Math 4001 - Analysis II


Fall 2014
Instructor: Janos Englander
 Math 324, Phone: 2-4846, E-mail:
Lectures: MWF 03:00 PM - 03:50 PM
HALE 240

Grader: Xiaorong.Liu@Colorado.EDU

Office Hours: MF 1-2 pm, or by appointment.
Text: Mathematical Analysis, Second Edition by Tom Apostol (Pearson). CLICK

Prerequisites: Math 3001 and MATH 3130.

Description: Provides a rigorous treatment of infinite series, sequences of functions, and an additional topic chosen later by the instructor (either the Lebesgue integral or Fourier analysis). 

Grading: 30% MT, 30% HW, 40% Final

Midterm: Oct. 17, Friday, in class.
(Closed notes and closed book. No electronic devices permitted.)

Final: Dec. 12, in class.
(Closed notes and closed book. No electronic devices permitted.)


Eating/drinking policy:
That is fine.

Texting Policy:
No texting. 


Why all `Leibniz’ conditions are necessary: Leibniz.counterex.pdf


HOMEWORK SETS (Nrs refer to textbook)

HW1 (Due Sept 12, 2014)
8.4, 8.5, 8.6, 8.8

Solutions HW1: CLICK
HW2 (Due Sept 19, 2014)
8.15 (g), 8.23, 8.24, 8.26

Solutions HW2: CLICK

HW3 (Due Oct 1 Wed, 2014)
8.30, 8.35 (Section 8.27 has more on the zeta-function), 8.37, 8.42

Solutions HW3: P1    P2

HW4 (Due Oct 8, 2014)
9.1, 9.2, 9.3, 9.4

Solutions HW4: CLICK

HW5 (Due Oct 20, 2014)
9.5, 9.6, 9.12, 9.16

Solutions HW5: CLICK
HW6 (Due Oct 31, 2014)
9.18, 9.22, 9.23, 9.27

Solutions HW6: CLICK

HW7 (Due Nov 7, 2014)    
9.30, 9.31, 9.33, 9.34

Solutions HW7: CLICK

HW8 (Due Nov 14, 2014)
10.1, 10.2, 10.3, 10.4 

Solutions HW8: CLICK

HW9 (Due Nov 21, 2014)
10.5, 10.6, 10.8, 10.11

Solutions HW9: CLICK

HW10 (Due Dec 10, 2014)
10.12, 10.19, 10.20(d), 10.21(a)

Solutions HW10: CLICK


Campus policy points:

(1) If you qualify for accommodations because of a disability, please submit to me a letter from Disability Services in a timely manner (for exam accommodations provide your letter at least one week prior to the exam) so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities. Contact Disability Services at 303-492-8671 or by e-mail at 

If you have a temporary medical condition or injury, see Temporary Injuries under Quick Links at Disability Services website and discuss your needs with me.

(2) Campus policy regarding religious observances requires that faculty make every effort to deal reasonably and fairly with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance. In this class, I will be happy to help you if you talk to me at least 2 weeks before the upcoming holiday.
See full details at

(3) Faculty and students should be aware of the campus ‘Classroom Behavior’ policy as well as faculty rights and responsibilities, 

These documents describe examples of unacceptable classroom behavior and provide information on how to handle such circumstances should they arise. 

Students and faculty each have responsibility for maintaining an appropriate learning environment. Those who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, color, culture, religion, creed, politics, veteran’s status, sexual orientation, gender, gender identity and gender expression, age, disability, and nationalities. Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. See policies at and at