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.

  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 ({\mathbb R}^n). 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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