wrote more calculus, fixed latex positioning problem

3 files changed, 20 insertions, 3 deletions

diff --git a/src/style.php b/src/style.php
index a04d94d..a3a8dcb 100644
--- a/src/style.php
+++ b/src/style.php
@@ -135,5 +135,6 @@ hr {
 }
 .centermath {
 	text-align: center;
+	text-indent: 0px;
 	margin: 14px 40px 14px 40px;
 }
diff --git a/src/writing/derivative.php b/src/writing/calculus.php
index aad4332..ddfdd0c 100644
--- a/src/writing/derivative.php
+++ b/src/writing/calculus.php
@@ -15,6 +15,7 @@ function tex($latex) {
 	or method for the analysis of some set of problems. The fact that the <i>calculus of infinitesimals</i>

 	has come to be known in this way is a testament to its importance.

 </p>

+<h2>Functions</h2>

 <p>

 	To understand calculus, it is critical to understand the derivative. Let us begin with

 	the definition of a function.

@@ -69,7 +70,7 @@ function tex($latex) {
 	rapidly eclipsing the straight line.

 </p>

 <p>

-	Suppose we wish to know the slope of a function not over an interval but at a point.

+	Suppose we wished to know the slope of a function not over an interval but at a point.

 	This is easily accomplished with a linear function--it is observed that the slope of a

 	linear function is the same over any interval, and so it is reasonable to extend that

 	to a single point. It is more difficult, however, with non-linear functions.

@@ -94,6 +95,21 @@ function tex($latex) {
 	This would continue infinitely, with m never reaching 2. A new calculus is needed

 	to precisely describe the slope of non-linear functions at a point. This value,

 	the rate that the function will change over the next infinitesimally small interval,

-	is known as its <i>instant rate of change</i> at a point.

+	is known as its <i>instantantaneous rate of change</i> at a point.

+</p>

+<h2>Limits</h2>

+<p>

+	The </i>limit</i> of a function is the value L it approaches as its argument approaches

+	c.

+</p>

+<p class="centermath"><?php echo(tex("\$\\lim_{x\\to c} f(x) = L\$")); ?></p>

+<p>

+	Limits enable us to make statements about the behaviour of functions near a point,

+	even when the behaviour differs <i>at</i> that point. For example, 1/0 is undefined,

+	but <?php echo(tex("\$\\lim_{x\\to 0} \\frac{1}{x} = \\infty$")); ?>. This is fairly

+	self-evident--division by an infinitely small number will produce an infinitely large one.

+	The limit is formally defined as follows:

+</p>

+<p class="centermath"><?php echo(tex("\$\\lim_{x\\to c}f(x)=L\\ \\textup{if}\\ \\forall\\epsilon\\in\\mathbb{R},\\ \\epsilon>0\\ \\exists\\delta\\in\\mathbb{R},\\newline|f(x)-L|<\\epsilon\\ \\textup{whenever}\\ 0 < |x-c| < \\delta\$")); ?></p>

 </p>

 <?php require($_SERVER["DOCUMENT_ROOT"] . "/footer.php"); ?>

diff --git a/src/writing/index.php b/src/writing/index.php
index c354f70..f138822 100644
--- a/src/writing/index.php
+++ b/src/writing/index.php
@@ -22,7 +22,7 @@ require($_SERVER["DOCUMENT_ROOT"] . "/header.php");
 	My writing in Greek.

 </p>

 <ul>

-	<li><h3><a href="derivative.php">The Calculus of Infinitesimals</a> - an introduction</h3></li>

+	<li><h3><a href="calculus.php">The Calculus of Infinitesimals</a> - an introduction</h3></li>

 </ul>

 <h2>Manifestos</h2>

 <p>