MATHEMATICS 121 CALCULUS 1
JeffSpielman 270H Trexler 3752435
Office: 9:40 –10:40 MWF 1:00-2:00 Tues 2:45-3:45 Thurs 7:00 – 9:00 TuesdayEvening (Also by appointment)
Text: 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. Theseexercises 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
WedAug 291.1Preview, small group discussion
ThuAug30Lab 1: Introduction to the TI-89
FriAug 311.2The Concept of a Limit
MonSept 31.3Computation of Limits
WedSept 51.4Continuity and Its Consequences
ThuSept 6Lab 2: Loss of Significance Errors
FriSept 71.5Limits Involving Infinity
MonSept 102.1Tangent Lines and Velocity
WedSept 122.2The Derivative
ThuSept 13Lab 3: Velocity
FriSept 142.3The Power Rule
MonSept 172.4The Product and Quotient Rule
WedSept 19Review
ThuSept 20**** TEST 1 ****
FriSept 212.5The Chain Rule
MonSept 242.6Derivative of Trigonometric Functions
WedSept 262.7Derivatives of Exponential and Logarithmic Functions
ThuSept 27Lab 4: Parametric Equations
FriSept 282.8Implicit Differentiation
MonOct 12.9The Mean Value Theorem
WedOct 33.1Linear Approximations
ThuOct 4Lab 5: Newton’s Method
FriOct 53.2Indeterminate Forms, L’Hopitals Rule
MonOct 83.3Maximum and Minimum Values
WedOct 10Review
ThuOct 11**** TEST 2 ****
FriOct 123.4Increasing and Decreasing Functions
Fall Break
MonOct 223.5Concavity
WedOct 243.5Curve Sketching
ThuOct 25Lab 6: Curve Sketching
FriOct 263.6Optimization
MonOct 293.7Rates of Change Applications
WedOct 314.1Area Under a Curve
ThuNov 1Lab 7: Sums and Area
FriNov 24.1Area Under A Curve/The Definite Integral
MonNov 54.2The Definite Integral
WedNov 7Review
ThuNov 8**** TEST 3 ****
FriNov 94.3Antiderivatives
MonNov 124.4The Fundamental Theorem of Calculus
WedNov 144.5Integration By Substitution
ThuNov 15Lab 8: Numerical Integration
FriNov 164.6Integration By Parts
MonNov 194.6Integration By Parts Cont…
Thanksgiving
MonNov 264.10Improper Integrals
WedNov 284.10Improper Integrals Cont…
ThuNov 29Lab 9: Calculator Integration
FriNov 30 6.1Growth and Decay
MonDec 3 6.2Separable Differential Equations
WedDec 5Review
ThuDec 6**** TEST 4 ****
FriDec 7Review for Final Exam
MonDec 10 8:30 – 11:30amFinal 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 = 400 points
Reading Surveys= 75 points
Graded Homework= 75 points
Lab assignments = 100 points
Final examination = 100 points
Total = 750 points
Grading scale (Percent of total)
92100 A 8889 B+ 7879 C+ 6869 D+ Below 60 F
90 91 A 8287 B 7277 C 6267 D
8081 B 7071 C 6061 D
Make-up Tests
As a general policy, makeup 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 RoanokeCollege". 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 withanotherstudent. Also, cellphones must be turned off and out of sight during tests.