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=Math 181 Honors Calculus=
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=Math [[MA181|181]] Honors Calculus, Fall 2008, Prof. Bell=
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[[MA181Fall2008bell:General_disclaimer_MA181Fall2008bell| Disclaimer]]
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=== Did 'ya Know? ===
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This week I thought that I'd demonstrate how to add ellipses in a LaTeX equation.
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<math>
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\begin{align}
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\sum_n &= 1 + 2 + 3 + ... + n + ... + \infty \\
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&= 0 + 1 + 2 + \cdots + n + \cdots + \infty
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\end{align}
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</math>
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In the first example, three consecutive dots were typed, but the second example uses LaTeX's \cdots command.  This stands for 'center dots'.  There are also other 'dot' functions.
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{|
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|-
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| style="padding-right: 2em;" | \ldots || style="padding-right: 2em;" | <math>\ldots</math> || styl="padding-right: 2em;" | \therefore || <math>\therefore</math>
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|-
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| \cdots || <math>\cdots</math> || \dagger|| <math>\dagger</math>
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|-
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| \vdots || <math>\vdots</math> || \clubsuit || <math>\clubsuit</math>
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|-
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| \ddots || <math>\ddots</math> || \doteq|| <math>\doteq</math>
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|-
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|}
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<div style="float:right;clear:both;margin-right:5em;margin-bottom:2em;">~[[User:Dmsnell|His Not-quite-so-awesome-as-His-Awesomeness, Dennis Snell]]</div>
  
 
==[http://en.wikipedia.org/wiki/Help:Editing Getting started editing]==
 
==[http://en.wikipedia.org/wiki/Help:Editing Getting started editing]==
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[[Note on Kiwi display with LaTeX_MA181Fall2008bell]]
  
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==Lecture Notes==
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==[[Lecture Notes_MA181Fall2008bell]]==
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==Extra Credit==
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[[ExtraCreditRiemannSum_MA181Fall2008bell| Extra Credit - Riemann Sum]]
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[[ChallengeProblem _MA181Fall2008bell| Challenge Problem about the sum for  <math>\pi/4</math>]]
  
 
==Homework Help==
 
==Homework Help==
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Hello, this is gary from ma181.  let's solve the extra credit problem.
 
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Here is the problem in italics:
 
  
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<blockquote>
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[[Homework 8_MA181Fall2008bell]]
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Extra Credit Problem
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--------------------
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Suppose that  f(x)  is continuously differentiable
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[[Homework 9_MA181Fall2008bell]]
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on the interval  [a,b].  Let  N  be a positive integer
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and let <math> M = Max { |f'(x)| : a \leq x \leq b } </math>.  Let
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<math> h = \frac{(b-a)}{N}  </math> and let  <math> R_N </math>  denote the "right endpoint"
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Riemann Sum for the integral
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<math> I = \int_a^b f(x) dx .</math>
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In other words,
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<math> R_N = \sum_{n=1}^N f(a + n h) h .</math>
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Explain why the error, <math> E = | R_N - I | </math>, satisfies
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[[Homework 10_MA181Fall2008bell]]
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<math> E \le \frac{M(b-a)^2}{N}. </math>
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</blockquote>
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*So what does this equation "E < M(b-a)^2/N" mean.  This reads that the error is less than the Maximum value of the derivative of the function of x multiplied by the interval squared from x=a to x=b all divided by the total number of subintervals N.
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[[Homework 11_MA181Fall2008bell]]
  
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*I don't understand why this must be true.  Maybe I'm wrong, but if f(x) were a horizontal line, wouldn't E=0 and M(b-a)^2/N also be =0.  That would mean it is a false statement that E < M(b-a)^2/N.  Are we to assume that E <= M(b-a)^2/N?
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[[Homework 12_MA181Fall2008bell]]
  
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*Chumbert - Yeah, he said in class today (Wed.) to assume that, right?
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[[Homework 13_MA181Fall2008bell]]
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*Bell - Oops!  Sorry about that.  You're right.  It needs to be <math>\le</math>.  (I can show that the ''only'' time it is actually equal is when the function <math>f(x)</math> is a constant function.)
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*Ctuchek - I do remember him saying that we will need to use the Mean Value Theorem.
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*Chumbert - Logically, I think I got it, but I'm not entirely sure how to prove it mathematically:
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The <math>M(b-a)</math> gives the height of one section(slope=(y/x), so slope*x=y), where <math>\frac{(b-a)}{N}</math> gives the width, and when multiplied together, they give you a rectangle which, if you remember from class, is the error--take the R-sum, then stack the extra blocks on to of each other. Does anyone else remember that? Or should I explain it better?
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==Interesting Articles about Calculus==
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[[Homework 14_MA181Fall2008bell]]
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[[Homework 15_MA181Fall2008bell]]
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[[Homework 16_MA181Fall2008bell]]
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[[Homework 17_MA181Fall2008bell]]
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[[Homework 18_MA181Fall2008bell]]
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[[Homework 19_MA181Fall2008bell]]
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[[Homework 20_MA181Fall2008bell]]
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[[Fourier Series Homework_MA181Fall2008bell]]
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[[Homework Whatever_MA181Fall2008bell]] (the last one)
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== Cross-subject Issues ==
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Help! The ECE students are struggling with complex numbers. Can you shed some light [http://kiwi.ecn.purdue.edu/ECE301Fall2008chihw/index.php/Complex_norm_question here]?
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==Interesting Articles About Calculus and Math==
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[[MAPLE commands_MA181Fall2008bell]]
  
 
[[The minimum volume happens at the average_MA181Fall2008bell]]
 
[[The minimum volume happens at the average_MA181Fall2008bell]]
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[[interesting_integration_MA181Fall2008bell| Interesting Integration]]
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Not Calculus: [[Area of a triangle defined by three tangential circles_MA181Fall2008bell]]
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[[Cycloid Function_MA181Fall2008bell]]??
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[[Single Elimination Forever_MA181Fall2008bell]] - Simple question to make you think a little.
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[[A Tough Integral_MA181Fall2008bell]]
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[[A Baffling Fact_MA181Fall2008bell]]
  
 
==[[Learn LaTeX_MA181Fall2008bell]]==
 
==[[Learn LaTeX_MA181Fall2008bell]]==
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Common Latex Commands  http://authors.aps.org/latex/
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==[[Solution to Exams_MA181Fall2008bell]]==
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==[[Useful Formulas_MA181Fall2008bell]]==
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==Study Guides==
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[[Exam II_MA181Fall2008bell]]

Latest revision as of 05:35, 10 August 2010

Math 181 Honors Calculus, Fall 2008, Prof. Bell

Disclaimer

Did 'ya Know?

This week I thought that I'd demonstrate how to add ellipses in a LaTeX equation.

$ \begin{align} \sum_n &= 1 + 2 + 3 + ... + n + ... + \infty \\ &= 0 + 1 + 2 + \cdots + n + \cdots + \infty \end{align} $

In the first example, three consecutive dots were typed, but the second example uses LaTeX's \cdots command. This stands for 'center dots'. There are also other 'dot' functions.

\ldots $ \ldots $ \therefore $ \therefore $
\cdots $ \cdots $ \dagger $ \dagger $
\vdots $ \vdots $ \clubsuit $ \clubsuit $
\ddots $ \ddots $ \doteq $ \doteq $

Getting started editing

Note on Kiwi display with LaTeX_MA181Fall2008bell

Lecture Notes_MA181Fall2008bell

Extra Credit

Extra Credit - Riemann Sum

Challenge Problem about the sum for $ \pi/4 $

Homework Help

Homework 8_MA181Fall2008bell

Homework 9_MA181Fall2008bell

Homework 10_MA181Fall2008bell

Homework 11_MA181Fall2008bell

Homework 12_MA181Fall2008bell

Homework 13_MA181Fall2008bell

Homework 14_MA181Fall2008bell

Homework 15_MA181Fall2008bell

Homework 16_MA181Fall2008bell

Homework 17_MA181Fall2008bell

Homework 18_MA181Fall2008bell

Homework 19_MA181Fall2008bell

Homework 20_MA181Fall2008bell

Fourier Series Homework_MA181Fall2008bell

Homework Whatever_MA181Fall2008bell (the last one)

Cross-subject Issues

Help! The ECE students are struggling with complex numbers. Can you shed some light here?

Interesting Articles About Calculus and Math

MAPLE commands_MA181Fall2008bell

The minimum volume happens at the average_MA181Fall2008bell

Interesting Integration

Not Calculus: Area of a triangle defined by three tangential circles_MA181Fall2008bell

Cycloid Function_MA181Fall2008bell??

Single Elimination Forever_MA181Fall2008bell - Simple question to make you think a little.

A Tough Integral_MA181Fall2008bell

A Baffling Fact_MA181Fall2008bell

Learn LaTeX_MA181Fall2008bell

Common Latex Commands http://authors.aps.org/latex/

Solution to Exams_MA181Fall2008bell

Useful Formulas_MA181Fall2008bell

Study Guides

Exam II_MA181Fall2008bell

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