Syllabus
MAT 2020, Fall 2022.
Instructor: L. Makar-Limanov
Office: 1119 FAB
Office Hours: Tuesday Thursday 1:00 pm – 2:00 pm.
e-mail: lml@wayne.edu
Required Text:
1. James Stewart, Daniel Clegg, and Saleem Watson,Calculus: Early Transcendentals, Ninth Edition, Cengage Learning, Boston, MA, 2021.
Course description 1. In this course you will learn how to recognize problems
in which the answer is given by an integral and how to write the answer in the
form of an integral.
2. You will learn several methods of calculating the integrals. In order to
be able to do this you must recall properties of derivatives and derivatives of
elementary functions. (See chapters 2 and 3 in your book.)
These two themes are covered in chapters 5, 6, 7, and 8.
3. In chapter 10 you will learn a new system of coordinatization of a plane
and a new method of describing curves on the plane.
4. We are also covering in our course so-called sequences and series. (Chapter
11.) You will learn how to make sense of sums with infinitely many terms and
how to represent some functions as “infinite polynomials”.
For this topic you have to repeat chapter 2 (limits).
If you want to write tests successfully you must spend as much time as you
can solving problems from your book.
Please send me questions you have about problems or other material from your
book by e-mail.
You are going to have 3 tests during the semester (100 points each).
The tests are going to be on Tuesdays with (at least) one week notice.
The final exam (200 points) will be on Tuesday December 20, 2:45–5:00 pm.
Your grade will be determined by the final exam and two better tests.
In order to pass the course your average grade must be at least 70%
and you should get at least 50 % on the final exam.
After completing this course, students will be able to evaluate integrals with
the following techniques: direct substitution, integration by parts, partial fractions, approximate integration, and to use tables of integrals.
Know the definition of an improper integral and how to compute improper integrals.
Be familiar with common applications of integration: finding the area between
curves; finding the volume of a solid; finding the work done by a nonconstant
force; computing the average value of a function; computing the moments and
center of mass of a laminar plate; and applications to economy such as computing consumer surplus.
Be able to recognize and to work with parametric and polar equations. Students should be able to sketch parametric and polar curves (with a graphing
calculator), compute tangents to the curve at a given point, and compute the
areas enclosed by such curves.
Be able to use the derivative to form a linear approximation to a curve at a
specified point, and use Newton’s method to find the root of an equation.
Know what a sequence is and how to take the limit of a sequence. Recognize
the difference between a sequence and a series. Find the sum of a geometric
series and of a telescoping series.
Be prepared to determine the convergence or divergence of an infinite series
using a variety of tests including the integral test, comparison tests, alternating
series test, ratio test and root test. Understand the difference between absolute
and conditional convergence.
Recognize a power series and functions defined in terms of power series. Find
the radius of convergence and interval of convergence of a given power series.
Write the Taylor or Maclaurin series expansion of a given function. Use Taylor
series to approximate a function with an nth order polynomial for applications
in physics and engineering.
Understand Cartesian and polar forms of complex numbers and be able to convert between them. Use DeMoivre’s Theorem to find the roots of a complex
number. Students will also be exposed to complex exponentials and Euler’s
formula.
Student Disabilities Services (edited statement from the SDS web site) If
you have a documented disability that requires accommodations, you will need
to register with Student Disability Services for coordination of your academic
accommodations. The Student Disability Services (SDS) office is located in the
Adamany Undergraduate Library. The SDS telephone number is 313-577-1851
or 313-202-4216 (Videophone use only). Once your accommodation is in place,
someone can meet with you privately to discuss your special needs. Student
Disability Services’ mission is to assist the university in creating an accessible
community where students with disabilities have an equal opportunity to fully
participate in their educational experience at Wayne State University.
Students who are registered with Student Disability Services and who are
eligible for alternate testing accommodations such as extended test time and/or
a distraction-reduced environment should present the required test permit to
the professor at least one week in advance of the exam. Federal law requires
that a student registered with SDS is entitled to the reasonable accommodations
specified in the students accommodation letter, which might include allowing
the student to take the final exam on a day different than the rest of the class.
Academic Dishonesty Plagiarism and Cheating (edited statement from the
DOSOs web site): Academic misbehavior means any activity that tends to
compromise the academic integrity of the institution or subvert the education
process. All forms of academic misbehavior are prohibited at Wayne State University, as outlined in the Student Code of Conduct
(http://www.doso.wayne.edu/student-conduct-services.html). Students who commit or assist in committing dishonest acts are subject to downgrading (to a
failing grade for the test, paper, or other course-related activity in question, or
for the entire course) and/or additional sanctions as described in the Student
Code of Conduct.
Cheating: Intentionally using or attempting to use, or intentionally providing or attempting to provide, unauthorized materials, information or assistance
in any academic exercise. Examples include: (a) copying from another students
test paper; (b) allowing another student to copy from a test paper; (c) using
unauthorized material such as a ”cheat sheet” during an exam.
Fabrication: Intentional and unauthorized falsification of any information
or citation. Examples include: (a) citation of information not taken from the
source indicated; (b) listing sources in a bibliography not used in a research
paper.
Plagiarism: To take and use anothers words or ideas as ones own. Examples
include: (a) failure to use appropriate referencing when using the words or ideas
of other persons; (b) altering the language, paraphrasing, omitting, rearranging,
or forming new combinations of words in an attempt to make the thoughts of
another appear as your own.
Other forms of academic misbehavior include, but are not limited to: (a)
unauthorized use of resources, or any attempt to limit another students access
to educational resources, or any attempt to alter equipment so as to lead to an
incorrect answer for subsequent users; (b) enlisting the assistance of a substitute in the taking of examinations; (c) violating course rules as defined in the
course syllabus or other written information provided to the student; (d) selling,
buying or stealing all or part of an un-administered test or answers to the test;
(e) changing or altering a grade on a test or other academic grade records.
Course Drops and Withdrawals In the first two weeks of the (full) term,
students can drop this class and receive 100% tuition and course fee cancelation. After the end of the second week there is no tuition or fee cancellation.
Students may drop for an additional two weeks without instructor permission
but will not receive a refund. Drops during the first four weeks of the term will
be removed from the students record. Students who wish to withdraw from the
class after the first four weeks can initiate a withdrawal request on Pipeline.
If the instructor approves the request, you will receive a transcript notation of
WP (passing), WF (failing), or WN (no graded work) at the time of withdrawal.
No withdrawals can be initiated after the end of the tenth week. Students enrolled in the tenth week and beyond will receive a grade. Because withdrawing
from courses may have negative academic and financial consequences, students
considering course withdrawal should make sure they fully understand all the
consequences before taking this step. More information on this can be found
at: http://reg.wayne.edu/pdf-policies/students.pdf
Student services The Academic Success Center (1600 Undergraduate Library)
assists student with content in select courses and in strengthening study skills.
Visit www.success.wayne.edu for schedules and information on study skills workshops, tutoring and supplemental instruction (primarily in 1000 and 2000 level
courses).
We are going to cover the following sections:
Chapter 5. 5.2, 5.3, 5.5 (1 and 1/2 lecture)
Chapter 6. 6.1, 6.2, 6.4, 6.5 (3 and 1/2 lectures
Chapter 7. 7.1, 7.2, 7.4, 7.6 – 7.8 (4 and 1/2 lectures)
First Test
Chapter 7. 7.4, 7.6 – 7.8 (4 and 1/2 lectures)
Chapter 8. 8.3, 8.4 (2 lectures)
Chapter 10. 10.1–10.4 (3 and 1/2 lecture)
Second Test
Chapters 3 and 4. 3.10, 4.8 (1 lecture)
Chapter 11. 11.1–11.11 (9 lectures)
Complex numbers (1 lecture).
Third Test