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Math 1010 “Analysis: Functions
of One Variable” (Spring 2011) |
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Lecture |
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Instructor:
Armen Vagharshakyan E-mail:
armen[at]math[dot]brown[dot]edu Lecture
meeting time: MWF 2pm - 2:50pm Office
hours: T 3:30-4:30pm, F 12:30pm-1:30pm My office
is: Kassar House, Room 219 |
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General Course Information
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Textbook
We will
mostly rely on online lecture notes and the book of Trench uploaded down
there. |
Course description in short The official
departmental syllabus can be found at: Math 1010.
We cover the elementary Math. Logic, naive Set Theory (up to the axiom of
choice), introduce real numbers rigorously (up to existence of roots), cover
continuity (up to Peano curves), differentiability, Riemann integral (incl.
improper and Riemann-Stieltjes integrals), numerical series, power series
(incl. Taylor series), functional series in C[0,1] (up to Arzela-Ascoli) and
convex functions. |
Grading Policy Best 10 out of 12 homework - 20%.
First midterm - 20%.
Second midterm - 25%.
Final exam - 35%.
Passing: those
who score more than 50% will pass the class, some others might also pass the
class.
Grade: at
least 30% (of those registered for a letter grade) will get ‘A’. At most 25%
(of those registered for a letter grade) will get ‘C’.
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Assignments (in compliance with the DETAILED CLASS/HOMEWORK SCHEDULE) |
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Homework |
Notes |
Exams |
HW 1: Problems, Solutions
(average 28/30)
HW 2: Problems, Solutions
(average 23/30)
HW 3: Problems, Solutions
(average 25/30)
HW 4: Problems, Solutions
(average 23/30)
HW 5: Problems, Solutions
(average 24/30)
_________________________________________ HW 6: Problems, Solutions
(average 28/30)
HW 7: Problems, Solutions
(average 28/30)
HW 8: Problems, Solutions
(average 27/30)
HW 9: Problems, Solutions
(average 27/30)
_________________________________________ HW10: Problems, Solutions
(average 28/30)
HW11: Problems, Solutions
(average 28/30)
HW12: Problems, Solutions (average
28/30)
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1. Lecture
Notes (Elementary Math Logic and Real Numbers) 3. Convergence Tests: Kummer’s Test, Abel’s Test, Dirichlet’s Test 5[additional topic]. Arzela-Ascoli (in a bit more abstract setting than I prove in class) 6[additional
topic]. Some
stuff on Polynomial approximations 7[additional topic]. A proof of Weierstrass theorem (a bit more involved than I prove in class) |
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