Courses:

Analysis I >> Content Detail



Syllabus



Syllabus

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Prerequisites


Multivariable Calculus (18.02); Differential Equations (18.03) or Honors Differential Equations (18.034)



Text


Amazon logo Rudin, W. Principles of Mathematical Analysis. 3rd ed. McGraw-Hill Science/Engineering/Math, New York, NY: McGraw-Hill, 1976. ISBN: 007054235X.



Assignments


Weekly homework is due each Friday at 3 PM. Late homework will not be accepted, but the lowest score will be dropped.



Exams


There will be two midterms and a final exam.



Grading



ACTIVITIESPERCENTAGES
Ten Problem Sets40%
Exam 115%
Exam 215%
Final Exam30%



Calendar



WEEK #TOPICSKEY DATES
1Sets and Fields, The Real Numbers
2Countability, Metric SpacesProblem set 1 due
3Closed Sets, Compact SpacesProblem set 2 due
4Compact Subsets of Euclidean SpaceProblem set 3 due
5Completeness, Sequences and SeriesProblem set 4 due
6Continuity
Exam 1
7Continuity and CompactnessProblem set 5 due
8Differentiability, Mean Value TheoremProblem set 6 due
9Taylor Series, Riemann-Stieltjes IntegralProblem set 7 due
10Integrability, Fundamental Theorem of CalculusProblem set 8 due
11Sequences of Functions
Exam 2
12Uniform Convergence
13Uniform Convergence, EquicontinuityProblem set 9 due
14Power Series, Fundamental Theorem of AlgebraProblem set 10 due
15Final Review
Final Exam

 








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