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authorKai Stevenson <kai@kaistevenson.com>2023-08-01 20:36:04 -0700
committerKai Stevenson <kai@kaistevenson.com>2023-08-01 20:36:04 -0700
commit1ebf6a6467167ae9ec0db0c069cfe6170dbcc18f (patch)
tree6b9adb4cd20c8e4b0db7da620bcf6dfa55642666
parent88bbd745f7ce7c3b0a4e91777ba1b34e22821c34 (diff)
started calculus, fixed error in colorspace for phplatex
-rw-r--r--src/phplatex.php2
-rw-r--r--src/style.php7
-rw-r--r--src/writing/derivative.php25
3 files changed, 29 insertions, 5 deletions
diff --git a/src/phplatex.php b/src/phplatex.php
index 6557ff0..4d2c60b 100644
--- a/src/phplatex.php
+++ b/src/phplatex.php
@@ -119,7 +119,7 @@ function texify($string,$dpi='90',$fore="",$back="",$extraprelude="",$trans=FALS
if ($trans) {
$convert_cmd .= ' -transparent-color "#'.$back.'" -transparent "#'.$back.'"';
}
- $convert_cmd .= ' -colorspace RGB -density '.$dpi.' -trim +page '.$tfn.'.ps '.$tfn.'.'.$imgfmt;
+ $convert_cmd .= ' -colorspace sRGB -density '.$dpi.' -trim +page '.$tfn.'.ps '.$tfn.'.'.$imgfmt;
exec($convert_cmd);
#Note: +page OR -page +0+0 OR +repage moves the image to the cropped area (kills offset)
diff --git a/src/style.php b/src/style.php
index b55bb90..52fd66a 100644
--- a/src/style.php
+++ b/src/style.php
@@ -39,7 +39,7 @@ p {
font-family: 'Quicksand', sans-serif;
font-size: 16pt;
color: var(--text);
- padding: 8px 50px 8px 50px;
+ margin: 8px 75px 8px 75px;
}
h1 {
@@ -94,7 +94,6 @@ ul p {
font-family: 'Quicksand', sans-serif;
font-size: 16pt;
color: var(--text);
- padding: 8px 50px 8px 50px;
}
a {
@@ -134,3 +133,7 @@ hr {
.ascii {
color: var(--secondary);
}
+.center {
+ text-align: center;
+ margin: 14px 40px 14px 40px;
+}
diff --git a/src/writing/derivative.php b/src/writing/derivative.php
index a7a369a..17f2e7f 100644
--- a/src/writing/derivative.php
+++ b/src/writing/derivative.php
@@ -3,7 +3,11 @@ $title = "The Calculus of Infinitesimals";
require($_SERVER["DOCUMENT_ROOT"] . "/head.php");
require($_SERVER["DOCUMENT_ROOT"] . "/header.php");
include($_SERVER["DOCUMENT_ROOT"] . "/phplatex.php");
-include($_SERVER["DOCUMENT_ROOT"] . "/vars.php");
+require($_SERVER["DOCUMENT_ROOT"] . "/vars.php");
+function tex($latex) {
+ global $c_fg, $c_bg;
+ return texify($latex, 130, $c_fg, $c_bg, "", FALSE);
+}
?>
<p>
<i>Calculus</i> is often used as the complete name of a branch of mathematics dealing with
@@ -12,6 +16,23 @@ include($_SERVER["DOCUMENT_ROOT"] . "/vars.php");
has come to be known in this way is a testament to its importance.
</p>
<p>
- Cube root of two: <?php echo(texify("$\\sqrt[3]{2}\$", 160, $c_fg, $c_bg, "", TRUE)); ?>
+ To understand calculus, it is critical to understand the derivative. Let us begin with
+ the definition of a function.
+</p>
+<p class="center"><?php echo(tex("\$y=f(x)\$")); ?></p>
+<p>
+ This expression defines a relation between two quantities <i>x</i> and <i>y</i>. It can be said that
+ y is given <i>in terms of</i> x. Specifically, we have defined a function <i>f</i> that provides
+ a mapping for values of x. The actual mapping of a given function varies; what follows is
+ one example.
+</p>
+<p class="center"><?php echo(tex("\$f(x)=ax\$")); ?></p>
+<p>
+ Here, the value of the function is said to be equal to the product of its argument, and
+ a constant <i>a</i>. Take note of the fact that this is a constant multiple, as it means that
+ the function is said to be linear--an important property. Evidently,
+ <?php echo(tex("\$y=f(x)=ax\\Rightarrow y=ax\$")); ?> by the transitive property.
+ Here, the relation between y and x becomes clear; y is greater than x by a multiple a.
+ Observe the pattern that forms when evaluating f at various x.
</p>
<?php require($_SERVER["DOCUMENT_ROOT"] . "/footer.php"); ?>