Math 442: Honors Real Analysis II

Course Information

Professor: Kiril Datchev
Lectures: Tuesdays and Thursdays, 1:30 to 2:45, in SCHM 309.
Office hours: After class, Wednesdays 1-3 in MATH 602, or by appointment.

Textbooks: We will draw material from Introduction to Analysis in Several Variables, by Michael E. Taylor, also available as a preprint, and from Multivariable Mathematics, by Theodore Shifrin.

The topics we will cover include differentiation and integration of functions on Euclidean space, including an introduction to differential forms and manifolds, with examples from differential equations, geometry, and physics.

Grading will be based on
  • Almost weekly homework assignments, worth 35% of the total grade,
  • an in-class midterm exam, worth 25% of the total grade,
  • a final exam, as scheduled here, worth 40% of the total grade.

  • Homework

    Homework is due on paper in class on Thursdays. Here are the assignments:

    Homework 1, due January 18th.
    Homework 2, due January 25th.
    Homework 3, due February 1st.
    Homework 4, due February 8th.
    Homework 5, due February 15th. See also these notes on geodesics.
    Review problems for the midterm on February 27th.
    Homework 6, due March 7th, will be posted later.

    Additional Reading

    How much detail?

    The two classic introductions to multivariable analysis and differential forms are Calculus on Manifolds, by Michael Spivak and Analysis on Manifolds, by James R. Munkres. The former is concise and all business while the latter covers the material in more detail and depth.

    Finally, a list of general policies and procedures can be found here.