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index.html
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<!doctype html>
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<html>
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| 1 |
<!doctype html>
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<html lang="en">
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<head>
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<meta charset="utf-8" />
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<meta name="viewport" content="width=device-width,initial-scale=1" />
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<title>Calculus Portfolio — Introduction to Calculus</title>
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<!-- Google Font (single external resource) -->
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<link href="https://fonts.googleapis.com/css2?family=Inter:wght@300;400;600;800&display=swap" rel="stylesheet">
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<style>
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:root{
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--bg:#0f1724;
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--card:#0b1020;
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--muted:#9aa7bf;
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--accent:#7dd3fc;
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--accent-2:#60a5fa;
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--glass: rgba(255,255,255,0.04);
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--success:#34d399;
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--danger:#fb7185;
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--radius:16px;
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font-family: "Inter", system-ui, -apple-system, "Segoe UI", Roboto, "Helvetica Neue", Arial;
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}
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*{box-sizing:border-box}
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html,body{height:100%}
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body{
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margin:0;
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background: linear-gradient(180deg, #071028 0%, #071a2e 65%);
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color:#e6eef8;
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-webkit-font-smoothing:antialiased;
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-moz-osx-font-smoothing:grayscale;
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padding:32px;
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}
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.wrap{
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max-width:1100px;
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margin:0 auto;
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display:grid;
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grid-template-columns: 380px 1fr;
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gap:28px;
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}
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/* SIDEBAR */
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aside{
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background:linear-gradient(180deg, rgba(255,255,255,0.03), rgba(255,255,255,0.02));
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border-radius:var(--radius);
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padding:22px;
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box-shadow: 0 6px 30px rgba(2,6,23,0.6), inset 0 1px 0 rgba(255,255,255,0.02);
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min-height:520px;
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position:sticky;
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top:32px;
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overflow:hidden;
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}
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.logo{
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display:flex;
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gap:14px;
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align-items:center;
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margin-bottom:12px;
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}
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.logo .mark{
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width:62px;
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height:62px;
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border-radius:12px;
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background:linear-gradient(135deg,var(--accent),var(--accent-2));
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display:flex;
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align-items:center;
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justify-content:center;
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font-weight:800;
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color:#04263b;
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font-size:20px;
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| 73 |
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box-shadow: 0 8px 20px rgba(96,165,250,0.14);
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}
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.logo h1{
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font-size:16px;
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| 77 |
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margin:0;
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line-height:1;
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letter-spacing:0.2px;
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}
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| 81 |
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.logo p{margin:0;margin-top:4px;color:var(--muted);font-size:13px}
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| 82 |
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.meta{
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display:flex;
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| 85 |
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gap:12px;
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| 86 |
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flex-wrap:wrap;
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| 87 |
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margin:18px 0 12px;
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| 88 |
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}
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| 89 |
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.chip{
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background:var(--glass);
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| 91 |
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padding:8px 10px;
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| 92 |
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border-radius:10px;
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| 93 |
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font-size:13px;
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| 94 |
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color:var(--muted);
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| 95 |
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box-shadow: 0 3px 10px rgba(2,6,23,0.45);
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}
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| 97 |
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| 98 |
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.summary{
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color:var(--muted);
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| 100 |
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font-size:14px;
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| 101 |
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line-height:1.55;
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| 102 |
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margin-bottom:14px;
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| 103 |
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}
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| 104 |
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| 105 |
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.objectives{
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margin-top:12px;
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| 107 |
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}
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| 108 |
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.objectives h3{font-size:13px;margin:0 0 8px;color:var(--accent)}
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| 109 |
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.objectives ul{margin:0;padding-left:18px;color:var(--muted);line-height:1.6;font-size:14px}
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| 110 |
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| 111 |
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/* MAIN */
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| 112 |
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main{
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| 113 |
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background: linear-gradient(180deg, rgba(255,255,255,0.02), rgba(255,255,255,0.01));
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| 114 |
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border-radius:var(--radius);
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| 115 |
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padding:26px;
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| 116 |
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min-height:520px;
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| 117 |
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box-shadow: 0 6px 40px rgba(2,6,23,0.6);
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| 118 |
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}
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| 119 |
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header.port{
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display:flex;
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align-items:center;
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| 123 |
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justify-content:space-between;
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| 124 |
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gap:12px;
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| 125 |
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margin-bottom:20px;
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| 126 |
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}
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| 127 |
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.title{
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| 128 |
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display:flex;
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| 129 |
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gap:16px;
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| 130 |
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align-items:center;
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| 131 |
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}
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| 132 |
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.title h2{
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margin:0;font-size:20px;
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}
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.title p{margin:0;color:var(--muted);font-size:13px}
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| 136 |
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.badge{
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| 138 |
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background:linear-gradient(90deg,var(--accent-2),var(--accent));
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| 139 |
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color:#04263b;
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| 140 |
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padding:10px 14px;
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| 141 |
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border-radius:12px;
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| 142 |
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font-weight:700;
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| 143 |
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box-shadow: 0 8px 30px rgba(96,165,250,0.08);
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| 144 |
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}
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| 145 |
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| 146 |
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/* Sections */
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| 147 |
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section.block{
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margin-bottom:20px;
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border-radius:6px;
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+
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}
|
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/* tiny legend dots */
|
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|
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|
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|
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|
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|
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</head>
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+
<body>
|
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+
<div class="wrap" role="main">
|
| 248 |
+
<!-- SIDEBAR -->
|
| 249 |
+
<aside aria-label="Course overview">
|
| 250 |
+
<div class="logo" role="banner">
|
| 251 |
+
<div class="mark">∫d</div>
|
| 252 |
+
<div>
|
| 253 |
+
<h1>Calculus Portfolio</h1>
|
| 254 |
+
<p>Introduction to Calculus — Differential & Integral</p>
|
| 255 |
+
</div>
|
| 256 |
+
</div>
|
| 257 |
+
|
| 258 |
+
<div class="sparkle" aria-hidden="true"></div>
|
| 259 |
+
|
| 260 |
+
<div class="meta" aria-hidden="true">
|
| 261 |
+
<div class="chip">Level: Introductory</div>
|
| 262 |
+
<div class="chip">Duration: 10–12 weeks</div>
|
| 263 |
+
<div class="chip">Format: Theory + Demo</div>
|
| 264 |
+
</div>
|
| 265 |
+
|
| 266 |
+
<p class="summary">
|
| 267 |
+
Calculus studies continuous change. This portfolio summarizes the course objectives, outline, key concepts (limits, derivatives, integrals), and includes a tiny interactive demo illustrating how a secant slope approaches a derivative (tangent slope).
|
| 268 |
+
</p>
|
| 269 |
+
|
| 270 |
+
<div class="objectives" aria-labelledby="obj">
|
| 271 |
+
<h3 id="obj">Course Objectives</h3>
|
| 272 |
+
<ul>
|
| 273 |
+
<li>Understand limits, derivatives & integrals</li>
|
| 274 |
+
<li>Apply techniques to physics, engineering & economics</li>
|
| 275 |
+
<li>Analyze & model real-world functions</li>
|
| 276 |
+
<li>Use derivatives to find maxima/minima</li>
|
| 277 |
+
</ul>
|
| 278 |
+
</div>
|
| 279 |
+
|
| 280 |
+
<div style="margin-top:14px">
|
| 281 |
+
<button class="cta" id="downloadBtn" title="Save as PDF (print)">
|
| 282 |
+
📄 Save / Print
|
| 283 |
+
</button>
|
| 284 |
+
</div>
|
| 285 |
+
|
| 286 |
+
<div style="margin-top:18px">
|
| 287 |
+
<small style="color:var(--muted)">Author: Calculus Instructor • Prepared as a student portfolio</small>
|
| 288 |
+
</div>
|
| 289 |
+
</aside>
|
| 290 |
+
|
| 291 |
+
<!-- MAIN -->
|
| 292 |
+
<main>
|
| 293 |
+
<header class="port">
|
| 294 |
+
<div class="title">
|
| 295 |
+
<div>
|
| 296 |
+
<h2>Introduction to Calculus</h2>
|
| 297 |
+
<p>Understanding differential & integral calculus — core ideas, examples, and applications.</p>
|
| 298 |
+
</div>
|
| 299 |
+
</div>
|
| 300 |
+
|
| 301 |
+
<div class="badge">Essentials</div>
|
| 302 |
+
</header>
|
| 303 |
+
|
| 304 |
+
<!-- Course Outline -->
|
| 305 |
+
<section class="block" aria-labelledby="outlineTitle">
|
| 306 |
+
<h3 id="outlineTitle">Course Outline</h3>
|
| 307 |
+
<div class="outline-grid" role="list">
|
| 308 |
+
<div class="outline-item" role="listitem">
|
| 309 |
+
<strong>Differential Calculus</strong>
|
| 310 |
+
Limits • Derivatives • Applications (tangent lines, rates, optimization)
|
| 311 |
+
</div>
|
| 312 |
+
<div class="outline-item" role="listitem">
|
| 313 |
+
<strong>Integral Calculus</strong>
|
| 314 |
+
Indefinite/Definite Integrals • Techniques • Area & accumulation problems
|
| 315 |
+
</div>
|
| 316 |
+
<div class="outline-item" role="listitem">
|
| 317 |
+
<strong>Foundations</strong>
|
| 318 |
+
Limits, continuity, algebra of functions
|
| 319 |
+
</div>
|
| 320 |
+
<div class="outline-item" role="listitem">
|
| 321 |
+
<strong>Applications</strong>
|
| 322 |
+
Physics (velocity/acceleration), engineering, economics & area computations
|
| 323 |
+
</div>
|
| 324 |
+
</div>
|
| 325 |
+
</section>
|
| 326 |
+
|
| 327 |
+
<!-- Definitions and Concepts -->
|
| 328 |
+
<section class="block" aria-labelledby="defs">
|
| 329 |
+
<h3 id="defs">What is Calculus?</h3>
|
| 330 |
+
<p>
|
| 331 |
+
Calculus is the study of continuous change. Historically developed by Newton and Leibniz, it focuses on two complementary ideas:
|
| 332 |
+
</p>
|
| 333 |
+
|
| 334 |
+
<div class="accordion" id="accordion">
|
| 335 |
+
<div class="acco-item">
|
| 336 |
+
<button class="acco-head" data-target="a1"><h4>Differential Calculus</h4><span>▸</span></button>
|
| 337 |
+
<div class="acco-body" id="a1">
|
| 338 |
+
Differential calculus studies rates of change (derivatives). The derivative f'(x) = dy/dx measures how the function y = f(x) changes as x changes. It arises from the limit of a quotient: the slope of the secant line approaches the slope of the tangent line.
|
| 339 |
+
</div>
|
| 340 |
+
</div>
|
| 341 |
+
|
| 342 |
+
<div class="acco-item">
|
| 343 |
+
<button class="acco-head" data-target="a2"><h4>Integral Calculus</h4><span>▸</span></button>
|
| 344 |
+
<div class="acco-body" id="a2">
|
| 345 |
+
Integral calculus reverses differentiation: integration accumulates small pieces to get a whole. Indefinite integrals include an arbitrary constant (C); definite integrals compute accumulated values like area under a curve.
|
| 346 |
+
</div>
|
| 347 |
+
</div>
|
| 348 |
+
|
| 349 |
+
<div class="acco-item">
|
| 350 |
+
<button class="acco-head" data-target="a3"><h4>Limits & Continuity</h4><span>▸</span></button>
|
| 351 |
+
<div class="acco-body" id="a3">
|
| 352 |
+
Limits describe the behavior of a function as the input approaches a certain value. Continuity means the limit equals the function value. Limits are the foundation on which both derivatives and integrals are built.
|
| 353 |
+
</div>
|
| 354 |
+
</div>
|
| 355 |
+
</div>
|
| 356 |
+
</section>
|
| 357 |
+
|
| 358 |
+
<!-- Interactive mini-demo -->
|
| 359 |
+
<section class="block" aria-labelledby="demoTitle">
|
| 360 |
+
<h3 id="demoTitle">Interactive Demo — Secant → Tangent (Derivative)</h3>
|
| 361 |
+
<p style="margin-bottom:12px;color:var(--muted)">Use the slider to move the second point (h). The slope of the secant line approaches the tangent slope as h → 0 for f(x) = x² at x = 1.</p>
|
| 362 |
+
|
| 363 |
+
<div class="demo" role="application" aria-label="Derivative demo">
|
| 364 |
+
<div class="graph" id="svgWrap" aria-hidden="false">
|
| 365 |
+
<!-- SVG will be injected by JS -->
|
| 366 |
+
<svg id="calcSVG" width="100%" height="260" viewBox="0 0 600 260" preserveAspectRatio="xMinYMin meet" aria-label="Graph area" role="img"></svg>
|
| 367 |
+
</div>
|
| 368 |
+
|
| 369 |
+
<div class="controls" aria-hidden="false">
|
| 370 |
+
<label for="hRange">h (distance between points): <span id="hVal">0.8</span></label>
|
| 371 |
+
<input id="hRange" type="range" min="0.01" max="2" step="0.01" value="0.8" />
|
| 372 |
+
<div style="margin-top:12px">
|
| 373 |
+
<label for="xInput">Point x (evaluation point):</label>
|
| 374 |
+
<input id="xInput" type="number" value="1" step="0.1" style="width:100%;padding:8px;border-radius:8px;border:1px solid rgba(255,255,255,0.04);background:transparent;color:#e6eef8" />
|
| 375 |
+
</div>
|
| 376 |
+
|
| 377 |
+
<div class="val" style="margin-top:12px">
|
| 378 |
+
Secant slope: <strong id="secSlope">2.6</strong>
|
| 379 |
+
</div>
|
| 380 |
+
<div class="val" style="margin-top:6px">
|
| 381 |
+
Tangent (derivative) at x: <strong id="tanSlope">2</strong>
|
| 382 |
+
</div>
|
| 383 |
+
|
| 384 |
+
<div style="height:10px"></div>
|
| 385 |
+
|
| 386 |
+
<div class="legend" style="margin-top:10px">
|
| 387 |
+
<div class="dot sec" aria-hidden="true"></div><span>Secant</span>
|
| 388 |
+
<div style="width:8px"></div>
|
| 389 |
+
<div class="dot tan" aria-hidden="true"></div><span>Tangent</span>
|
| 390 |
+
</div>
|
| 391 |
+
</div>
|
| 392 |
+
</div>
|
| 393 |
+
|
| 394 |
+
<footer class="note">
|
| 395 |
+
<span>Formula shown uses f(x)=x². Derivative f'(x)=2x (so at x=1, tangent slope = 2).</span>
|
| 396 |
+
<span style="opacity:0.9">Try h → 0 to see secant slope approach 2.</span>
|
| 397 |
+
</footer>
|
| 398 |
+
</section>
|
| 399 |
+
|
| 400 |
+
<!-- More content -->
|
| 401 |
+
<section class="block" aria-labelledby="addTitle">
|
| 402 |
+
<h3 id="addTitle">Key Formulas & Notes</h3>
|
| 403 |
+
<p style="margin-bottom:8px;color:var(--muted)">
|
| 404 |
+
<strong>Derivative:</strong> f'(x) = limₕ→0 (f(x+h) - f(x))/h<br>
|
| 405 |
+
<strong>Indefinite Integral:</strong> ∫ f(x) dx = F(x) + C<br>
|
| 406 |
+
<strong>Definite Integral:</strong> ∫ₐᵇ f(x) dx = F(b) - F(a)
|
| 407 |
+
</p>
|
| 408 |
+
|
| 409 |
+
<div style="display:flex;gap:12px;flex-wrap:wrap;margin-top:8px">
|
| 410 |
+
<div class="chip">Applications: Motion, Area, Optimization</div>
|
| 411 |
+
<div class="chip">Tools: Analytical techniques, substitution, parts</div>
|
| 412 |
+
<div class="chip">Prereqs: Functions, algebra, exponents</div>
|
| 413 |
+
</div>
|
| 414 |
+
</section>
|
| 415 |
+
|
| 416 |
+
<!-- Closing -->
|
| 417 |
+
<section style="display:flex;justify-content:space-between;align-items:center;margin-top:8px">
|
| 418 |
+
<small style="color:var(--muted)">Prepared as a student portfolio • Clean, shareable, printable</small>
|
| 419 |
+
<div>
|
| 420 |
+
<button class="cta" id="toggleTheme">🌙 Toggle Theme</button>
|
| 421 |
+
</div>
|
| 422 |
+
</section>
|
| 423 |
+
</main>
|
| 424 |
+
</div>
|
| 425 |
+
|
| 426 |
+
<script>
|
| 427 |
+
/* ---------- Accordion ---------- */
|
| 428 |
+
document.querySelectorAll('.acco-head').forEach(btn=>{
|
| 429 |
+
btn.addEventListener('click', ()=>{
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| 430 |
+
const target = btn.getAttribute('data-target');
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| 431 |
+
const body = document.getElementById(target);
|
| 432 |
+
const open = body.style.display === 'block';
|
| 433 |
+
// close all
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| 434 |
+
document.querySelectorAll('.acco-body').forEach(b=>b.style.display='none');
|
| 435 |
+
// rotate arrows
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| 436 |
+
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| 437 |
+
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| 438 |
+
body.style.display='block';
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| 444 |
+
// default open first
|
| 445 |
+
document.querySelector('.acco-head')?.click();
|
| 446 |
+
|
| 447 |
+
/* ---------- Print / Download ---------- */
|
| 448 |
+
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| 449 |
+
window.print();
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| 450 |
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+
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|
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| 469 |
+
/* ---------- Interactive derivative demo (f(x)=x^2) ---------- */
|
| 470 |
+
(function(){
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| 471 |
+
const svg = document.getElementById('calcSVG');
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+
const w = 600, h = 260;
|
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+
svg.setAttribute('viewBox','0 0 '+w+' '+h);
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| 474 |
+
|
| 475 |
+
// coordinate mapping (x from -1 to 3, y from -1 to 9)
|
| 476 |
+
const xMin = -1, xMax = 3, yMin = -1, yMax = 9;
|
| 477 |
+
const mapX = x => ( (x - xMin) / (xMax - xMin) ) * (w-60) + 40;
|
| 478 |
+
const mapY = y => h - ( (y - yMin) / (yMax - yMin) ) * (h-40) - 20;
|
| 479 |
+
|
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+
// draw axes + grid
|
| 481 |
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+
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|
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// grid lines
|
| 486 |
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line.setAttribute('x1',xPos); line.setAttribute('x2',xPos);
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|
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| 497 |
+
txt.setAttribute('y', h-6);
|
| 498 |
+
txt.setAttribute('fill','rgba(230,238,248,0.45)');
|
| 499 |
+
txt.setAttribute('font-size','10');
|
| 500 |
+
txt.setAttribute('text-anchor','middle');
|
| 501 |
+
txt.textContent = gx;
|
| 502 |
+
svg.appendChild(txt);
|
| 503 |
+
}
|
| 504 |
+
|
| 505 |
+
for(let gy = 0; gy<=8; gy+=1){
|
| 506 |
+
const yPos = mapY(gy);
|
| 507 |
+
const line = document.createElementNS(ns,'line');
|
| 508 |
+
line.setAttribute('y1',yPos); line.setAttribute('y2',yPos);
|
| 509 |
+
line.setAttribute('x1',40); line.setAttribute('x2',w-20);
|
| 510 |
+
line.setAttribute('stroke','rgba(255,255,255,0.02)');
|
| 511 |
+
line.setAttribute('stroke-width','1');
|
| 512 |
+
svg.appendChild(line);
|
| 513 |
+
}
|
| 514 |
+
|
| 515 |
+
// axes
|
| 516 |
+
const axisX = document.createElementNS(ns,'line');
|
| 517 |
+
axisX.setAttribute('x1',mapX(xMin)); axisX.setAttribute('x2',mapX(xMax));
|
| 518 |
+
axisX.setAttribute('y1', mapY(0)); axisX.setAttribute('y2', mapY(0));
|
| 519 |
+
axisX.setAttribute('stroke','rgba(230,238,248,0.12)');
|
| 520 |
+
axisX.setAttribute('stroke-width','1.5');
|
| 521 |
+
svg.appendChild(axisX);
|
| 522 |
+
|
| 523 |
+
const axisY = document.createElementNS(ns,'line');
|
| 524 |
+
axisY.setAttribute('x1',mapX(0)); axisY.setAttribute('x2',mapX(0));
|
| 525 |
+
axisY.setAttribute('y1', mapY(yMin)); axisY.setAttribute('y2', mapY(yMax));
|
| 526 |
+
axisY.setAttribute('stroke','rgba(230,238,248,0.12)');
|
| 527 |
+
axisY.setAttribute('stroke-width','1.5');
|
| 528 |
+
svg.appendChild(axisY);
|
| 529 |
+
}
|
| 530 |
+
|
| 531 |
+
function plotFunction(){
|
| 532 |
+
const ns = 'http://www.w3.org/2000/svg';
|
| 533 |
+
const path = document.createElementNS(ns,'path');
|
| 534 |
+
let d = '';
|
| 535 |
+
const steps = 200;
|
| 536 |
+
for(let i=0;i<=steps;i++){
|
| 537 |
+
const t = i/steps;
|
| 538 |
+
const x = xMin + t*(xMax - xMin);
|
| 539 |
+
const y = x*x; // f(x)=x^2
|
| 540 |
+
const px = mapX(x), py = mapY(y);
|
| 541 |
+
d += (i===0? 'M':'L') + px + ' ' + py + ' ';
|
| 542 |
+
}
|
| 543 |
+
path.setAttribute('d', d);
|
| 544 |
+
path.setAttribute('stroke','rgba(125,211,252,0.95)');
|
| 545 |
+
path.setAttribute('stroke-width','2.2');
|
| 546 |
+
path.setAttribute('fill','none');
|
| 547 |
+
svg.appendChild(path);
|
| 548 |
+
}
|
| 549 |
+
|
| 550 |
+
function drawPoints(x, h){
|
| 551 |
+
const ns = 'http://www.w3.org/2000/svg';
|
| 552 |
+
const x1 = x;
|
| 553 |
+
const x2 = x + h;
|
| 554 |
+
const y1 = x1*x1;
|
| 555 |
+
const y2 = x2*x2;
|
| 556 |
+
|
| 557 |
+
const p1x = mapX(x1), p1y = mapY(y1);
|
| 558 |
+
const p2x = mapX(x2), p2y = mapY(y2);
|
| 559 |
+
|
| 560 |
+
// points
|
| 561 |
+
const c1 = document.createElementNS(ns,'circle');
|
| 562 |
+
c1.setAttribute('cx',p1x); c1.setAttribute('cy',p1y); c1.setAttribute.
|