3 credits
Spring 2025 Lecture HonorsUpper Division
Real analysis in one and n-dimensional Euclidean spaces--continued from MA 44000. Topics include mappings of Euclidean spaces and their derivatives, multivariable chain rule, inverse function theorem and implicit function theorem, sets with content and integration in n dimensions, the integrability theorem, Jacobian and change of variables theorem, related topics.
Learning Outcomes1Determine points at which derivatives exist and compute linear approximations for mappings of Euclidean spaces.
2Perform rigorous applications of the multivariable chain rule, inverse function theorem and implicit function theorem in Euclidean spaces.
3Apply the integrability theorem on the existence of Riemann integrals of functions in bounded sets in Euclidean spaces.
4Perform rigorous applications of the change of variables theorem for integrals of functions on smooth transformations of domains in a Euclidean spaces.
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