| Course Content || || |
- The real number system and finite dimensional Euclidean space: axiomatic introduction of the real numbers, the Euclidean space RN, functions, 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.
| Textbooks || || None required, but the following are recommended.
I will follow my TeXed lecture notes, which I plan to slightly revise as the term progresses.
- 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.