Other Course , Spring 2010 , Prof. Francis Su

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Other Course , Spring 2010 , Prof. Francis Su

Contents:

Constructing the rational numbers,Properties of Q,Construction of R,The Least Upper Bound Property,Complex Numbers,The Principle of Induction,Countable and Uncountable Sets,Cantor Diagonalization, Metric Spaces, Limit Points,Relationship b/t open and closed sets,Compact Sets,Relationship b/t compact, closed sets,Compactness, Heine-Borel Theorem,Connected Sets, Cantor Sets,Convergence of Sequences,Subsequences, Cauchy Sequences. ,Complete Spaces,Series,Series Convergence Tests,Functions - Limits and Continuity,Continuous Functions,Uniform Continuity,Discontinuous Functions. ,The Derivative, Mean Value Theorem,Taylor's Theorem,Ordinal Numbers, Transfinite Induction.

Constructing the rational numbers,Properties of Q,Construction of R,The Least Upper Bound Property,Complex Numbers,The Principle of Induction,Countable and Uncountable Sets,Cantor Diagonalization, Metric Spaces, Limit Points,Relationship b/t open and closed sets,Compact Sets,Relationship b/t compact, closed sets,Compactness, Heine-Borel Theorem,Connected Sets, Cantor Sets,Convergence of Sequences,Subsequences, Cauchy Sequences. ,Complete Spaces,Series,Series Convergence Tests,Functions - Limits and Continuity,Continuous Functions,Uniform Continuity,Discontinuous Functions. ,The Derivative, Mean Value Theorem,Taylor's Theorem,Ordinal Numbers, Transfinite Induction.

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3.1 (30 Ratings)

Real Analysis, Spring 2010, Harvey Mudd College, Professor Francis Su. Get notes and study tools at httpgosuapm.com

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- 1.Real Analysis, Lecture 1 Constructing the Rational Numbers
- 2.Real Analysis, Lecture 2 Properties of Q
- 3.Real Analysis, Lecture 3 Construction of the Reals
- 4.Real Analysis, Lecture 4 The Least Upper Bound Property
- 5.Real Analysis, Lecture 5 Complex Numbers
- 6.Real Analysis, Lecture 6 Principle of Induciton
- 7.Real Analysis, Lecture 7 Countable and Uncountable Sets
- 8.Real Analysis, Lecture 8 Cantor Diagonalization and Metric Spaces
- 9.Real Analysis, Lecture 9 Limit Points
- 10.Real Analysis, Lecture 10 The Relationship Between Open and Closed Sets
- 11.Real Analysis, Lecture 11 Compact Sets
- 12.Real Analysis, Lecture 12 Relationship of compact sets to closed sets
- 13.Real Analysis, Lecture 13 Compactness and the Heine-Borel Theorem
- 14.Real Analysis, Lecture 14 Connected Sets, Cantor Sets
- 15.Real Analysis, Lecture 15 Convergence of Sequences
- 16.Real Analysis, Lecture 16 Subsequences, Cauchy Sequences
- 17.Real Analysis, Lecture 17 Complete Spaces
- 18.Real Analysis, Lecture 18 Series
- 19.Real Analysis, Lecture 19 Series Convergence Tests, Absolute Convergence
- 20.Real Analysis, Lecture 20 Functions - Limits and Continuity
- 21.Real Analysis, Lecture 21 Continuous Functions
- 22.Real Analysis, Lecture 22 Uniform Continuity
- 23.Real Analysis, Lecture 23 Discontinuous Functions
- 24.Real Analysis, Lecture 24 The Derivative and the Mean Value Theorem
- 25.Real Analysis, Lecture 25 Taylors Theorem, Sequence of Functions
- 26.Real Analysis, Lecture 26 Ordinal Numbers and Transfinite Induction

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