ol class='roman outline'>\n",
" <li>\n",
" <h3>Improper Integrals</h3>\n",
" <span class='section'>7.8</span>\n",
" </li>\n",
" <li>\n",
" <h3>Sequences</h3>\n",
" <span class='section'>11.1</span>\n",
" <ol class='alpha'>\n",
" <li>Limit of Function/Limit of Sequence Relationship Theorem</li>\n",
" <li>Infinite Limit of a Sequence</li>\n",
" <li>__Limit Laws for Sequences__</li>\n",
" <li>Squeeze Theorem for Sequences</li>\n",
" <li>Limit of Absolute Value of a Sequence</li>\n",
" <li>__Convergence of Sequences__</li>\n",
" <li>Upper Bounds of Sequences</li>\n",
" <li>Lower Bounds of Sequences</li>\n",
" <li>Monotonic Sequences</li>\n",
" <li>Bounded Monotonic Sequences Converge</li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Series</h3>\n",
" <span class='section'>11.2</span>\n",
" <ol class='alpha'>\n",
" <li>Definition of Series Convergence</li>\n",
" <li>Definition of Series Divergence</li>\n",
" <li>Definition of Partial Sums</li>\n",
" <ol class='roman-l'>\n",
" <li>__Nth Partial Sum__</li>\n",
" <li>__Sequence of Partial Sums__</li>\n",
" </ol>\n",
" <li>\n",
" Geometric Series\n",
" <ol class='roman-l'>\n",
" <li>Common Ration</li>\n",
" <li>Convergence of Geometric Series ( $|r| < 1$ )</li>\n",
" <li>\n",
" Formula for the Sum of a Geometric Series<br/>\n",
" $\\sum_{n=1}^{\\infty} ar^{n-1} = \\frac{a}{1-r}$\n",
" </li>\n",
" </ol>\n",
" </li>\n",
" <li>Harmonic Series</li>\n",
" <li>\n",
" __Nth Term Test__<br/>\n",
" $\\sum_{n=1}^{\\infty}a_n$ diverges if $\\lim_{n\\to\\infty}a_n \\ne 0$ or _fails to exist._\n",
" </li>\n",
" <li>Adding or Deleting Terms in a Series (doesn't alter convergence/divergence)</li>\n",
" <li>Can change __index start value__</li>\n",
" <li>__Limit Laws for Series__</li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Integral Test</h3>\n",
" <span class='section'>11.3</span>\n",
" <ol class='alpha'>\n",
" <li>Non-Decreasing Partial Sums<br/>(only converges if bounded from above)</li>\n",
" <li>__Integral Test Theorem__</li>\n",
" <li>\n",
" P-Series<br/>\n",
" <ol class='roman-l'>\n",
" <li>Difference between _P-Series &amp; Geometric Series_\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" __Estimating Sums of Series__<br/>\n",
" <ol class='roman-l'>\n",
" <li>Estimating size of remainder</li>\n",
" <li>Bounds for remainder in _Integral Test_</li>\n",
" \n",
" </ol>\n",
" </li>\n",
" <li></li>\n",
" <li></li>\n",
" <li></li>\n",
" <li></li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Comparison Tests</h3>\n",
" <span class='section'>11.4</span>\n",
" <ol class='alpha'>\n",
" <li>__Comparison Test__</li>\n",
" <li>__Limit Comparison Test__</li>\n",
" <li>Estimating Sums with the Comparison &amp; Limit Comparison Tests</li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Alternating Series</h3>\n",
" <span class='section'>11.5</span>\n",
" <ol class='alpha'>\n",
" <li>Estimating Sums of Alternating Series<br/>\n",
" <ol class='roman-l'>\n",
" <li>Alternating Series Estimation Theorem</li>\n",
" \n",
" </ol>\n",
" </li>\n",
" <li>__Alternating Series Test__</li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Ratio &amp; Root Tests</h3>\n",
" <span class='section'>11.6</span>\n",
" <ol class='alpha'>\n",
" <li>__Absolute Convergence__</li>\n",
" <li>__Conditional Convergence__</li>\n",
" <li>__Ratio Test__</li>\n",
" <li>_Root Test__</li>\n",
" <li>__Rearranging Series__</li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Series Testing Strategy</h3>\n",
" <span class='section'>11.7</span>\n",
" <ol class='alpha'>\n",
" </ol>\n",
" </li>\n",
"</ol>"
]
},
{
"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
}
172 changes: 172 additions & 0 deletions Test_2_Study_Outline.ipynb
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,172 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Test II \n",
"\n",
"## Study Plan \n",
"\n",
"<p class='lead'>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.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"___\n",
"\n",
"<ol class='roman outline'>\n",
" <li>\n",
" <h3>Improper Integrals</h3>\n",
" <span class='section'>7.8</span>\n",
" </li>\n",
" <li>\n",
" <h3>Sequences</h3>\n",
" <span class='section'>11.1</span>\n",
" <ol class='alpha'>\n",
" <li>Limit of Function/Limit of Sequence Relationship Theorem</li>\n",
" <li>Infinite Limit of a Sequence</li>\n",
" <li>__Limit Laws for Sequences__</li>\n",
" <li>Squeeze Theorem for Sequences</li>\n",
" <li>Limit of Absolute Value of a Sequence</li>\n",
" <li>__Convergence of Sequences__</li>\n",
" <li>Upper Bounds of Sequences</li>\n",
" <li>Lower Bounds of Sequences</li>\n",
" <li>Monotonic Sequences</li>\n",
" <li>Bounded Monotonic Sequences Converge</li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Series</h3>\n",
" <span class='section'>11.2</span>\n",
" <ol class='alpha'>\n",
" <li>Definition of Series Convergence</li>\n",
" <li>Definition of Series Divergence</li>\n",
" <li>Definition of Partial Sums</li>\n",
" <ol class='roman-l'>\n",
" <li>__Nth Partial Sum__</li>\n",
" <li>__Sequence of Partial Sums__</li>\n",
" </ol>\n",
" <li>\n",
" Geometric Series\n",
" <ol class='roman-l'>\n",
" <li>Common Ration</li>\n",
" <li>Convergence of Geometric Series ( $|r| < 1$ )</li>\n",
" <li>\n",
" Formula for the Sum of a Geometric Series<br/>\n",
" $\\sum_{n=1}^{\\infty} ar^{n-1} = \\frac{a}{1-r}$\n",
" </li>\n",
" </ol>\n",
" </li>\n",
" <li>Harmonic Series</li>\n",
" <li>\n",
" __Nth Term Test__<br/>\n",
" $\\sum_{n=1}^{\\infty}a_n$ diverges if $\\lim_{n\\to\\infty}a_n \\ne 0$ or _fails to exist._\n",
" </li>\n",
" <li>Adding or Deleting Terms in a Series (doesn't alter convergence/divergence)</li>\n",
" <li>Can change __index start value__</li>\n",
" <li>__Limit Laws for Series__</li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Integral Test</h3>\n",
" <span class='section'>11.3</span>\n",
" <ol class='alpha'>\n",
" <li>Non-Decreasing Partial Sums<br/>(only converges if bounded from above)</li>\n",
" <li>__Integral Test Theorem__</li>\n",
" <li>\n",
" P-Series<br/>\n",
" <ol class='roman-l'>\n",
" <li>Difference between _P-Series &amp; Geometric Series_\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" __Estimating Sums of Series__<br/>\n",
" <ol class='roman-l'>\n",
" <li>Estimating size of remainder</li>\n",
" <li>Bounds for remainder in _Integral Test_</li>\n",
" \n",
" </ol>\n",
" </li>\n",
" <li></li>\n",
" <li></li>\n",
" <li></li>\n",
" <li></li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Comparison Tests</h3>\n",
" <span class='section'>11.4</span>\n",
" <ol class='alpha'>\n",
" <li>__Comparison Test__</li>\n",
" <li>__Limit Comparison Test__</li>\n",
" <li>Estimating Sums with the Comparison &amp; Limit Comparison Tests</li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Alternating Series</h3>\n",
" <span class='section'>11.5</span>\n",
" <ol class='alpha'>\n",
" <li>Estimating Sums of Alternating Series<br/>\n",
" <ol class='roman-l'>\n",
" <li>Alternating Series Estimation Theorem</li>\n",
" \n",
" </ol>\n",
" </li>\n",
" <li>__Alternating Series Test__</li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Ratio &amp; Root Tests</h3>\n",
" <span class='section'>11.6</span>\n",
" <ol class='alpha'>\n",
" <li>__Absolute Convergence__</li>\n",
" <li>__Conditional Convergence__</li>\n",
" <li>__Ratio Test__</li>\n",
" <li>_Root Test__</li>\n",
" <li>__Rearranging Series__</li>\n",
" </ol>\n",
" </li>\n",
" <li>\n",
" <h3>Series Testing Strategy</h3>\n",
" <span class='section'>11.7</span>\n",
" <ol class='alpha'>\n",
" </ol>\n",
" </li>\n",
"</ol>"
]
},
{
"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
}

0 comments on commit 593d9f6

Please sign in to comment.