414/514 – Advanced calculus aka Analysis I

Math 414/514: Advanced calculus.

Instructor: Andrés E. Caicedo.
Contact Information: See here.
Time: MTuWF 10:40-11:30 am.
Place: Mathematics/Geosciences building, Room 124.
Office Hours: MF 12:40-1:30 pm.
Text:

1. Pugh, Charles Chapman. Real mathematical analysis. Springer, 2002.
2. Spivak, Michael. Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus. Westview Press, 1971.

Contents: Math 414/514 is an introduction to Analysis on Euclidean spaces (). The emphasis is theoretical, as opposed to the more computational approach of calculus. From the Course Description on the Department’s site:

Introduction to fundamental elements of Analysis on Euclidean spaces including the basic differential and integral calculus. Topics include: Infinite series, sequences and series of function, uniform convergences, theory of integration, implicit function theorem and applications.

Grading: Based on homework. No late homework is allowed. Collaboration is encouraged, although you must turn in your own version of the solutions, and give credit to books/websites/… you consulted and people you talked/emailed/… to.

I do not want to have exams in this course. However, an important component of being proficient in mathematics is a certain amount of mental agility in recalling notions and basic arguments. I plan to assess these by requesting oral presentations of solutions to some of the homework problems throughout the term. If I find you lacking here, it will be necessary to have an exam or two. The final exam is currently scheduled for Wednesday December 14, 10:30 am – 12:30 pm.

I will use this website to post additional information, and encourage you to use the comments feature. If you leave a comment, please use your full name, which will simplify my life filtering spam out.

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