Prerequisites The successful completion of one year
each of high school algebra 1,2, and
geometry.
Course Credit and Schedule.
One Saint Mary’s College unit
Sec 1: MWF 9:10-10:10
Sec 2: MWF 10:20-11:20
Text:
Thomas’ Calculus by Weir, Hass & Giordano, 11th ed. (ISBN 0-
321-18558-7) and Mckeague, Intermediate Algebra, 7th ed.
Brooks/Cole (ISBN 0534418252)
Course Description:
How do structural engineers predict how much the Bay Bridge will
sway during an earthquake? How does the Federal Reserve analyze
stock market fluctuations to help determine when to cut interest
rates? What model do bio logists use to describe the rate of stem
cell growth in human embryos? The answer to all of these
questions involves mathematical objects called functions. The
study of functions is where calculus begins! We will mostly look at
functions which will be important to us in calculus namely,
polynomial, logarithmic and exponential functions.
One of the great accomplishments in modern mathematics is to
apply these functions to study real world situations. Calculus
teaches you how to use functions to study velocities and
accele rations of moving bodies, find the firing angle that gives a
cannon its greatest range, or calculate the area of irregular regions
in the plane. Calculus is a really fun subject because you will learn
to use powerful ideas that took centuries to develop. It is also a
really challenging subject because it requires solid algebra skills
and has thought provoking concepts.
Homework:
Problems will be as signed at the end of each class. It is important
for your success in the course that you attempt to do those
problems before the following class meeting. The struggle to solve
them prepares you for the following class.
You may discuss the homework by forming a group and studying
with your peers. If you need help please come to my office or go to
Sichel 105, the Academic Support and Achievement Program, and
ask for a tutor. Act fast and do not fall behind.
A completed homework assignment should be folded
lengthwise in half. On the outside front half, print your name,
the assignment number , the due date of the assignment, and
the time you spent doing the assignment. Please staple your
homework.
Attendance:
Attendance is required and roll will be taken at the
beginning of
each hour. If you are not in your seat when roll is taken, you may
be considered absent, so be on time. You are allowed to miss three
classes without affecting your grade. After your grade is dropped
one step (A- to B+, C+ to C, etc.). Thereafter, each two successive
absences your grade is dropped one step further. If there is a major
illness or incapacitation, speak to your instructor. SMC athletes are
excused to attend team commitments but are responsible for
notifying me ahead of time (see below).
Exams:
There will be three midterm examinations and a final exam.
Suppose a student receives the following grades.
| First Midterm |
 |
| Second Midterm |
| Third Midterm |
| Final Exam |
| Homework Grade |
Then the lowest of the Midterm/Final Exam grades above is
dropped. If you miss a midterm exam that is the grade you drop.
The final grade for the course is the average of the remaining five
grades, in this example a B-. The Homework Grade cannot be
dropped.
Honor code:
Students are expected to abide by the SMC honor code when
taking exams and doing course work.
Exam Dates:
Midterm exams:
Friday, September 22 classtime 1 hour exam
Wednesday, October 11 classtime 1 hour exam
Friday, November 10 classtime 1 hour exam
Final exam:
Sec 1 (9:10am class): Wednesday 9-11 Dec. 6
Sec 2 (10:20 am class) Monday 11:30-1:30 Dec. 4
SMC Athletes:
No later than September 10, I need to receive from each SM C
athlete a statement indicating:
Your name,
The sport you play, and
The class dates that you will miss due to team commitments,
This statement must be written and signed by the athlete.
Schedule of Topics
Week 1
Functions and relations, arrow diagrams, sets of ordered
pairs , domain and
range restrictions of a function, introduction to graphing.
Algebra review: real numbers, equations and inequalities in one variable ,
exponents
Week 2
Vertical and horizontal line test, graphing functions like
y=x5 and y=1/x,
square root function , piecewise functions, the inverse of a function.
Algebra review: exponents and polynomials, Foil, factoring
Week 3
Decomposition of functions, translates of basic functions
(for example
y=(x+3)2 +7 is a translate of y=x2) , introduction to limits
Algebra review: factoring, rational expressions , complex fractions
Week 4
Limits , review for test 1.
Algebra review: exponents and polynomials, rational expressions
Week 5
Limits, continuity
Algebra review: rational exponents and roots
Week 6
Introduction to the derivative: interpretations and
applications
Algebra review: rational exponents and roots
Week 7
The derivative of a function: interpretations.
Algebra review: complex numbers, rational exponents and roots
Week 8 Review for test 2
Week 9
Interpretations of the derivative, the power rule,
functions whose
derivative don’t exist
Algebra review: rational exponents and roots
Week 10
The derivative of a sum of functions , product rule,
quotient rule
Algebra review: quadratic functions
Week 11 Introduction to logs
Week 12 The derivative of log, review for test 3
Week 13 The chain rule, implicit differentiation
Week 14 Higher derivatives, applications of calculus to physics, review for
final
