Real Variables I
Prerequisites: Either
(a) a score of 68% or higher in MATH 226 or
(b) one of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263 and a score
of 80% or higher in MATH 220.
Instructor
Joel Feldman
Email 
feldman@math.ubc.ca 
Office  Math 221 
Phone  6048225660 
Home page  http://www.math.ubc.ca/~feldman/ 
Office hours 
Monday 10:0011:00, Tuesday 10:0011:00, Thursday 11:0012:00

Location of lectures  BUCH A104 
Time of lectures  Monday, Wednesday, Friday 9:009:50 
Text

Walter Rudin, Principles of Mathematical Analysis, third edition.
I will post all handouts, problem sets, etc. on the web
here.
Other References
Topics

Number Systems
(§1):
ordered fields
rational, real and complex numbers
Archimedian property
supremum, infimum, completeness

Sequences and Series of Real Numbers
(§3):
limits of sequences, algebra of limits
BolzanoWeierstrass Theorem
Cauchy sequences, liminf, limsup
limits of series, convergence tests, absolute and conditional convergence
power series

Metric Spaces (§2):
metric spaces
convergence, completeness, completion
open sets, closed sets, compact sets, Heine Borel Theorem
connected sets

Continuity (§4):
functions, cardinality
continuity
continuity and compactness, existence of
minimizers and maximizers, uniform continuity
continuity and connectedness, Intermediate Value Theorem
monotone functions and discontinuities

Differentiation (§5):
differentiation
Mean Value Theorem
L'Hôpital's Rule
Taylor's Theorem
Grading

There will be two midterms (on Wednesday, October 1 and Wednesday, November 5),
each accounting for about 20% of the final mark.

There will be weekly problem sets accounting for about 10% of the final mark.

The final exam will account for about 50% of the final mark.

Grades will probably be scaled.
Policies

The midterm and final examination will be strictly
closed book: no formula sheets or calculators will be allowed.

Late homework assignments receive a grade of 0.

Missing a homework or midterm normally results in a mark of 0.
Exceptions may be granted in two cases: prior consent of the instructor
or a medical emergency. In the latter case, the instructor must be
notified within 48 hours of the missed test, and presented with a doctor's
note immediately upon the student's return to UBC. When an exception is
granted for a missed midterm, there is no makeup midterm, and
the final exam mark will be used instead.