Math 4001-5001 Analysis II

Semester 1, 2021-2022

Course Lecturer:

Dr. Judith Packer, Dept. of Mathematics

Tel: (303) 492-6979
Office: Math 227

Course Syllabus: For course syllabus, click here! This syllabus contains all university rules and regulations. Please abide by the University Mask mandate in lectures.

Course Information:
This course is meant to continue to familiarize the student with the theory of functions of one or more real variables, with an initial emphasis on sequences and series of functions and different types of convergence, and with a continuation into the theory of vector-valued functions of vector variables, including the inverse function theorem and the implicit function theorem. Topics to be covered include: a rigorous treatment of infinite series of real numbers, sequences and series of functions, convergence and uniform convergence of sequences and series of functions, Taylor's Theorem, a brief review of vector spaces, in particular, n-dimensional Euclidean space; differentiation, including the definition of the total derivative and the chain rule; the mean value theorem, the inverse mapping theorem, and the implicit function theorem.

Math 3001 Analysis 1 and Math 2130 Linear Algebra (or Math 2135).

Course Text:
We will use the text "Undergraduate Analysis", by Serge Lang, Second Edition, Springer, 2005.

Assessment: Lecture Hours and Venue:
MWF 9:10 a.m.- 10:00 a.m. ECCR 118.

Office Hours:
10:30 a.m. - 11:30 a.m., by ZOOM or in Math 227 MWF, or by appointment on ZOOM.

Homework Assignments (subject to change):

Homework will be assigned weekly, and is due uploaded to Canvas at 11:59 p.m., usually on Fridays. Some, but not all of the problems will be graded. Show all your work.

Some famous mathematicians who worked in this area:
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Last modified August 23, 2021.