Advanced Calculus II

This site is based on a class at of Math 410 (Advanced Calculus II) at Texas A&M University. The materials are publically available for non-commercial use. In particular, they are not to be shared on for profit sites such as 'Course Hero'.

The lecture materials shared here are not at the carefully edited and revised level of a textbook and should not be viewed as such. I am grateful to anyone who points out errors of a typographical or mathematical nature. Recommended textbooks for this class include

  • B. S. Thomson, A. M. Bruckner, and J. B. Bruckner: Elementary Real Analysis

  • Vladimir Zorich: Mathematical Analysis I and II

Other popular books which can be used, but are probably a little less compatible with our approach are William Wade, 'An Introduction to Analysis' and Charles Pugh, 'Real Mathematical Analysis'. Other standard textbooks covering similar material are for example Michael Spivak's 'Calculus on Manifolds', Serge Lang's 'Undergraduate Analysis' and Walter Rudin's 'Principles of Mathematical Analysis', but these books are probably more theory heavy than this course. Note that the same authors have written books with similar sounding titles, which go much deeper into the matter and which are not recommended for a first introduction to the material.

Lecture notes

Homework: 1 2 3 4 5 6 7 8 9 10

Mock exams: First mideterm, second midterm, final