CALCULUS I
MATH 261 SPRING 2010
Instructor: Dr. R. P. Webber
Office and hours: East Ruffner 332. Hours MF, 2 - 3:30; T 2 - 3; and by appointment or coincidence
Telephone: 395-2192
email: webberrp@longwood.edu
Course description: The basic ideas of differential calculus and analytic geometry. Application of the derivative. Antiderivatives. 4 credits.
Course objectives: The student will be able to differentiate elementary functions. The student will be able to find antiderivatives by substitution. The student will be able to find the graph of a derivative, given the graph of its function, and conversely. The student will be able to calculate limits. The student will be able to find rates of change. The student will be able to use a computer algebra system to solve computationally difficult differential calculus problems.
Text: Rogawski, Single Variable Calculus Early Transcendentals. W.H. Freeman, 2008.
Computer algebra system: We will use Maple, which is available in the computer lab. Maple is a commercial product. You may purchase it for your PC if you like, although it is not required.
Course requirements and grading: There will be three tests, counted equally, which will comprise 40% of your course grade. Your composite lab grade will count 25% of your course grade, your class participation grade will count 10%, and the final exam will count the remaining 25%. The grading scale goes by tens: 90 - 100, A; 80 - 90, B; 70 - 80, C; 60 - 70, D; below 60, F.
Homework: Problems will be assigned regularly, and everyone is expected to do them. They will not be collected without warning, and it is your responsibility to do all of the assigned problems. Feel free to work with others on the homework problems, and ask me about problems that you cannot solve.
Labs: These problems will be done in groups. They will be computationally challenging (and thus best done on a computer) or intellectually challenging (and thus best done in cooperation with others), or occasionally both! You will be expected to begin work on these problems in the lab class meeting and to complete them out of class if necessary. You will hand in one solution to each problem from the group, and every member of the group will receive the same grade. Each lab assignment will have a due date, and failure to hand it in by the start of class on the due date will result in a penalty of 25% per class day late.
Class participation: Often you will be asked to work in groups in class. Working in small groups of three or four (which need not be the same groups as in the lab), you will be asked to solve a problem and present your results to the class. Missed class participation sessions cannot be made up, but you will be allowed one absence from a class participation session without penalty. You will receive a grade of 0 for each additional missed session.
Attendance: Your attendance is expected at all classes. Makeup tests will be given reluctantly, and then only upon presentation of a doctor's excuse. Makeup tests are always more difficult than regular tests, regardless of the reason for absence. You may not make up missed class participation sessions.
Honor code: I subscribe to the Longwood University honor system, which, among other things, assumes you do not cheat and that you take responsibility to see that others do not. Infractions will be dealt with harshly. A student who is convicted of an Honor Code offense involving this class will receive a course grade of F, in addition to any penalties imposed by the Honor Board.
Course schedule:
Week 1 Jan 12 - 15 | Chapter 1: Precalculus review |
Week 2 Jan 19 - 22 | 2.1 - 2.4: Limits done numerically and graphically |
Week 3 Jan 25 - 29 | 2.4 - 2.8: Limits done algebraically; Intermediate Value Theorem |
Week 4 Feb 1 - 5 | 3.1, 3.2: Derivatives done numerically and geometrically |
Week 5 Feb 9 - 12 | Review, catchup, TEST |
Week 6 Feb 15 - 19 | 3.3 - 3.5: Differentiation formulas |
Week 7 Feb 22 - Feb 26 | 3.6 - 3.9: Chain rule; more formulas |
Week 8 Mar 1 - 5 | 3.10 - 4.1: Related rates, linear approximation |
Spring Break | |
Week 9 Mar 15 - 19 | Review, catchup, TEST |
Week 10 Mar 22 - 26 | 4.2 - 4.4: Mean Value Theorem; graphing |
Week 11 Mar 29 - Apr 2 | 4.5, 4.6: Graphing; max-min problems |
Week 12 Apr 5 - 9 | 4.7 - 4.9: Finish differentiation; antiderivatives |
Week 13 Apr 12 - 16 | 5.6: Substitution |
Week 14 Apr 19 - 23 | Review, TEST, review |
Friday, April 30, 8 - 10:30 a.m. EXAM | In slot scheduled for 12:30-1:45 TR classes (i.e., during the lab time exam period) |
WHAT EVERY CALCULUS STUDENT SHOULD KNOW
ABOUT TRIG
Definitions of the trig functions
Basic identities
How to convert between radians and degrees
Values of the trig functions at the standard angles: and their multiples
Graphs of , cos x, and tan x and their periodic properties
Law of Sines and Law of Cosines
WHAT EVERY CALCULUS STUDENT SHOULD KNOW
ABOUT LOGS AND EXPONENTIALS
Their graphs
Where each is increasing and decreasing
Their limiting values
That they are inverses of each other
Their use in solving equations when the variable is in an exponent