University of North Texas at Dallas Spring 2012 SYLLABUS

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Steven R. Lay, Analysis, with an Introduction to Proof, Fourth Edition,. Prentice Hall ... Edward D. Gaughan, Introduction to analysis, Brooks/Cole Publishing.
University of North Texas at Dallas Spring 2012 SYLLABUS MATH 3610

REAL ANALYSIS II

Department of

Mathematics and Information Sciences

Division of

Liberal Arts & Sciences

Instructor Name:

Dr. Noureen Khan

Office Location:

Founders Hall - 223

Office Phone:

972 338 1567

Email Address:

[email protected]

Office Hours:

M-W T- R

3Hrs

1:00 - 2: 00 pm 11:30 - 2: 00 pm

Math Lab Hours: Classroom Location:

Founders Hall - 241

Class Meeting Days & Times:

T- R 10:00 am - 11:20 am

Course Catalog Description:

This course is continuation of MATH 3000. Topics include derivatives, integrals, limits of sequences of functions, Fourier series; and an introduction to multivariable analysis.

Prerequisites:

MATH 3000

Required Text:

Steven R. Lay, Analysis, with an Introduction to Proof, Fourth Edition, Prentice Hall, 2005.

Reference Books

 

Access to Learning Resources:

Walter Rudin, Principles of mathematical analysis, McGraw-Hill, New York 1964 Edward D. Gaughan, Introduction to analysis, Brooks/Cole Publishing Co., 1993.

UNT Dallas Library: phone: (972) 780-3625; web: http://www.unt.edu/unt-dallas/library.htm UNT Dallas Bookstore: phone: (972) 780-3652; e-mail: [email protected]

Course Goals: The goals of this course are to 1.

Learn the concepts of Completeness, Convergence, Subsequences, and Continuity.

2.

Define Derivatives and apply Mean Value Theorem and L’Hˆopital’s Rule to solve problems

3.

Define and use Limits of Functions, lim sup and lim inf, Monotone & Cauchy Sequences.

4.

State and proof Taylor’s Theorem, and Limit Theorems

5. Learn Integrals and proof of Fundamental Theorem of Calculus Learning Outcomes (Program): Math 3610 contributes to the following mathematics undergraduate program objectives: Mathematical Reasoning

MR 1. Read, understand, formulate, explain, and apply mathematical statements. MR 2. Formulate conjectures by considering examples that move from the specific to the general. MR 3. Distinguish between valid and fallacious arguments. MR 4. State and apply important results in key mathematical areas, with the ability to provide proofbased arguments of these and related results. MR 5. Use a variety of techniques – such as, mathematical induction, proof by contradiction, or direct application of axioms and previously proven theorems – to prove propositions. General skills

GS 1.

Solve mathematical problems individually and cooperatively.

GS 2.

Formulate strategies for solving novel analytical – both theoretical and applied – problems.

GS 3.

Communicate, both verbally and in writing, mathematical ideas at a variety of levels from technical to intuitive.

Course Outline: This course will examine the theoretical foundations of real analysis, or in other words, we will learn why calculus works. The course is also aimed at improving students’ proof writing abilities and getting them more comfortable with precise mathematical rigor. Prior experience with analytical and theoretical proofs will be assumed. Attendance is required for this class and is essential for effective learning. Home work will be assigned in every class meeting; you are expected to do all home work problems. UNT Dallas provides all possible help to assure student success, such as Math lab where Math Faculty is available to help most of the day. Due to the nature of this course, you are encouraged to make regular visits during my office hours or make an appointment for help.

Course Evaluation Methods: This course will utilize the following instruments to determine student grades and proficiency of the learning outcomes for the course. Home Work: Home work will be assigned in every class meeting and will be collected time to time without notice. Two lowest quiz grades will be replaced by two home work grades. You are required to do all your home work in a proper notebook throughout the semester. It’s your responsibility to obtain the missing class/home work from you class mates or by contacting me. Quizzes – Weekly short quizzes, mostly in the Thursday’s class. Exams – Two Midterm Exams Project – Groups (2-3 students) will work and present assigned projects. Final Exam – Comprehensive Final Exam at the end of semester. ************The schedule for the quizzes, exams and Final exams is attached. ************* Absolutely NO MAKE –UP Quizzes or Exams.

Grading Matrix: Instrument

Percentage %

Points

Quizzes

Best 10 quizzes

30

150

Project

Group Project

10

50

Exam

2 Mid Term Exams

40

200

Final Exam

One comprehensive final exam

20

100

100

500

Total: Grade Determination: Grade

Percentage %

Points

A B C D F

90 or better 80 – 89 70 – 79 60 – 69 less than 60

450 or more 400 – 449 350 – 399 300 – 349 299 or less

Calculator Policy: This course DOESN’T REQUIRE a graphing calculator.

Class Schedule: This schedule is subject to change by the professor. Any changes to this schedule will be communicated in class and/or posted on e-campus. Tuesday

Thursday

Week 1 Jan 17 & Jan 19

Topics Chapter 3: The Real Numbers

Week 2 Jan 24 & Jan 26

Quiz #1

Completeness Axioms, Compact Sets

Week 3 Jan 31 & Feb 02

Quiz #2

Chapter 4: Sequences Convergence, Limit Theorem

Week 4 Feb 07 & Feb 09

Quiz #3

Monotone and Cauchy Sequences, Subsequences

Week 5 Feb 14 & Feb 16

Quiz #4

Chapter 5: Limits and Continuity Limits of Function, Continuous Function

Week 6 Feb 21 & Feb 23

Quiz #5

Property of Continuous Function, Uniform Continuity

Week 7 Feb 28 & Mar 01

Test #1

Review

Week 8 Mar 06 & Mar 08

Quiz #6

Chapter 6: Differentiation The Mean Value Theorem

Week 9 Mar 13 & Mar 15

Quiz #7

L’Hospital Rule, Taylor’s Theorem

Week 10 Mar 20 & Mar 22

SPRIG

BREAK

Week 11 Mar 26 & Mar 28

Quiz #8

Chapter 7: Integration The Riemann Integral

Week 12 Apr 03 & Apr 05

Quiz #9

Properties of the Riemann Integral, The Fundamental Theorem of Calculus

Week 13 Apr 10 & Apr 12

Quiz #10

Chapter 8: Infinite Series Convergence of Infinite Series

Week 14 Apr 17 & Apr 19

Quiz #11

Convergence Tests, Power Tests

Week 15 Apr 24 & Apr 26

Test #2

Week 16 May 01& May 03 Week 17 May 08 & May 10

Review Review Final Exam

Final Exam

Comprehensive Final Exam May 10th ,2012 @

10:00am - 12:00 pm

University Policies and Procedures Students with Disabilities (ADA Compliance): The University of North Texas Dallas faculty is committed to complying with the Americans with Disabilities Act (ADA). Students' with documented disabilities are responsible for informing faculty of their needs for reasonable accommodations and providing written authorized documentation. For more information, you may visit the Office of Disability Accommodation/Student Development Office, Suite 115 or call at 972-780-3632.

Student Evaluation of Teaching Effectiveness Policy: The Student Evaluation of Teaching Effectiveness (SETE) is a requirement for all organized classes at UNT. This short survey will be made available to you at the end of the semester, providing you a chance to comment on how this class is taught. I am very interested in the feedback I get from students, as I work to continually improve my teaching. I consider the SETE to be an important part of your participation in this class.

Exam Policy: Exams should be taken as scheduled. No makeup examinations will be allowed except for documented emergencies (See Student Handbook). In the case of injury or illness, you need to provide a note from a health care professional affirming date and time of a medical office visit regarding the injury or illness and stating that you should not be in class that day. You must notify me no later than the end of the second working day after the missed exam.

Academic Integrity: Academic integrity is a hallmark of higher education. You are expected to abide by the University’s code of conduct and Academic Dishonesty policy. Any person suspected of academic dishonesty (i.e., cheating or plagiarism) will be handled in accordance with the University’s policies and procedures. Refer to the Student Code of Conduct at http://www.unt.edu/csrr/student_conduct/index.html for complete provisions of this code.

Attendance and Participation Policy: The University attendance policy is in effect for this course. Class attendance and participation is expected because the class is designed as a shared learning experience and because essential information not in the textbook will be discussed in class. The dynamic and intensive nature of this course makes it impossible for students to make-up or to receive credit for missed classes. Attendance and participation in all class meetings is essential to the integration of course material and your ability to demonstrate proficiency. Students are responsible to notify the instructor if they are missing class and for what reason. Students are also responsible to make up any work covered in class. It is recommended that each student coordinate with a student colleague to obtain a copy of the class notes, if they are absent. Excessive absences (more than 3 classes) may result in being dropped from the class or receiving an F for the course.

Diversity/Tolerance Policy: Students are encouraged to contribute their perspectives and insights to class discussions. However, offensive & inappropriate language (swearing) and remarks offensive to others of particular nationalities, ethnic groups, sexual preferences, religious groups, genders, or other ascribed statuses will not be tolerated. Disruptions which violate the Code of Student Conduct will be referred to the Center for Student Rights and Responsibilities as the instructor deems appropriate.

Copyright Policy: The handouts used in this course are copyrighted. By "handouts," I mean all materials generated for this course, which include but are not limited to syllabi, lecture notes, quizzes, exams, in-class materials, review sheets, projects, and problems sets. Because these materials are copyrighted, you do not have the right to copy and distribute the handouts, unless I expressly grant permission.

Miscellaneous Policy:  

Use of Cell Phones & other Electronic Gadgets (such as Laptops) are prohibited in the classroom. Food and drinks are not allowed during the lectures.