MATH 217 - Honors Advanced Calculus, I
Instructor    Volker Runde
Office hours    by appointment
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.
  1. Robert G. Bartle, The Elements of Real Analysis, Second Edition. Jossey-Bass, 1976.
  2. Patrick M. Fitzpatrick, Advanced Calculus. PWS Publishing Company, 1996.
  3. James S. Muldowney, Advanced Calculus Lecture Notes for Mathematics 217-317, I, Third Edition.
  4. William R. Wade, An Introduction to Analysis, Second Edition. Prentice Hall, 2000.
I will follow my TeXed lecture notes, which I plan to slightly revise as the term progresses.
Grading    The grade will be based on (approximately) weekly homework assignments (30%), an in-class midterm on October 19 (20%), and a final (50%).
Course materials   
Course Syllabus
Assignment #1 Solutions #1
Assignment #2 Solutions #2
Assignment #3 Solutions #3
Assignment #4 Solutions #4
Last update: September 28, 2020