Dr. Ravinder Kumar
Spring 2013
Calculus III Syllabus
QEP Theme: Advancing Student Learning Through Enhancement of Critical
Thinking and Analytical Reasoning
TOUGALOO COLLEGE
TOUGALOO, MS 39174
Mathematics Department
MAT 32101 Calculus III
3 semester hours
Dr. Ravinder Kumar
rkumar@tougaloo.edu
http//: www.ams.org/mathscinet, http//:www.quickmath.com,
,http://www.ilrn.com/ilrn/
Spring 2013
Name: ____________________
Date: 1/10/2013
Course Outline and Syllabus
Disclaimer: Dr. Ravinder Kumar reserves the right to review, and make changes to
this document as deemed necessary.
QEP Component for Course:
Mathematics is nothing but critical thinking and analytical reasoning among other things.
Critical Thinking:
In this course students continue to learn more ways in which infinite, infinitesimal, and
infinite processes help in the development of mathematical concepts. They learn how to represent
curves in different ways and how to use these representations in applications. They also learn how
some of the geometrical concepts can be studied and applied significantly using vectors.
Analytical Reasoning:
Students will apply the new representations of curves to solve area, volume, and arc length
problems. They will learn to choose and apply different rules of convergence and divergence of
sequences to a given problem. They will also learn the interpretation of vector functions in physical
context.
Office: K-2 Phone 977-7791 (O)
Schedule: 11:00 AM-1150 AM, MWF
Meeting Place: K-121
Course Description:
Polar coordinates, parametric equations, arc length, Vector calculus, curvature, surface area,
functions of several variables, partial derivative, gradient
Prerequisite: MAT222 with a minimum grade of C.
Textbooks: Required: James Stewart, Calculus Early Transcendentals Multivariable, Fifth Edition,
Brooks/Cole Publishing Company.
Supplementary Textbooks (Optional)
1. Swokowski, Olinick, and Pence, Calculus, Sixth Edition, PWS-KENT Publishing
Company.
2. Anton, Howard, Calculus with Analytic Geometry, Second Edition, John Wiley and
Sons Publishing Company.
3. Thomas and Finny, Calculus and Analytic Geometry, 8th Edition, Addison Wesley
Publishing Company.
Dr. Ravinder Kumar
Calculus III
Attendance: Each student is expected to be in class and to be on time. If a student is five or more
minutes late then the records will indicate a tardy. If a student is tardy twice then this will be
counted as an absence. If a student has more then three unexcused absences his/her semester grade
will automatically drop by one letter grade. All excuses must be reported to me with the proper
validation before they can be recorded in my class booklet as an excused absence. These policies are
stated on the current course catalog. “Tougaloo College believes that its students must learn to take major
responsibility for their own education. Tougaloo students are required to attend all of their classes and be responsible
for all assigned course material and all material covered in class. When students are absent from class, it is the
student’s responsibility to notify the instructor and ascertain what the instructor requires regarding missed material or
assignments”.
If you wish to withdraw, do so officially. The "W" will not hurt your grade point average whereas
the F will. (Course withdrawal period Ends: Check the academic calendar)
Academic Integrity:
It is expected that a student attending Tougaloo College will be scrupulously honest.
Therefore, plagiarism, cheating or any form of dishonesty associated with this course will be dealt
with in accordance with the policies of Tougaloo College. These policies are stated on the current
student handbook .
Class Structure: Part of each class will be used to discuss problems with previous homework
assignments. New topics will be introduced and discussed. Quizzes and tests will be given. You
should read the section(s) to be covered before the lecture, and should pay careful attention to what
material is being developed in the lecture. Use the lecture as a guide to what material you will need
to study. There is a lot of information in the book that won't be covered in the lecture but which is
valuable to you as background information for better understanding the material you are expected to
learn.
I encourage calculators and/or computers usage in this class. A scientific calculator or
graphic calculator (TI-82 or TI-85) will be fine.
Graphing calculators or computers may be used to help the student solve homework problems. If a
student needs a graphing calculator he/she may see Dr. Kumar (Kincheloe Hall, Mathematics
Department, K-1). The students may use the computers in Supplemental Instructions Lab
(Kincheloe 105). While the department encourages the use of calculators, students are not permitted
to use calculators of the following series during evaluation (i.e. exams, quizzes, and final exam)
because of the built in Computer Algebra Systems:
Casio: ClassPad, CFX-9970G (including, for example, CFX-9970GE) and Algebra fx
2.0
Texas Instruments: TI-86, TI-89 and TI-92 (including, for example, TI-92 Plus), TIVoyage
Hewlett-Packard: HP-40G and HP-49G
Or any other calculators with equivalent capability
Students may not use calculators that can communicate wirelessly with other calculators
Departmental calculators with be used during one-hour exams and final exam.
What is calculus?
What distinguishes calculus from your previous mathematics courses of algebra, geometry,
and trigonometry is the transition from static or discrete applications to those that are dynamic or
continuous. For example, in elementary mathematics you consider the slope of a line, but in calculus
we define the (non-constant) slope of a nonlinear curve. In elementary mathematics you found
average changes in quantities such as the position and velocity of a moving object, but in calculus
Dr. Ravinder Kumar
Calculus III
__________________________________________________________________________
we can find instantaneous changes in the same quantities. In elementary mathematics you found the
average of a finite collection of numbers, but in calculus we find the average value of a function
with infinitely many values over an interval.
You might think of calculus as the culmination of all of your mathematical studies. To a
certain extent that is true, but it is also the beginning of your study of mathematics as it applies to the
real world around us. Calculus is a three-semester course that begins your college work in
mathematics. All your prior work in mathematics is considered elementary mathematics, with
calculus the dividing line between elementary mathematics and mathematics as it is used in a variety
of theoretical and applied topics.
Calculus is the mathematics of motion and change. Its development in the seventeenth
century by Newton (1642-1727) and Leibniz (1646-1716) was the result of their attempts to answer
some fundamental questions about the world and the way things work. These investigations led to
two fundamental concepts-namely, the derivative and the integral. The breakthrough in the
development of these concepts was the formulation of a mathematical tool called a limit.
1- Limit: The limit is a mathematical tool for studying the tendency of a function as its
variable approaches some value. Calculus is based on the concept of limit. We introduce
the limit of a function informally in Section 2.1 and then examine the concept more
formally in Sections 2.2, 2.3, 2.4 & 2.5.
2- Derivative: The derivative is defined as a limit, and it is used initially to compute rates of
change and slopes of tangent lines to curves. The study of derivatives is called
differential calculus. Derivatives can be used in sketching graphs and in finding the
extreme (largest and smallest) values of functions. The derivative will be introduced and
developed in Chapter 3, and its applications are examined in Chapter 4.
3- Integral: The integral is founded by taking a special limit of a sum of terms, and the
study of this process is called integral calculus. Areas, volume, arc length, work, and
hydrostatic forces are a few of the many quantities that can be expressed as integrals.
Integrals and their applications are studied in chapter 5, 6, 7, and 8.
Assignments: Homework will be given at most meetings. These assignments should be completed in
preparation for quizzes, tests and final examinations. If you don't do your homework you will not do
well in class. You will be asked to do problems that you may not be very good at doing. You should
always try to do the best job you can, because that is how you improve your skills. Never give up.
Never try to do the minimum. Just "getting by" is a sure bad idea. If you have problems with the
course, you should make an appointment with me and make plans to solve these problems early in
the semester.
Assignments will be administered online using WebWork hosted by Tougaloo
College server. Complete information on WebWork will be given in the class. You
can log onto WebWork using the url
http://tc-webwork.tougaloo.edu/webwork2/MAT321/
Evaluation:
1.
2.
3.
4.
5.
In-Class/Online quizzes (100 Points)
Online assignments
(50 Points)
Class participation and class attendance (50 Points)
Two in-class tests
(100 points each)
A Take-Home before the final exam
(100 points)
Dr. Ravinder Kumar
Calculus III
6. Midterm
7. Final
(100 Points)
(200 Points)
Letter grades will be assigned as follows:
A
More than 85%
B
More than 75%
C
More than 55%
D
More than 40%
F
Less than 40%
8. No make-up homework assignments/quizzes will be given.
9. Extra points may be awarded for superior work.
10. An important part of studying is getting ready for a test. This includes testing yourself
to see if you can answer the kinds of questions you are likely to be asked.
11. Quizzes and Exams will be closed book and notes, and will include all material
covered, including any homework.
12. If a student has an excused absence for a test or exam, he/she will be required to
make-up the same. You must take the make-up exam within a week of the regular
exam, and you should be aware that the make-up would be harder.
13. Mid-term grades will be determined by Exams, homework, quizzes and in class
activities, given prior to the day of midterm.
Course Outline and Suggested Homework Problems from the textbook:
#
Topics
Homework assignment (Problems)
Chapter 10 Parametric Equations
10.1 1-6
and Polar Coordinates
i.e. 1-6-11-16-21-26-31-36-41-46-51-56
10.2 2-7
i.e. 2-7-12-17-22-27-32-37-42
10.3 1-6
10.4 2-7
10.5 1-6
10.6
4 Points Quiz #1 Sections 10.1-6
Chapter 11 Infinite Sequences and 11.1 1,5,9,11,15,17,19,23,29,31,39,41,43,45,49,51
Series
11.2 1,5,9,12,17,21,23,25,29,33,37,41,47,49,51,53,59,63
11.3 1,11,13,17,21,27,29,39,45,47,50,54,59,65+Quiz11.1-2
one point
11.4 All odd+16 Points Test #1 (Ch10+ 11.1-4)
11.5 1,5,11,21,27,33
11.6 1,11,25,31,37 Quiz 11.5-6 one point
11.7 1,5,13,15,23,27,35
11.8 1,7,9,15,17,23,29,37,39 Quiz 11.7-8 one point
11.9 1,3,7,17,19,25
11.10 Do the examles only Quiz 11.9-10 one point
11.11 1, 5. 9, 13
16 Points Test #2
Dr. Ravinder Kumar
Calculus III
__________________________________________________________________________
Chapter 12 Vectors and Geometry 12.1 1-6
of Space
12.2 2-7
12.3 1-6
12.4 2-7
12.5 1-6
12.6 2-7
12.7 1-6
4 Points Quiz #3 Sections 12.1-7
Chapter 13 Vector Function
13.1 1-6
13.2 2-7
13.3 1-6
13.4 2-7
16 points Test #3 Ch12 and 13
Chapter 14 Partial Derivatives
14.1 1-6
14.2 2-7
14.3 1-6
14.4 2-7
The evaluation for this chapter will be a part of Final Exam
Test Dates:
Test/Exam dates will be announced in class as well as on WebWork page at least one week
in advance
I am here to help you learn the material. If you are having problems, see me right away. Do
not wait until the day before a test. You do need an appointment to see me even during my office
hours. Talk with me to set up a time when we can get together.
Note to seniors and other students.
If you are taking this course to satisfy the graduation requirements, I cannot treat you any
different from any other student. Your final grade is strictly as a result of your performance in
homework, quizzes, tests, and other class activities. There is no extra credit by any means. Please
drop the class or withdraw. Make your decision right now before it is too late. I am sorry I am
not of any more help to you.
Special Needs Statement (Proposed):
If you have a disability for which you are or may be requesting an
accommodation, you are encouraged to contact both your instructor and the Student
Disabilities Service team.
Expected Tougaloo College Student Outcomes:
The expected outcomes are stated on the current course catalog.
STUDY HINTS
Mathematics is different from other subjects in that the quantity of reading material is usually
not great. It is much more important to remember that each word of a reading assignment must be
understood. It is not unusual for a student to read a section in the textbook several times. Reading
speed is of little benefit in mathematics. In general, it is better to go quite slowly, letting the
Dr. Ravinder Kumar
Calculus III
meanings seep in. Also, pausing frequently to go over in your mind what you have just read, saying
these ideas in your own words, and trying to relate them to what you have already learned are
excellent steps to learning. Time spent on thoroughly understanding the reading material will mean
that less time will usually be required to do the problems.
The great temptation is to go immediately to the written assignment and look back in
the text to find an example to fit the requirements of the problem at hand. This method may
work on some problems, but the overall goal of understanding the course material is defeated.
Problems worked in this way rarely stay in the memory long.
First, carefully read all the examples given, and actually work them with paper and pencil
along with authors, then use the written assignment as a mini test, looking back for hints in the text
only when you need to. In this way you will find that the idea in the section will become your own.
This means that when test time rolls around, review of your lessons will bring back to your mind all
that you have learned, and you will be equipped to perform well on the test without the crutch of the
text examples.
I am here to assist you in learning the content of this course. I welcome the opportunity to
serve you. Please don't hesitate to contact members in mathematics department, and/or myself as
soon as you feel that you need additional help.
Computer Use at Tougaloo College:
The Microcomputer Labs, located on H-21 and K-105, offer IBM compatible for use by
Tougaloo students. A variety of software applications, including word processing, spreadsheet,
database management are provided.
Remember: NOT WHAT YOU LEARN BUT WHAT YOU CAN RECALL MAKES YOU A
WISE STUDENT.
Helpful Websites:
http://www-history.mcs.st-and.ac.uk/
http://tutorial.math.lamar.edu/
http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx
http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx
http://www.analyzemath.com/calculus.html
http://people.hofstra.edu/Stefan_Waner/tccalcp.html
http://freetutorials.name/Reference1/Calculus%20tutorials.html
http://www.wiziq.com/tutorials/integral-calculus
http://www.brookscole.com/math_d/templates/student_resources/0534393667_stewart/weblinks/ch1
1.html
http://archives.math.utk.edu/visual.calculus/
http://www.ltcconline.net/greenl/courses/107/PolarParam/PolarParam.htm