【金-元】元好问

绿叶阴浓,遍池亭水阁,偏趁凉多。海榴初绽,朵朵簇红罗。乳燕雏莺弄语,有高柳鸣蝉相和。骤雨过,似琼珠乱撒,打遍新荷。

人生百年有几,念良辰美景,休放虚过。穷通前定,何用苦张罗。命友邀宾玩赏,对芳樽浅酌低歌。且酩酊,任他两轮日月,来往如梭。

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【金-元】元好问

重冈已隔红尘断,村落更年丰。移居要就,窗中远岫,舍后长松。 十年种木,一年种谷,都付儿童。老夫惟有,醒来明月,醉后清风。

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This post records the roadmap and resources for my physics learning, with the goal of understanding the conceptual structure of modern physics as a non-physicist.

For the mathematical background used in physics, please refer to my math learning roadmap.

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This note explains how infinitesimal changes transform under coordinate maps via the Jacobian matrix—from differential displacement to differential area and volume—in Cartesian, cylindrical, and spherical coordinates.

Note: Everything here is 3D and the cross product is used. In general dimensions, area/volume elements are best expressed using differential forms (wedge products); the 3D vector formulas here are a special case.

Sources:

  1. Fawwaz Ulaby. (2020). Chapter 3: Vector Analysis. Fundamentals of applied electromagnetics (8rd ed., pp. 130–163). Pearson.
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