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| MA 44200 - Honors Real Analysis II |
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Credit Hours: 3.00. 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.
3.000 Credit hours Syllabus Available Levels: Undergraduate, Graduate, Professional Schedule Types: Distance Learning, Lecture Offered By: College of Science Department: Mathematics Course Attributes: Honors, Upper Division May be offered at any of the following campuses: West Lafayette Learning Outcomes: 1. Determine points at which derivatives exist and compute linear approximations for mappings of Euclidean spaces. 2. Perform rigorous applications of the multivariable chain rule, inverse function theorem and implicit function theorem in Euclidean spaces. 3. Apply the integrability theorem on the existence of Riemann integrals of functions in bounded sets in Euclidean spaces. 4. Perform rigorous applications of the change of variables theorem for integrals of functions on smooth transformations of domains in a Euclidean spaces. Prerequisites: (Undergraduate level MA 26500 Minimum Grade of B- or Undergraduate level MA 35100 Minimum Grade of B-) and Undergraduate level MA 44000 Minimum Grade of C- |
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