Mathematics 320, Section 101

Real Variables I

Department of Mathematics,  University of British Columbia

Prerequisites: Either (a) a score of 68% or higher in MATH 226 or (b) MATH 200 and a score of 80% or higher in MATH 220.

Instructor

Joel Feldman

Text

• Walter Rudin, Principles of Mathematical Analysis, third edition.

Other References

• Tom M. Apostol, Mathematical Analysis
• Robert G. Bartle, The Elements of Real Analysis
• Murray Protter and Charles Morrey, A First Course in Real Analysis

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

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