Mathematics 320

Real Variables I

Department of Mathematics University of British Columbia

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

 E-mail    feldman@math.ubc.ca 
 Office  Math 221
 Phone  604-822-5660
 Home page  http://www.math.ubc.ca/~feldman/
 Office hours   Monday 10:00-11:00, Tuesday 10:00-11:00, Thursday 11:00-12:00
 Location of lectures   GEOG 200
 Time of lectures   Monday, Wednesday, Friday 9:00-9:50

Text

I will post all handouts, problem sets, etc. on the web here.


Other References


Topics

  1. Number Systems (§1):
        ordered fields
        rational, real and complex numbers
        Archimedian property
        supremum, infimum, completeness
  2. Sequences and Series of Real Numbers (§3):
        limits of sequences, algebra of limits
        Bolzano-Weierstrass Theorem
        Cauchy sequences, liminf, limsup
        limits of series, convergence tests, absolute and conditional convergence
        power series
  3. Metric Spaces (§2):
        metric spaces
        convergence, completeness, completion
        open sets, closed sets, compact sets, Heine Borel Theorem
        connected sets
  4. 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
  5. Differentiation (§5):
        differentiation
        Mean Value Theorem
        L'Hôpital's Rule
        Taylor's Theorem

Grading


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