PICTURE
MATH 427/527 - Advance Calculus I

Fall Semester 2007               Download Syllabus

InstructorBasant K. Karna, Ph.D.
Office: Smith Hall, Room 741B
Phone: (304) 696-4332
E-Mail: karna@marshall.edu
Class Hours
TR 5:00-6:15 PM.     Room: Smith Hall 511
Office Hours
My regular office hours are: MTWR 2:00-3:00 & MW 5:00-6:00.     Others by appointment.
Text

Introduction to Real Analysis by Robert G. Bartle & Donald R. Sherbert, 3rd Edition

Syllabus

         Course Syllabus      MTH 427/527           Section 101        Fall 2007  

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Course Title:

Advance Calculus I

Course Number:

MTH 427/527 -- Section 101 -- CRN 3502/3512 -- Credit: 3 Hours 

Textbook:

Introduction to Real Analysis by Robert G. Bartle and Donald R. Sherbert,

Third Edition, John Wiley & Sons, Inc.

Sections Covered:

1.1-1.3, 2.1-2.5, 3.1-3.7,  4.1-4.3, 5.1-5.6

Course Description:

A rigorous study of the real number system, continuity and differentiability of functions of a single variable, integration of functions of a single variable, infinite series.                                                                                                         functions of one variable, including the transcendental functions.

Prerequisites:

MTH 231 (Calculus III), MTH 300 (Introduction to Higher Mathematics)

Meeting Time:

TR: 5:00 – 6:15 PM

Classroom:

Smith Hall 511

 

 

Instructor:

Dr. Basant Karna

Office:

Smith Hall 741B

Office Hours:

2:00-3:00 MTWR, 5:00-6:00 MW, Others by appointment

Phone/Email:

Phone: (304) 696-4332, Email: karna@marshall.edu

Webpage:

http://www.science.marshall.edu/karna/index.asp  (Check for updates)

 

 

Course Objectives:

This course is a comprehensive study of the real number system and functions defined on the real line.  We will begin with discussions of properties of the real number system.  From there we will study the behavior of sequences and series of real numbers.  The theorems you were introduced to in your calculus courses will take on an added dimension after our discussions of how these results can be verified through proof and reinforced by application.  Next we expand our scope to the characteristics of continuous functions and the derivatives and integrals of these functions.  From there we consider a sequence of functions and discuss point-wise and uniform convergence.  The notion of absolute convergence of infinite series is our next topic and we will finish with a discussion of the generalized Riemann integral.  

 

 

Course Contents:

- Preliminaries

- The Real Numbers

- Sequences and Series

- Limits

- Continuous Functions

 

 

Attendance Policy:

Attendance is required and you must come with your text. It is your responsibility to determine what you missed in the event you are unable to attend class.  Borderline grades will be determined by class attendance.

 

 

Important Dates:

August 27, Monday – “W” Withdrawal period begins

September 3, Monday – Labor day – No Class

October 26, Friday – Last day to drop

Nov 19, Mon – Nov 24, Sat – Thanksgiving  – No Class

December 4, Tuesday – Last class day

 

 

Exam Dates:

Midterm – October 9 (Tuesday)

Final Exam: December 6 @ 5:00 PM(Thursday) in SH 511

 

 

 

Grading Policy:

You grade will be calculated using the following percentages:

Homework  –  20%,  Quiz/Boardwork  –  20%,   Midterm – 30%,  Final – 30%

There will be two tests during the semester, a midterm (Tuesday, October 9) and a final exam (Thursday, December 6, 5:00 P.M. – 7:00 P.M.). In the event you are not able to take the exam on the scheduled date because of serious circumstances, (see Undergraduate Catalog, pp. 121 – 122 or Graduate Catalog pp. 47 – 48 for the list of excused absences) please contact me before the scheduled exam time so that we can plan a time for you to take the exam early.

If you don’t take final exam, you will receive “F” for the class.  

You will be assigned homework in almost every class period. 

I will ask you to present some of your works at the board (mostly 527 students). Random quizzes will be given (I will let you know in advance).                                   

Your final grade will be determined using the following scale:

A: 90% - 100%,  B: 80% - 89%, C: 70% - 79%, D: 60% - 69%, F: 0% - 59%

 

Success in the course will be measured by your ability to meet the following objectives:

> To expand your understanding of concepts in differential and integral calculus and apply the ideas and proof techniques to related problem settings.

> To comprehend and apply the ideas found in classical theorems (and proofs of the theorems) in function theory of real variables to related problem settings.   

> To be able to construct (as well as recreate in your own words) formal proofs of theorems that address ideas discussed during the course of the semester.

> To be able to present your work clearly and concisely in both written and oral form. Organization and logical flow will be the secrets to success in meeting this objective.

> To learn to recognize and appreciate various approaches to the same problem.

 

 

 

Cell Phones:

All electronic devices should be shut off during class.

Academic Honesty:

Students should not cheat on exams or on assignments. Those found cheating will be dealt seriously. Please read pages 105 – 110 of the undergraduate catalogue for details. Or follow the link  http://www.marshall.edu/ucomm/catalog/ug_05-07.pdf

 

 

 


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