数学5102。2:分析多个变量的函数。(4小时)
仍在继续数学5101。在几个变量研究的基础分析。主题包括导数和偏导数;收缩原理;逆函数和隐函数定理;高阶导数;泰勒公式在几个变量;微分积分取决于参数;函数的几个变量的集成;改变变量的积分; differential forms and their integration over simplexes and chains; external multiplication of forms; differential of forms; Stokes’ formula; set functions; Lebesgue measure; measure spaces; measurable functions; integration; comparison with the Riemann integral; L2 as a Hilbert space; and Parseval theorem and Riesz-Fischer theorem. Requires permission of instructor and head advisor for undergraduate students.