Winter 2011
Math 112: Calculus 1
Professor: Dr. Blake Peterson
Office: TMCB 193B
Office Phone: 422-7784
Class Time: MWF 11:00-11:50
Office Hours: MWF 10-10:45, W 1:30-2:30
and by appointment
email: blake@byu.edu
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 satisfied 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
final. 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 ”save without
submitting” button. Select this after each answer. If you lose your internet connection,
you can come back and finish the quiz later. Select ”submit all” when you are done with
the exam. You will need to finish 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
3 Midterms (175 pts each)
Final
225 pts.
525 pts.
250 pts.
1000 pts.
Learning Outcomes:
Students are expected to master the ”core topics” of Math 112, consisting of the material in the
first five 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 definition of limit, be able to use the definition of
limit to prove simple limit statements, recall and use limit theorems in evaluating limits
explain and use one-sided limits, limits at infinity, and infinite limits, apply limits to the
description of asymptotes of functions, and find lim f (x) for functions which are not
x®a
defined at a.
Continuity: Students will be able to recognize the definition 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 definition of a derivative and be able to use it to compute the derivative
of a function, use the differentiation formulas to find 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 find the first derivative of an
implicitly defined function, explain and use the interpretations of the second derivative,
compute derivatives of higher order, and be proficient 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
Rolle’s 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 first and second derivative tests to classify extrema, use the derivatives to find
critical points, inflection 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 L’Hopital’s Rules to evaluate limits.
The Definite Integral: Students will be able to explain and apply the graphical interpretation of
the definite integral as area, explain and apply the dynamic interpretation of the definite
integral as total change (given the velocity or acceleration, how do you find the
displacement?), recognize a correct definition of the definite integral, recall and use the
definition of the definite integral as a limit of Riemann sums, (that is, find 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 definite
integrals. “Interval properties” are properties pertaining to the interval of integration like
ò
b
a
f (x)dx = - ò f (x)dx and
a
b
ò
b
a
f (x)dx + ò f (x) dx =
c
b
ò
c
a
f (x) dx , recall and explain the
Fundamental Theorem of Calculus, find derivatives of functions defined as definite
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 definite integrals by antidifferentiation, and use a simple
substitution to find 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
Exam 2
Exam 3
Thursday-Saturday
Thursday-Saturday
Thursday-Saturday
January 27-29
February 24-26
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%
90% - 92%
87% - 89%
83% - 86%
80% - 82%
77% - 79%
73% - 76%
70% - 72%
67% - 69%
63% - 66%
60% - 62%
Below 60%
A
AB+
B
BC+
C
CD+
D
DE
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 qualified 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.