Latest revision as of 06:35, 10 August 2010

Math 181 Honors Calculus, Fall 2008, Prof. Bell

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	$\doteq$

~His Not-quite-so-awesome-as-His-Awesomeness, Dennis Snell

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

@@ 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]==
+[[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==
-Hello, this is gary from ma181.  let's solve the extra credit problem.
-Here is the problem in italics:
-"Extra Credit Problem
+[[Homework 8_MA181Fall2008bell]]
---------------------
-Suppose that  f(x)  is continuously differentiable
+[[Homework 9_MA181Fall2008bell]]
-on the interval  [a,b].  Let  N  be a positive integer
-and let  M = Max { |f'(x)| : a <= x <= b }.  Let
-h = (b-a)/N  and let  R_N  denote the "right endpoint"
-Riemann Sum for the integral
-I = int( f(x), x=a..b).
+[[Homework 10_MA181Fall2008bell]]
-In other words,
+[[Homework 11_MA181Fall2008bell]]
-R_N = sum( f(a + n*h)*h , n=1..N ).
+[[Homework 12_MA181Fall2008bell]]
-Explain why the error, E = | R_N - I |, satisfies
+[[Homework 13_MA181Fall2008bell]]
-E < M(b-a)^2/N."
+[[Homework 14_MA181Fall2008bell]]
-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 15_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 16_MA181Fall2008bell]]
-==Interesting Articles about Calculus==
+[[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]]
+[[interesting_integration_MA181Fall2008bell| Interesting Integration]]
-it is the right riemann is the eror is the last one
+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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