Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 127B: Real Analysis
Approved: 2015-11-06, John Hunter and Janko Gravner

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Stephen Abbott, Understanding Analysis, 2nd ed., Springer 2015. (Alternative: Kenneth Ross, Elementary Analysis, Springer, 2nd ed., Springer, 2013.)

Course Description:

Derivatives, integrals, sequences of functions, and power series.

Suggested Schedule:

Suggested number of lectures are indicated in parentheses.

  • (2) Derivatives. Algebraic properties.
  • (1) Chain rule.
  • (1) Extreme value theorem.
  • (2) Mean value theorem. Consequences.
  • (1) Sequences and series of functions.
  • (3) Pointwise and uniform convergence. Continuity of uniform limits.
  • (1) Power series. Radius of convergence.
  • (2) Definition of the Riemann integral.
  • (3) Properties of the Riemann integral.
  • (2) Fundamental theorem of calculus.
  • (1) Exchange of integral and limits.
  • (2) Taylor series. Integral form and Lagrange of the remainder.
  • (2) Integration and differentiation of power series.
  • (2) Improper integrals.
  • (1) Integral test for series.

Total: 26 lectures