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Math 21-123 : Calculus of Approximations
Spring 2011
"The essence of mathematics is not to make simple things complicated, but to make complicated
things simple." -- S. Gudder
Instructor: Dr. Meghna Mittal
Class Location: BH A51
Class Timings: 10:30 - 11:20 am MWF
Office Location: Wean Hall 8204
Office hours: 2:30 - 4:00 M, 3:30 - 5:00 W and by appointment
Email: mittal@math.cmu.edu
Remember: Feel free to come to my office hours or schedule an appointment for individual meeting.
I would be more than willing to help you with any questions you may have. The best part about these hours
is that I will be able to devote individual attention to all your questions and concerns.
Help : In addition to the help from the class, recitation sessions, TA, and my office hours, the University
operates a walk-in tutoring in the residence halls. The advantage of this walk-in tutoring can be taken at various hours and location.
In Cyert B6A (Beginning 1/17): MW from 4:00-6:00 p.m.
In the Mudge Library and Donner Reading Room (Beginning 1/16): Sun thru Wed from 8:30-11:00 p.m.
In the Engineering and Science Library (Beginning 1/17): MW from 8:30-11:00 p.m.
EXTRA OFFICE HOURS:
Monday(Feb 28) --- 4:00 - 5:00
Tuesday(March 01) --- 3:00 - 5:00
Wednesday(March 02) --- 10:30 - 12:20
NEWS:
First homework will be posted on Jan 11 and will be due on Thursday, Jan 20 in your recitation section.
First quiz of the semester will be held on Thursday, Jan 20 in recitation in your recitation section.
Hand written Lecture notes from Jan 17 have been posted on the Lecture page.
Homework 2 has been posted.
Office hours on Wed has been changed.
Group Project details have been posted on the homework page.
Homework 3 has been posted.
Check out the Exam I review sheet below.
Details of the Group Project II have been posted on the homework page.
Check out the Exam II review sheet below.
My regular office hours on Wednesday(March 02) have been canceled.
Some Daily Useful Links:
Exam Stuff:
Textbook: Essential Calculus -- Early Transcendental, by James Stewart.
Course Description: In this course, we shall cover chapter 8 of textbook.
As the name of the course suggests, we plan to learn some neat techniques of approximation in this mini course.
In earlier Calculus courses, you might have learnt methods to find the exact answers but this is not always essential and in fact
possible in real life problems. To be able to find ``good" approximations is an important piece of knowledge which
is used in solving many real life problems. You must have learnt about method of linear approximation and differentials
to find an approximate values in your earlier Calculus courses. In this course, we shall learn even more
sophisticated methods of approximation. Also, we will be able to estimate how good the approximation is, that is, estimation of error.
For instance, if we are looking for the value of sin(10 degree). We shall not be able to find an exact value of this
number unless we have memorised this particular value or make use of the calculuator. From our prior knowledge, we
know that x is an approximation of the function sin x when is x is small. Indeed, this follows from the fact that
sin(x) / x approaches to 1 whenever x approaches to 0. Since x = 10 degrees is not really a small number so it might
not be that good a approximation. Later, we will be able to employ methods from this course to be able to
find better and more sophisticated techniques that allow us to find even better approximations to sin(x) in terms
of a polynomial in ``x". We shall learn this technique in general to be able to deal with wide range of complicated functions.
Stay Tuned!
Lecture : There will be no attendance in class but tardiness and absence from class is
strongly discouraged. You are encouraged to ask questions and participate in class. You are responsible for all of the announcements
made and the material covered in the class. You are not permitted to use laptops or any other electronic device such as
cell phones, mp3 players and so on during lecture.
Recitation : There are only two lab section for this class both conducted by Daniel DeCapria. His office hours will be held in Wean 7315 starting from 10:30am to 12:20am on Tuesdays and Thursdays.
Section A3 meets at 8:30 am on TuTh WEH 5302.
Section B3 meets at 9:30 am on TuTh WEH 5302.
Homework: Homework will normally be posted each Tuesday
and will be collected the following week at the start of your Thursday recitation. Your first homework assignment will
be posted on this Tuesday (Jan 11). Click here to be able to access the
list of the homework problems. Homework is the most important part of this course.
You should do ALL the assigned homework problems as they represent a significant class of
prototypical exam problems. Each homework should be turned in a specific format,
the link to which will be provided on the homework page. You should print it and
follow all the instructions written on it's cover page to recieve full credit in your
homework assignment. Absolutely no late homework assignments will be accepted.
If you are unable to attend your recitation, you must coordinate with your TA to turn in your homework
prior to the deadline.
Caution:
It is University policy that the work submitted by each student should
be that student's own work, and not the work of some other individual.
In the case of homework assignments, students are allowed to consult
outside sources such as books, tutors, websites, and friends, but it is
important that the submitted homework is written in the student's own
words and reflects that student's understanding of the homework
exercises. In particular, students who copy another individual's work
may be subject to significant penalty.
Quizzes: There will be a 10 minutes quiz
in your recitation every Thursday except the first week and the midterm exam weeks.
In these weekly quizzes, you will normally be tested upon the sections that were due in that day's homework.
There will NO make-up quiz except when a student documents an illness or
emergency at the earliest possible time.
Poppers: To encourage participation and attendance in recitation, you can expect a
short popper quiz which will typically contain multiple choice questions(MCQ). These MCQs are typically a simple check of
your understanding of the material. Your TA will have the authority to give that popper quiz at any time during the
session either on Tuesday or on Thursday. The points recieved in these will be counted as a bonus grade to your final
score. You can earn upto maximum of 5 points which can straight away be added to your final
score out of 100. Great advantage...Enjoy collecting points by going to recitation!
Note: It is your TA's responsibility to turn in your graded
assignments and quizzes in a timely manner. If you have any questions or concerns regarding the homework or quiz grading, you should first
consider to contact your TA. In case, it does not get resolved there then feel free to
schedule an appointment with me.
Exams: There will be two 50 mins in-class exams, scheduled as follows:
Exam I : Feb 04 (Friday)
Exam II : March 04 (Friday)
Exam Policies: All the exams will be closed book and
calculators will not be allowed. There will be no make-up exam except in the case of documented
illness or family emergency or documented University sponsored trips. If you wish to get your
exam regraded, you should staple a brief explanation (no more than 3 lines for each question)
and turn in to your TA within one week of the day the graded exam was returned to your section.
Student elligible for special accomodation must contact me at least
two weeks prior to the exam to the make arrangements.
Caution : Do not make any travel plans before the end date of the semester since no arrangements
can be made for scheduling the exam earlier than the official scheduled date.
Grading Scheme:
Low Exam score :30%
High Exam Score: 40%
Homework (drop lowest) : 15%
Quizzes (drop lowest) : 15%
Grading Scale:
A : 89.5 - 100
B : 79.5 - 89.4
C: 69.5 - 79.4
D : 59.5 - 69.4
The above grading scale is subject to change (these cut offs might be lowered slightly but will not be increased).
Academic Dishonesty:
A student's answers on a test or final exam are expected to reflect
that student's problem-solving ability. Students will not be allowed to
use calculators, books, or other materials unless otherwise indicated.
Communication with other individuals is also forbidden during tests and
the final exam. Students who violate this policy could recieve an "R" for that particular test, fail the course,
or even be brought up for university disciplinary action
(see http://www.cmu.edu/policies/documents/AcadRegs.html), possibly resulting in expulsion.
Email: Students are responsible for information about the course that is emailed to them using the email address
that the students provide to the CourseWare site or the PeopleSoft site. It is the student's responsibility to keep the email address on
file current and to make arrangements for email from the instructor, PeopleSoft, and CourseWare to reach the student.
Expectation:
You can expect to recieve a reply to your email within 24 hours during weekdays and within
48 hours during weekend.
Tentative week by week schedule
Week |
Topics |
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Jan 10 - 14
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Welcome and Introduction
Sequences (Sec. 8.1)
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Jan 17 - 21
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Newton's Method (Sec. 4.6)
Series (Sec. 8.2)
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Jan 24 - 28
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Integral and comparison Test (Sec. 8.3)
Alternating series and AST (Sec. 8.4)
Absolutely and conditionally convergent series(Sec 8.4)
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Jan 31 - Feb 04
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Ratio and Root Test
Exam I review
Exam I
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Exam I: Feb 04 |
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Feb 07 - 11
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Power series (Sec. 8.5)
TBA
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Feb 14 - 18
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TBA
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Feb 21 - 25
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TBA
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Feb 28 - Mar 04
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Review
Exam II
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Feb 28 : Last day of class
Exam I: Feb 04 |
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