MATHEMATICS 121 - CALCULUS 1
Jeff Spielman
270H Trexler
spielman@roanoke.edu
Office: 9:40 –10:40 MWF 1:00-2:00 Tues 2:45-3:45 Thurs
(Also by appointment)
Text:
375-2435
7:00 – 9:00 Tuesday Evening
Calculus, Concepts and Connections by Smith and Minton
Course Objectives
The main objective of this course will be to give you the opportunity to learn as much as
possible about the important and relevant topics associated with differential and integral calculus.
It is well-known that the study of Calculus provides the gateway to modern science and
mathematics. Calculus is also used extensively by Economists, Social Scientists, and Computer
Scientists: even the weatherman uses Calculus! Calculus has been around for hundreds of years
already and it sure looks like it will be a vital topic of study for many hundreds more.
The opportunity to learn will consist, on a daily basis, of a reading assignment with an
associated set of exercises a few of which are to be completed and handed in at the next class
meeting. During class we will discuss the reading material and exercises and you will be required
to participate in a daily Reading Survey. The hand-in exercises will be graded and returned
promptly; the reading survey results will be almost immediate. The appropriate sections from the
text are listed separately with the day on which they will be covered in class. In addition to in-class
discussions, I will have regular office hours of which I encourage you to take advantage, when the
need arises. Also, one of the four faculty members teaching freshman calculus this semester will
available from 7 until 9 in the evening, four different evenings per week, for any student in this
course.
Reading the Text
While it is certainly important to read the examples of worked out problems and the techniques that
are used for solving them, be very careful that you do not concentrate completely on these parts of
the text. It is probably a better idea to first make sure that you understand the purpose of the
section and how the current material might depend on previous material. This will help you to
avoid the pitfall of temporarily memorizing a few techniques without any real depth to your
understanding. The main idea here is to learn something that will stay with you.
Course Topics
This course is an introduction to the study of differential and integral calculus. The main goal of this
course is to provide you with an understanding of the concepts associated with this subject; in
particular, a conceptual understanding of the derivative and integral will have the highest priority.
Also emphasized will be the ability to use calculus in applications and to recognize those
applications for which calculus is an appropriate analytic tool. The concepts of this course will be
developed by using symbolic, graphical and numerical strategies. A Course Outline is provided on
a separate page.
Assigned Homework
Exercises will be assigned every day to give you the opportunity to enhance your understanding of
the concepts and to practice the required mechanical skills. These exercises will be collected
every day and graded, partially based on completeness and partially on correctness. As mentioned
earlier, pay careful attention to the context in which these exercises are assigned, so that you can
more easily learn and remember the techniques needed for actually solving them. Your success in
this course will depend greatly upon the quality of your work. Spending “extra” time redoing some
of the exercises can be of some benefit, but is much less important than using that same time to
increase your understanding of the concepts that those exercises represent.
Co-curricular Requirement
You are required to attend two Mathematics Department sponsored co-curricular events and to
write a report (one to two paragraphs) about each event. Your report should contain two pieces
of information: (1) a summary of the event and (2) a personal reflection. Each report will count
the same as one homework grade.
Course Outline for Mathematics 121, Fall 2005
Wed
Aug 29
Thu
Aug 30
Fri
Aug 31
Mon
Sept 3
Wed
Sept 5
Thu
Sept 6
Fri
Sept 7
Mon
Sept 10
Wed
Sept 12
Thu
Sept 13
Fri
Sept 14
Mon
Sept 17
Wed
Sept 19
Thu
Sept 20
Fri
Sept 21
Mon
Sept 24
Wed
Sept 26
Thu
Sept 27
Fri
Sept 28
Mon
Oct 1
Wed
Oct 3
Thu
Oct 4
Fri
Oct 5
Mon
Oct 8
Wed
Oct 10
Thu
Oct 11
Fri
Oct 12
Fall Break
Mon
Oct 22
Wed
Oct 24
Thu
Oct 25
Fri
Oct 26
Mon
Oct 29
Wed
Oct 31
Thu
Nov 1
Fri
Nov 2
Mon
Nov 5
Wed
Nov 7
Thu
Nov 8
Fri
Nov 9
Mon
Nov 12
Wed
Nov 14
Thu
Nov 15
Fri
Nov 16
Mon
Nov 19
Thanksgiving
Mon
Nov 26
Wed
Nov 28
Thu
Nov 29
Fri
Nov 30
Mon
Dec 3
Wed
Dec 5
Thu
Dec 6
Fri
Dec 7
Mon
Dec 10
1.1
Preview, small group discussion
Lab 1: Introduction to the TI-89
1.2
The Concept of a Limit
1.3
Computation of Limits
1.4
Continuity and Its Consequences
Lab 2: Loss of Significance Errors
1.5
Limits Involving Infinity
2.1
Tangent Lines and Velocity
2.2
The Derivative
Lab 3: Velocity
2.3
The Power Rule
2.4
The Product and Quotient Rule
Review
**** TEST 1 ****
2.5
The Chain Rule
2.6
Derivative of Trigonometric Functions
2.7
Derivatives of Exponential and Logarithmic Functions
Lab 4: Parametric Equations
2.8
Implicit Differentiation
2.9
The Mean Value Theorem
3.1
Linear Approximations
Lab 5: Newton’s Method
3.2
Indeterminate Forms, L’Hopitals Rule
3.3
Maximum and Minimum Values
Review
**** TEST 2 ****
3.4
Increasing and Decreasing Functions
3.5
3.5
Concavity
Curve Sketching
Lab 6: Curve Sketching
3.6
Optimization
3.7
Rates of Change Applications
4.1
Area Under a Curve
Lab 7: Sums and Area
4.1
Area Under A Curve/The Definite Integral
4.2
The Definite Integral
Review
**** TEST 3 ****
4.3
Antiderivatives
4.4
The Fundamental Theorem of Calculus
4.5
Integration By Substitution
Lab 8: Numerical Integration
4.6
Integration By Parts
4.6
Integration By Parts Cont…
4.10
4.10
Improper Integrals
Improper Integrals Cont…
Lab 9: Calculator Integration
6.1
Growth and Decay
6.2
Separable Differential Equations
Review
**** TEST 4 ****
Review for Final Exam
8:30 – 11:30am
Final Exam
Reading Surveys
These will normally be administered through the use of the i-clicker system. You are responsible
for (1) bringing your “clicker” to every class meeting and (2) being certain that your “clicker” is set to
the class frequency during the survey. Instructions will be given and reminders will be frequent.
The system is not complicated to use, but you do need to pay attention.
Grading Policy
The grade in this course will be based on 4 tests, graded homework, nine lab assignments, and a
comprehensive final as described:
4 tests @ 100 points
Reading Surveys
Graded Homework
Lab assignments
Final examination
Total
= 400 points
= 75 points
= 75 points
= 100 points
= 100 points
= 750 points
Grading scale (Percent of total)
92-100 A
90- 91 A80-81 B-
88-89 B+
82-87 B
70-71 C-
78-79 C+
72-77 C
60-61 D-
68-69 D+
62-67 D
Below 60 F
Make-up Tests
As a general policy, make-up tests will not be given. If you miss a test (not the final!), your
course grade will be based on the remaining 600 points (plus whatever sympathy you can wring
out of me!) with the percentages given above still in effect.
Late Homework
This is an undefined term! Homework assignments are due at the beginning of class on the due
date. If you anticipate a problem, you certainly may hand the assignment in early!
Attendance Policy
Attendance in all classes is extremely important and is expected. You are responsible for all
classes missed. Be sure to read the attendance policy in the catalog. While there is on official
attendance policy for this course, attendance will be taken into consideration for “border-line” final
course grades.
Academic Integrity
Absolute academic integrity is expected of all students at all times; the details of this policy are
given in the brochure, "Academic integrity at Roanoke College". In particular, you are expected to
do your own work on all tests and on all other graded work (including lab write-ups). Also, see
"Calculator/Technology Policy" below.
Calculator/Technology Policy
We will be using the TI-89 for much of the work in this course and you are certainly encouraged to
use your calculator to help with any work done in this course. During tests, however, you may
not, under any circumstances, share a calculator with another student. Also, cell phones
must be turned off and out of sight during tests.