Date 
topic/section 
HW assigned 
HW due/solutions 
January 

12 
definition of Riemann and
RS integrals a nonintegrable function 


14 
examples of RS integrals upper and lower sum and refinement results central tool of RS integrability 
HW#1 

16 
continuity implies RS integrability  
19 
MLK Day 

21 
monotonicity and
integrability piecewise cts implies integrability compositions 

23 
an example properties of RS integrals 
HW#2 
HW#1 
26 
products of integrable
functions RS integral wrt a step function 

28 
snow day BC closed 

30 
RS integral wrt a
differentiable function start of FTC, I 

February 

2 
snow day BC closed  

4 
FTC, integration by parts  HW#3  HW#2 
6 
Schwarz inequality, odds and ends  
9 
snow day BC closed  

11 
sequences and series of
functions intro 
HW#3  
13 
uniform convergence,
examples, tools 

16 
Cauchy criterion, etc. 
HW#4 

18 
uniform convergence and
integrability 

20 
application; uniform convergence and continuity (metric space setting)  
23 
R(X) is a complete metric
space uniform convergence and differentiability 
HW#4 

25 
midterm 1 solutions 

27 
more on uniform
convergence and differentiability a continuous everywhere, differentiable nowhere function 

March 

2 
spring break 

4 
spring break 

6 
spring break 

9 
uniform boundedness and
equicontinuity of a sequence of functions 
HW#5 

11 
convergence of a subsequence of functions  
13 
approximating a function; Bernstein polynomials 

16 
proof of Weierstrass's approximation theorem  HW#5 

18 
power series introduction 

20 
Taylor/MacLaurin series 
HW#6 

23 
remainder term; a
MacLaurin series that converges to its function only at
0 

25 
convergence of M. series
to the function; exp and log functions 

27 
E(x), L(x) 
HW#6 

30 
class canceled 

April 

1 
class canceled 

3 
Easter break 

6 
Easter break 

8 
why does L(E(x))=x? a
series answer start of orthonormal sets, inner product spaces 
HW#7 

10 
Fourier series intro 

13 
F. series examples,
convergence 
HW#7 

15 
midterm 2 solutions 

17 
F. series on other
intervals; convergence proof 

20 
Patriots' Day  
22 
sigma algebras on a set 

24 
Lebesgue measurable sets 

27 
Lebesgue measurable
functions 

29 
Lebesgue
integration sample problems solutions 

May 

6 
final exam 12:30 pm 