MATH 31 - First Day Handout
Calculus II - Fall 2024
General information
The class webpage is a good source
for all class related information; in particular, homework
assignments will be posted on the class webpage weekly. Please
check it regularly.
Course description
A continuation of Mathematics 30.
Topics to be covered include techniques and applications of
integration, polar coordinates, improper integrals, introduction to differential
equations, infinite
series and power series representation of a function.
Prerequisite:
Mathematics 30 or placement.
Material to be
covered
The following chapters/sections of the textbook will be covered:
Chapter 6:
Sections 6.1 - 6.5
Chapter 7:
Sections 7.1 - 7.4, 7.7 - 7.8
Chapter 8:
Sections 8.1 - 8.2
Chapter 9:
Sections 9.3, 9.5
Chapter 10:
Sections 10.3 - 10.4
Chapter 11:
Sections 11.1 - 11.10
The particular week-by-week schedule of the course will correspond
to the weekly homework assignments, which are displayed on the
class webpage.
Teaching philosophy:
The main goal of this liberal arts GE course is to present the
mathematical way of thinking, centering on rigorous logic and
analytical reasoning. We will do this on the example of the
classical material of Integral Calculus and Infinite Series, going
back to the fundamental 17th century work of Isaac Newton and
Gottfried Wilhelm Leibniz and its 19th century presentation by
Augustin-Louis Cauchy and Karl Theodor Wilhelm Weierstrass, along
with other important mathematicians. The approach we take will be
largely theoretical, aiming to not only demonstrate computational
methods, but also to understand what makes them work. While we
will not be able to prove all the results presented, we will see
some proofs and discuss the underlying logic behind the main
concepts. In this way, this course will also serve as an
introductory exposition of the art of mathematical proof, which
may be different from a more computational approach to Calculus
taken in many high school courses.
Expected effort and learning outcomes:
A serious effort is usually required in order to
succeed in this class, including (but possibly not limited to) the
following:
- Regularly attending class, listening to lectures and taking
the lecture notes
- Carefully reading the material we cover in the textbook and
reviewing the lecture notes
- Doing all the homework assignments
While the actual time needed to perform these
tasks may depend on an individual student, you should plan for a
serious time investment in this course with 2-3 hours at home for
each hour in class, on average.
The main expected learning outcome for this class
is developing an understanding of the mathematical reasoning and
logic as demonstrated on the analytic theory of functions
discussed during course of this class. More specifically, we will
aim to develop basic familiarity with the following major topics:
- Mathematical meaning and applications of the Riemann integral
- Techniques of integration
- The theory of infinite series
- Function representation and integration using infinite series
- Performing necessary computations without a calculator
Grading policy
Class attendance and homework
completion are required parts of the course. Homework
assignments will be regularly posted on the course webpage and
collected in class on Thursdays. Late homework will not
be accepted.
There will be two in-class
midterm exams and the comprehensive final exam. Here is the exam schedule.
Midterm 1:
Thursday, October 10, in class
Midterm 2:
Thursday, November 7, in class
Final Exam:
Wednesday, December 11, 2:00 - 5:00 pm in Davidson
Make-up
exams are generally not given; exceptions will be
considered only in extraordinary circumstances, substantiated by
accompanying documentation and should be discussed with the
instructor as soon as possible.
The grade break-down will
be as follows:
The grading scale used for this
class will be:
- 95-100% = A, 90-94% = A-
- 85-89% = B+, 80-84% = B, 75-79% = B-
- 70-74% = C+, 65-69 % = C, 60-64% = C-
- 57-59% = D+, 52-56% = D, 50-51% = D-
- 0-49% = F
I reserve the right to introduce a curve (up or down) at the end
of the semester depending on the class's overall performance.
Additional resources
Tutoring
help is available at the Murty Sunak Quantitative and
Computing Lab (QCL): our designated QCL mentor is Ivan
Kolesnikov. QCL is the centralized hub for support
with all sorts of quantitative issues at CMC, including course
mentoring, training workshops and senior thesis and research
project assistance. QCL services are available by appointment
and on a walk-in basis. Please consult the QCL website for more
detailed information about the
services provided:
Class policies
The following are basic rules that all students should follow in
order not to disturb the class.
- Please make sure to turn off or silence your cell phones and
any other devices that make noise before entering class. Please
do not text or multitask in any way during the lecture: you are
expected to focus and pay full attention during our meetings.
- Please do not come late or leave early; if on some occasion it
is necessary and cannot be avoided, please do it in a way that
does not disturb the class.
The use of
calculators, or any other electronic devices, as well as any books
or notes, is prohibited during all tests.
Important dates
- September 8,
Monday: Last day for adding courses for the
Fall semester.
- October 14-15,
Monday-Tuesday: Fall break.
- October 17,
Thursday: Last day to drop courses without record.
- November 15, Friday: Last day to opt for CR/NC
grading in elective courses; last day to withdraw
voluntarily from a full semester course with a grade of "W".
- December 5, Thursday:
Last class meeting.
The instructor reserves the right to make changes to the
class policies.