https://ironegg.com.cn/research/ResearchesHugoBlox Kit (https://hugoblox.com)en-ushttps://ironegg.com.cn/media/icon_hu_29d01506278977f5.pnghttps://ironegg.com.cn/research/https://ironegg.com.cn/research/research1/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/research/research1/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Linear approximation"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 003 · <time datetime="2026-10-07">2026-10-07</time> · Notes </span> <h3 class="ie-document__title">Linear approximation</h3> <p class="ie-document__description">Tangent-line estimates and worked examples.</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/research/research1/linear-approximation.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Linear approximation">Read PDF</a> </div> </article> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="The product rule"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 002 · <time datetime="2026-10-06">2026-10-06</time> · Notes </span> <h3 class="ie-document__title">The product rule</h3> <p class="ie-document__description">A derivation and a worked example.</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/research/research1/product-rule.pdf" target="_blank" rel="noopener" aria-label="Read PDF: The product rule">Read PDF</a> </div> </article> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="The chain rule"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 001 · <time datetime="2026-10-05">2026-10-05</time> · Notes </span> <h3 class="ie-document__title">The chain rule</h3> <p class="ie-document__description">The rule, its reasoning, and worked examples.</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/research/research1/chain-rule.pdf" target="_blank" rel="noopener" aria-label="Read PDF: The chain rule">Read PDF</a> </div> </article>