教材导言所指的基础微分与积分学。身份已核对；这些出处只是学科提及，不冒充形式定义。当前定义记录缺失。
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Nakahara · second-edition-local · PDF 第86页
In the present chapter we introduce elementary concepts in the theory of maps, vector spaces and topology. A modest knowledge of undergraduate mathematics, such as set theory, calculus, complex analysis and linear algebra is assumed.教材导言所指的基础微分与积分学。身份已核对；这些出处只是学科提及，不冒充形式定义。当前定义记录缺失。
Szekeres · source-snapshot-bc3404156f6e · §1
The object of mathematical physics is to describe the physical world in purely mathematical terms. Although it had its origins in the science of ancient Greece, with the work of Archimedes, Euclid and Aristotle, it was not until the discoveries of Galileo and Newton that mathematical physics as we know it today had its true beginnings. Newton’s discovery of the calculus and its application to physics was undoubtedly the defining moment. This was built upon by generations of brilliant mathematicians such as Euler, Lagrange, Hamilton and Gauss, who essentially formulated physical law in terms of differential equations. With the advent of new and unintuitive theories such as relativity and quantum mechanics in the twentieth century, the reliance on mathematics moved to increasingly recondite areas such as abstract algebra, topology, functional analysis and differential geometry. Even classical areas such as the mechanics of Lagrange and Hamilton, as well as classical thermodynamics, can be lifted almost directly into the language of modern differential geometry. Today, the emphasis is often more structural than analytical, and it is commonly believed that finding the right mathematical structure is the most important aspect of any physical theory. Analysis, or the consequences of theories, still has a part to play in mathematical physics – indeed, most research is of this nature – but it is possibly less fundamental in the total overview of the subject.教材导言所指的基础微分与积分学。身份已核对；这些出处只是学科提及，不冒充形式定义。当前定义记录缺失。
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Nakahara · second-edition-local
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§5.2 · zh-CN · machine_draft · unreviewed
正文请在原位置阅读；长段落、数学边界或未定位引用不截断嵌入，精确范围与指纹保存在结构化索引。