447

MATH 447 Honors: Advanced Calculus I
Fall 2014

Syllabus: The printable version of the syllabus can be found here .

Course meeting and place:

MWF, 9:05 am–9:55 am, Ayers Hall 120

Instructor contact information:

Name: Dr. Tadele Mengesha
E-mail: mengesha (at) utk.edu,
Office: 324 Ayres Hall,
Phone: 865-974-4271
Office hours: MWF, 10:30 am–11:30 am or By appointment.

Course description:
In this course we go beyond the routine manipulation of formulas and rigorously develop the foundation of calculus from basic principles. We will examine fundamental properties of the real number system, study sequences and the concept of limit, discuss the theory of a class of functions: continuity and differentiability; and finally deal with theory of Riemann integration.

Course objective:
After successfully completing the course, a student will develop the ability to analyze,criticize and construct proofs, using deductive reasoning, to many of the theorems in Calculus (more broadly
theorems in elementary real analysis). This course is a prerequisite to Math 448: Advanced Calculus II that will be given in the Spring semester.

Course Textbook :

(Required text) Introduction to Real Analysis, Robert Bartle and Donald Sherbert, Wiley, 4th edition, 2011. We will be covering (essentially) the first 7 chapters of this book.

Other References:

Postmodern Analysis, Jurgen Jost, Springer, Universitext Series, 3rd edition, 2005.

Basic Analysis, Introduction to real analysis, Jiri Lebl, 2013, http://www.jirka.org/ra/realanal.pdf

Blackboard:
All your grades (homework/quiz and exam) and other necessary information and announcements will be made on Blackboard at Online@UT. Please make it your habit to visit the site frequently.

Grading and evaluation:

Homework/quiz:-

Homework problems from the textbook will be assigned and collected regularly. I encourage you to discuss homework problems with your classmates. However, you should write up your own solution for the exercises to submit. Quizzes that help you prepare for exams will be given frequently. I will let you know in advance when the quizzes will be given. Given a writing-intensive nature of the course, your solution to homework and quizzes should be neat and professionally prepared. Please write in complete sentences. Incomplete and sloppy arguments
with no proper justification are not acceptable. No late homework is acceptable, and there are no make up quizzes.

As part of homework I may assign a project to each of you that challenges you to apply the techniques you learned in the course. The projects are topics in analysis that you will read on, report and present at the end of the semester.

Tests:-

There will be two mid-term exams during the semester and a comprehensive final examination that will be given during the final examination period. No books, notes, or calculators may
be used in the examinations. The midterm exams will be on the following dates:

Midterm Examination I: Friday, October 03, 2014

Midterm Examination II: Friday, November 14, 2014

Grading policy:-

Scores for graded assignments will be available on Online@UT. The final grade will be computed using the following weights
Homework/Quiz 30%, Examination I/II 40% and Final Examination 30%.

Letter grades will be based on the following scale

Grade	A	A-	B+	B	B-	C+	C	C-	D	F
%-score	93-100	90-92	87-89	83-86	80-82	77-79	73-76	70-73	60-69	0-59

(For graduate students A- = A and B- = B, C- = C.)

Attendance:-

Every student is expected to attend every class. Your attendance is an indication of your seriousness
in the course and may be used (among other factors) in making borderline grade decisions.

Other notes:

Retain all graded tests, and homework up to the end of the semester. Your grades will be posted on Online@UTK. Please contact me when you see any discrepancy.

Please do not use cell phones during class in any form (voice, text messaging, calculator).

Information on this syllabus may change (if I find the change helpful for all of the students) by e-mail or verbal announcement made in class.

Course Schedule:

Week	Day	Date	Section
1	Wednesday	August 20, 2014	Introduction
	Friday	August 22, 2014	Mathematical Logic
2	Monday	August 25	Logical quantifiers and proofs
	Wednesday	August 27	Basic set theory
	Friday	August 29	Function
3	Monday	September 1	Labor Day
	Wednesday	September 3	Mathematical induction Homework #1 Due PDF Solution: by Ian Francis PDF by Pawel Grzegrzolka PDF
	Friday	September 5	Set of real numbers Quiz 1 PDF Solution: PDF
4	Monday	September 8	Order properties of the set of real numers
	Wednesday	September 10	Absolute value and the number line Homework #2 Due PDF Solution: by Ian Francis PDF by Pawel Grzegrzolka PDF
	Friday	September 12	The Completeness Property of the set of real numbers Quiz 2 PDF Solution: PDF
5	Monday	September 15	Application of the Completeness Property
	Wednesday	September 17	Homework #3 Due PDF Solution: By Michael Wise PDF
	Friday	September 19	Quiz 3 Solution: PDF
	Monday	September 22	Sequences and limit of a sequence
	Wednesday	September 24	Limit theorems Homework #4 Due PDF Solution:
	Friday	September 26	Limit theorems, Monotone sequences Quiz 4 Solution: PDF
	Monday	September 29
	Wednesday	October 01	Homework #5 Due
	Friday	October 03	Midterm exam 1 Solution PDF
	Monday	October 05
	Wednesday	October 08
	Friday	October 10
	Monday	October 13
	Wednesday	October 15	Homework #6 Due Solution By Ian Francis PDF
	Friday	October 17	FALL BREAK No Class
	Monday	October 20	Cauchy Criterion, contractive sequences
	Wednesday	October 22	Introduction to infinite series
	Friday	October 24	Homework #7 Due Quiz 5