(→‎Homework Help)
 
(79 intermediate revisions by 12 users not shown)
Line 1: Line 1:
−
=Math 181 Honors Calculus=
+
=Math [[MA181|181]] Honors Calculus, Fall 2008, Prof. Bell=
 +
[[MA181Fall2008bell:General_disclaimer_MA181Fall2008bell| Disclaimer]]
 +
=== Did 'ya Know? ===
 +
This week I thought that I'd demonstrate how to add ellipses in a LaTeX equation.
 +
 
 +
<math>
 +
\begin{align}
 +
\sum_n &= 1 + 2 + 3 + ... + n + ... + \infty \\
 +
&= 0 + 1 + 2 + \cdots + n + \cdots + \infty
 +
\end{align}
 +
</math>
 +
 
 +
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.
 +
 
 +
{|
 +
|-
 +
| style="padding-right: 2em;" | \ldots || style="padding-right: 2em;" | <math>\ldots</math> || styl="padding-right: 2em;" | \therefore || <math>\therefore</math>
 +
|-
 +
| \cdots || <math>\cdots</math> || \dagger|| <math>\dagger</math>
 +
|-
 +
| \vdots || <math>\vdots</math> || \clubsuit || <math>\clubsuit</math>
 +
|-
 +
| \ddots || <math>\ddots</math> || \doteq|| <math>\doteq</math>
 +
|-
 +
|}
 +
 
 +
<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]==
 +
[[Note on Kiwi display with LaTeX_MA181Fall2008bell]]
  
−
==Lecture Notes==
+
==[[Lecture Notes_MA181Fall2008bell]]==
 +
 
 +
==Extra Credit==
 +
 
 +
[[ExtraCreditRiemannSum_MA181Fall2008bell| Extra Credit - Riemann Sum]]
 +
 
 +
[[ChallengeProblem _MA181Fall2008bell| Challenge Problem about the sum for  <math>\pi/4</math>]]
  
 
==Homework Help==
 
==Homework Help==
−
Hello, this is gary from ma181.  let's solve the extra credit problem.
 
−
Here is the problem in italics:
 
  
−
<blockquote>
+
[[Homework 8_MA181Fall2008bell]]
−
Extra Credit Problem
+
−
--------------------
+
  
−
Suppose that  f(x)  is continuously differentiable
+
[[Homework 9_MA181Fall2008bell]]
−
on the interval  [a,b].  Let  N  be a positive integer
+
−
and let <math> M = Max { |f'(x)| : a \leq x \leq b } </math>.  Let
+
−
<math> h = \frac{(b-a)}{N}  </math> and let  <math> R_N </math>  denote the "right endpoint"
+
−
Riemann Sum for the integral
+
−
<math> I = \int_a^b f(x) dx .</math>
+
−
In other words,
+
−
<math> R_N = \sum_{n=1}^N f(a + n h) h .</math>
+
  
−
Explain why the error, <math> E = | R_N - I | </math>, satisfies
+
[[Homework 10_MA181Fall2008bell]]
−
<math> E < \frac{M(b-a)^2}{N}. </math>
+
−
</blockquote>
+
  
−
*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.
+
[[Homework 11_MA181Fall2008bell]]
  
−
*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?
+
[[Homework 12_MA181Fall2008bell]]
  
−
*Chumbert: Yeah, he said in class today (Wed.) to assume that, right?
+
[[Homework 13_MA181Fall2008bell]]
−
*Ctuchek - I do remember him saying that we will need to use the Mean Value Theorem.
+
  
−
==Interesting Articles about Calculus==
+
[[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 [http://kiwi.ecn.purdue.edu/ECE301Fall2008chihw/index.php/Complex_norm_question here]?
 +
 
 +
==Interesting Articles About Calculus and Math==
 +
 
 +
[[MAPLE commands_MA181Fall2008bell]]
  
 
[[The minimum volume happens at the average_MA181Fall2008bell]]
 
[[The minimum volume happens at the average_MA181Fall2008bell]]
 +
 +
[[interesting_integration_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]]==
 
==[[Learn LaTeX_MA181Fall2008bell]]==
 +
Common Latex Commands  http://authors.aps.org/latex/
 +
 +
==[[Solution to Exams_MA181Fall2008bell]]==
 +
 +
==[[Useful Formulas_MA181Fall2008bell]]==
 +
 +
==Study Guides==
 +
[[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

Retrieved from "https://www.projectrhea.org/rhea/index.php?title=Main_Page_MA181Fall2008bell&oldid=39701"
Shortcuts
Help Main Wiki Page Random Page Special Pages Log in
Search

Alumni Liaison

To all math majors: "Mathematics is a wonderfully rich subject."

Dr. Paul Garrett