Winter 2011

**Math 112: Calculus 1**

**Professor: **Dr.
Blake Peterson

**Office: **TMCB
193B

**Office Phone: **422-7784 **email:** blake@byu.edu

**Class Time: **MWF
11:00-11:50

**Office Hours: **MWF 10-10:45, W 1:30-2:30

and by
appointment

**Texts: ***Single
Variable CALCULUS: Early Transcendentals * - 6th Ed**.** Volume 1, written by James Stewart

**Prerequisites: **

Math 110 and 111 or the
equivalent. This includes College Algebra and Trigonometry, but could also be
satisŽed with a good course in PreCalculus. Students will also be required to
take a pretest in order to exhibit competency in these areas. (See below).

**Pretest: **

Successful completion of
Math 112 requires a solid background in both College Algebra and Trigonometry.
Students are required to take a pretest on these topics. While the pretest may
be worth only one assignment, it is also required before we will grade the
Žnal. A pretest review can be found at the site http://mathonline.byu.edu. Log
in with your route y id and password. Click on Pretests and placement exams.
Scroll down to the Math 112 section. The review is one link, the exam the
other. When you are ready to take the pretest, make sure you select the correct
link! There are 3 pretests on the site.

While you take the pretest,
you will notice at the bottom of the page a Ósave without submittingÓ button.
Select this after each answer. If you lose your internet connection, you can
come back and Žnish the quiz later. Select Ósubmit allÓ when you are done with
the exam. You will need to Žnish the pretest before January 17 at 11:55 p.m.
You are allowed 2 chances to pass. If your score is below 75% then you do not
have the necessary skills to succeed in Calculus. Talk to your instructor about
your options, and what you can do to better prepare yourself.

**Preparation Time: **

Adequately prepared students
should expect to spend a minimum of two hours of work out of class for each
hour in class. This adds up to a minimum of 10 hours per week (plus class time)
for math 112. A minimal time commitment is likely to lead to an average grade
B-/C+ or lower. Much more time may be required to achieve excellence.

**Grading: ** Homework 225
pts.

3
Midterms (175 pts each) 525
pts.

Final __250
pts.__

1000 pts.

**Learning Outcomes: **

Students
are expected to master the Ócore topicsÓ of Math 112, consisting of the
material in the Žrst Žve chapters of the text. In particular, students are
expected to master the following topics:

*Limits of
Functions:* Students will be able to
explain intuitively and graphically the concept of limit of a function,
recognize the correct deŽnition of limit, be able to use the deŽnition of limit
to prove simple limit statements, recall and use limit theorems in evaluating
limits explain and use one-sided limits, limits at inŽnity, and inŽnite limits,
apply limits to the description of asymptotes of functions, and Žnd for
functions which are not deŽned at a.

*Continuity:* Students will be able to recognize the deŽnition of
continuity at a point, explain the graphical interpretation of continuity,
understand diﬀerent types of
discontinuities which can be rewritten so as to be continuous, use continuity
in evaluating limits of composite functions, apply the Extreme Value and
Intermediate Value theorems and know a correct statement of these theorems.

*The
Derivative*: Students will be able to
explain and apply the graphical interpretation of the derivative as slope,
explain and apply the dynamic interpretation of the derivative as rate of
change, know the deŽnition of a derivative and be able to use it to compute the
derivative of a function, use the diﬀerentiation formulas to Žnd the derivative of any elementary function (polynomial,
rational, root, exponential, logarithmic, trigonometric, inverse trigonometric,
hyperbolic, and all combinations and compositions thereof ), recognize and use
the common notations for the derivative, recall and use the relationship
between diﬀerentiability and
continuity, use implicit diﬀerentiation to Žnd the Žrst derivative of an implicitly deŽned function,
explain and use the interpretations of the second derivative, compute
derivatives of higher order, and be proŽcient in all the diﬀerentiation techniques, including the product rule,
and chain rule.

*Applications
of the Derivative*: Students will be
able to recall and explain the meaning of RolleÕs Theorem and the Mean Value
Theorem, use the derivative to describe the monotonicity of a function, use the
second derivative to describe the concavity of a function, use Žrst and second
derivative tests to classify extrema, use the derivatives to Žnd critical
points, inßection points, and local extrema, use derivatives to aid in
sketching, by hand, the graph of a function, solve optimization problems, solve
related rates problems, and use LÕHopitalÕs Rules to evaluate limits.

*The DeŽnite
Integral*: Students will be able to explain
and apply the graphical interpretation of the deŽnite integral as area, explain
and apply the dynamic interpretation of the deŽnite integral as total change
(given the velocity or acceleration, how do you Žnd the displacement?),
recognize a correct deŽnition of the deŽnite integral, recall and use the
deŽnition of the deŽnite integral as a limit of Riemann sums, (that is, Žnd
what a certain limit of Riemann sums is in terms of an integral), recognize an
integral which corresponds to a sequence of Riemann sums, recall and use
linearity and interval properties of deŽnite integrals. ŅInterval propertiesÓ
are properties pertaining to the interval of integration like and , recall and explain the Fundamental Theorem of
Calculus, Žnd derivatives of functions deŽned as deŽnite integrals with variable
limits including situations which will require the use of other rules of diﬀerentiation in conjunction with the fundamental
theorem of calculus; use the Fundamental Theorem to evaluate deŽnite integrals
by antidiﬀerentiation, and
use a simple substitution to Žnd an antiderivative.

**Calculators:**

Just like a pencil, paper,
or a textbook, a calculator is simply a tool that can be used to better
understand mathematics. __It is not a substitute for understanding.__ I will
use calculators on a regular basis to aid in the visualization of concepts and
you will be allowed to use a calculator on homework and midterm exams. If you
already have a graphing calculator, there is no need to buy a new one. If you
are going to buy a new one, I would recommend a TI-89 because it is what I will
be using for demonstration purposes in class.

**Homework: **

Homework will be collected
in class each Monday, Wednesday, and Friday. Any homework not handed in during
class is considered late. The lowest four homework scores will be dropped so __no ____late homework will be
accepted__. Only a portion of the homework assignment will be graded each day
so it becomes extremely important that you *attempt
every problem*. Although homework assignments will be handed in
individually, I strongly encourage students to *discuss homework with your classmates* in some form of informal
study groups. Solutions should be clearly labeled and in order. The style of
your written solutions should be very much like that of a text book example;
solutions should contain enough explanation so that one of your classmates
would be able to easily understand what you have done. The process of
justifying your own solution does a lot for solidifying the concept in your own
mind.

**Midterms: **

The midterm examinations
will take place about every 4-5 weeks as outlined by the dates below. The
midterms will be administered through the testing center. The midterm exams
will have two parts: a calculator portion and a non-calculator portion but
these exams are closed book and closed note.

*Exam 1 Thursday-Saturday January 27-29*

*Exam 2 Thursday-Saturday February 24-26*

*Exam 3 Thursday-Saturday March 24-26*

**Final:**

The final will be common to
all sections of calculus 1 and will be on Saturday, April 16 from 7-10 pm. __Calculators
will NOT be allowed on the final exam__.

**Math Lab:**

If
you feel that you would like extra help, please take advantage of the free
tutoring in the Math Lab on the first floor of the TMCB.

**Grade
Distribution:** The grades will be
distributed according to the scale below. If you obtain the specified
percentage indicated below, you are assured the grade associated with that
percentage.

93% - 100% A

90% - 92% A-

87% - 89% B+

83% - 86% B

80% - 82% B-

77% - 79% C+

73% - 76% C

70% - 72% C-

67% - 69% D+

63% - 66% D

60% - 62% D-

Below 60% E

**Preventing
Sexual Harassment: **

Title IX of the Education
Amendments of 1972 prohibits sex discrimination against any participant in an
educational program or activity that receives federal funds. The act is
intended to eliminate sex discrimination in education and pertains to
admissions, academic and athletic programs, and university-sponsored
activities. Title IX also prohibits sexual harassment of students by university
employees, other students, and visitors to campus. If you encounter sexual
harassment or gender-based discrimination, please talk to your professor;
contact the Equal Employment Oﬃce at 801-422-5895 or 1-888-238-1062 (24-hours), or
http://www.ethicspoint.com; or contact the Honor Code Oﬃce at 801-422-2847.

**Students
with Disabilities: **

BYU is committed to
providing reasonable accommodation to qualiŽed persons with disabilities. If
you have any disability that may adversely aﬀect your success in this course, please contact the
University Accessibility Center at 422-2767. Services deemed appropriate will
be coordinated with the student and instructor by that oﬃce.

**Academic Honesty:**

BYU students should seek to
be totally honest in their dealings with others. They should complete their own
work and be evaluated based upon that work. They should avoid academic
dishonesty and misconduct in all its forms, including plagiarism, fabrication
or falsification, cheating, and other academic misconduct. Students are responsible
not only to adhere to the Honor Code requirement to be honest but also to
assist other students in fulfilling their commitment to be honest.