Math 447, Real Variables

Section P13, Spring 2017

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Instructor: Prof. Zhong-Jin Ruan

Classroom: 141AH, TuTh 11:00am - 12:20pm

Office Hour: TuTh 1-2 pm, or by appointment.

Office: 353 Altgeld Hall

Email: z-ruan@illinois.edu

Web page: https://faculty.math.illinois.edu/~ruan/447Spring17.html



This course provides a careful development of elementary analysis for those who intend to take graduate courses in mathematics. Topics include completeness property of real number system; basic topological properties of n-dimensional space; convergence of numerical sequences and series of functions; properties of continuous functions; and basic theorems concerning differentiation and Riemann integration.

Textbook: Elementary Analysis: The Theory of Calculus by Kenneth Ross, 2nd edition, 2013.

Pre-requisite: Math 242 and Math 347, or equivalent.

Homework: Homework will be assigned each week and will be due in class on the following dates:
Part I: Thursdays Jan 26, Feb 2, 9, 16;
Part II: Thursdays Mar 9, 16, 30, Apr 6;
Part III: Tuesdays Apr 25, May 2.

No late homework will be accepted. If you have a reasonable excuse for missing an assignment, I will score it by the average of the other assignments.

Exams: We will have two midterm exams and a final exam.

Exam1: Thursday February 23
Exam2: Thursday April 13

Final Exam: Thursday May 11, 7-10pm at 141Altgeld Hall.

Grading policy: There will be total of 500 points, which can be computed as follows.

Homework:10 x 10 pts 100 pts
Exams:2 x 100 pts 200 pts
Final Exam:  200 pts
Total:  500 pts

Your grade will be based on the total scores.


Homework
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HW#1: #4.5, 4.6, 4.7, 4.14a), 4.16. Due Thursday, January 26, 2017.

HW#2: #8.2c),d), 8.4, 8.6a), 8.8a), 8.10. Due Thursday, February 2, 2017. Solution [pdf]"
Practice HW (No need to hand in): #9.1, 9.2, 9.4, 9.8a), c), 9.15.


HW#3: #10.6a), b), 10.7, 10.10, 12.2, 12.4, 12.10. Due Thursday, February 9, 2017. Solution [pdf]"
Practice HW (No need to hand in): 10.1, 10.4, 12.3.


HW#4: #11.4 consider (x_n), (z_n); 11.6; 12.6 a), c); 14.2 e), f), g); 14.4a), b); 14.12. Due Thursday February 16, 2017. Solution [pdf]"
Practice HW (No need to hand in): #11.11, 14.7, 14.10.

The 1st exam will be given on Thursday February 23, 2017 from 11:00am to 12:15pm Solution [pdf]"

HW#5: #13.4, 13.12, 13.13; 17.10a), b), 17.12a), b). Due Thursday March 2, 2017. Solution [pdf]"
Practice HW (No need to hand in): #13.3, 13.9, 13.11; 17.3, 17.9c), d).

HW#6: #18.2, 18.4, 18.6, 18.8, 19.2c), 19.6a), b). Due Thursday March 9, 2017. Solution [pdf]"

HW#7: #13.8a), 19.7a), b), 19.10, 21.2, 21.8, 21.10a),d). Due Thursday March 16, 2017. Solution [pdf]"
Practice HW (No need to hand in) #21.1, 21.3, 21.7.

HW#8: #22.2, 22.4a),b),c), 22.6a), 22.8, 23.2b),d), 23.6. Due Thursday March 30, 2017. Solution [pdf]"
(Hint: You may apply 22.3 to 22.4b).)
Practice HW (No need to hand in). #22.1, 22.5, 22.11, 23.1.

HW#9: #24.4, 24.6, 24.14, 25.4, 25.6, 25.10. Due Thursday April 6, 2017 Solution [pdf]"
Practice HW (No need to hand in) #24.7, 24.11, 24.13, 25.5, 25.9.

For section 28 and 29, we only have practice homework (No need to hand in): #28.4, 28.6, 28.8, 28.14, 29.10, 29.12, 29.14.

The 2nd exam will be given on Thursday April 13, 2017 from 11am to 12:15pm. Solution [pdf]"

HW#10: #32.2, 32.6, 32.8, 33.4, 33.8a), 33.10. Due Tuesday April 25, 2017. Solution [pdf]"
Practice HW (No need to hand in) #33.3, 33.7

HW11: #33.14, 34.2a), 34.4, 34.6, 34.7, 34.8a). Due Tuesday May 2, 2017. Solution [pdf]"

Final Exam Review: I will hold a final exam review session at 343AH, 5pm - 6pm on Tuesday May 9, 2017.

Extra Office Hour: I will add an office hour on Thursday May 11, 11am-noon at my office 353AH.

Final Exam will be given at classroom (141 Altgeld Hall) on Thursday May 11, 2017 from 7pm to 10pm.
Notice 1: This is a close book exam. So no book, no notes, and no cell phone will be allowed during the exam.
Notice 2: Let me know if you have any potential conflicts. Otherwise, do not miss this final exam. I will not give any make-up exam unless you have a strong reason.