MATH 5102: Analysis 2: Functions of Several Variables
Lecture - 4 credits
- Continues MATH 5101.
- Studies basics of analysis in several variables.
- Topics include derivative and partial derivatives; the contraction principle; the inverse function and implicit function theorems; derivatives of higher order; Taylor formula in several variables; differentiation of integrals depending on parameters; integration of functions of several variables; change of variables in integrals; 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.
Continues MATH 5101. Show more.