Math 4001-5001 Analysis II

Semester 1, 2016-2017

Course Lecturer:

Dr. Judith Packer, Dept. of Mathematics

Tel: (303) 492-6979
Office: Math 227
Email: packer@colorado.edu
URL: http://spot.colorado.edu/~packer


Course Syllabus: For course syllabus, complete with list of university policies, click here!

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. This includes most of Chapters 3, 7, 8 and 9 of the textbook.

Prerequisite:
Math 3001 Analysis 1 and Math 3130 Linear Algebra.

Course Text:
We will use the text "Principles of Mathematical Analysis", by Walter Rudin, Third Edition, MacGraw Hill.


Lecture Hours and Venue:
MWF, 3 - 3:50 p.m., ECCR 118.

Consultation Hours:
MWF 1-2 p.m., and by appointment.

Assessment: If you are absent from an exam, or do not hand in the take-home exam on time, without a valid excuse, you will receive a grade of "F" for that exam. Examples of valid excuse are: documented illness (doctor's letter required), religious observance, and serious family emergency.


Homework Assignments:



Homework:
Homework will be assigned weekly, and is due at the beginning of class, usually on Mondays. 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 September 13, 2016.