MATH 217 - Honors Advanced Calculus, I
The real number system and finite dimensional Euclidean space
- axiomatic introduction of the real numbers
- the Euclidean space RN
- topology in RN
Limits and continuity
- limits of sequences
- limits of functions
- global properties of continuous functions
- uniform continuity
Differentiation in RN
- differentiation of real valued functions of a real variable
- partial derivatives
- vector fields
- total differentiability
- Taylor's theorem
- classification of stationary points
Integration in RN
- content in RN
- the Riemann integral in RN
- calculation of integrals
- Fubini's theorem
- integration in polar, spherical, and cylindrical coordinates
None required, but the following are recommended.
- Robert G. Bartle, The Elements of Real Analysis, Second Edition. Jossey-Bass, 1976.
- Patrick M. Fitzpatrick, Advanced Calculus. PWS Publishing Company, 1996.
- James S. Muldowney, Advanced Calculus Lecture Notes for Mathematics 217-317, I, Third Edition.
- William R. Wade, An Introduction to Analysis, Second Edition. Prentice Hall, 2000.
I will more or less follow my notes, but I plan to revise them thoroughly during the course and make the updated version also available online.
The grade will be based on (approximately) weekly homework assignments (30%), an in-class-midterm on October 20 (20%), and a final (50%).
Last update: 01/12/18.