SYLLABUS
Math 111 - Calculus I.
Fall 2003
INSTRUCTOR: John Harrison
OFFICE NO: Stark Learning Center Room 231
OFFICE PHONE: X4845
OFFICE HOURS: MWF 9 – 10 AM or by appointment
COURSE TOPICS
In the first part of this two-semester sequence in calculus, we'll study the basic concepts of differential calculus which includes the study of some fundamental properties of real-valued functions. These concepts are limit of a function at a point, continuity, differentiability and integrability of functions. We shall also apply these concepts to help us solve some applied problems generated from many different areas including biology, buisness, physics, and engineering.
In this course, we will make extensive use of the graphing calculator as a tool to help analyze these functions. A graphing calculator(preferably a TI-83 or TI-83 Plus) is REQUIRED of all students in this course. Some of the hand-in homework problems and examination questions which you will be assigned in this course will require the use of a graphing calculator.
COURSE OBJECTIVES
Upon completion of this course, the student will have achieved the following objectives.
· Understanding of the notions of limit, derivative, and integral and their applications in solving the classical tangent line/velocity problems and the area problems.
· Ability to effectively compute limits, derivatives and some antiderivatives using classical techniques.
· Ability to estimate limits, derivatives and some antiderivatives/definite integrals using technology (in particular, the graphing calculator).
· Ability to apply limits, derivatives and integrals as tools for solving selected problems that arise in biology, business, the physical sciences, and engineering.
· Ability to articulate their solutions to such problems in both oral and, in particular, written form, through selected homework problems, in-class discussions, quiz questions, and examination questions.
You will be assigned a set of exercises at the end of each class. The exercises are selected from the textbook and are intended as examples of the types of problems you should be able to solve. This list is of course NOT COMPLETE. Read over your notes and textbook before doing these exercises and prepare your solutions so we can DISCUSS then during discussion sections. Mathematics is not a spectator sport, you must do the problems to learn the material.
TEXTBOOK: Calculus: Concepts and Contexts, 2nd Edition by Stewart, Brooks/Cole Publishing, Inc.
EVALUATION
Three one-hour examinations, hand-in homework assignments, weekly quizzes (usually on Fridays except for weeks of examinations/holiday weeks -- no quiz week of November 25th due to Thanksgiving) and a comprehensive final examination will make up the components of your grade in this course. The grade components will be weighted as follows:
Weighting of Grades
High Exam Grade: 20%
Median Exam Grade: 15%
Low Exam Grade: 10%
Weekly Quizzes: 15%
Hand-In Assignments: 10%
Final Examination: 30%
MAKEUP POLICY ON EXAMINATIONS, QUIZZES, and HOMEWORK ASSIGNMENTS
(1) Quizzes can not be taken at a later date unless there is documented evidence of serious, long term illness or a family emergency (greater than a minimum of fourteen consecutive days) signed by a physician and the Dean of Student Affairs. Under these conditions, arrangements will be made with the student to make up the necessary quizzes. Under NO OTHER CIRCUMSTANCES is it allowable to make up a quiz. Your TWO LOWEST QUIZ GRADES will be dropped from your quiz average.
(2) Homework assignments are expected to be turned in ON TIME. Late homework assignments will not be accepted unless there is documented evidence of illness or a family emergency (see (1) above).
(3) Semester examinations can not be made up unless there is a documented justification on why the student was unable to take the exam on the specified date. The justification must be approved by me in consultation with the student and the Dean of Student Affairs (if necessary). The student should make every effort to contact me IN ADVANCE if he/she is unable to attend an examination to make such a request.
WORST CASE GRADE CUTOFFS
If your grade falls within the interval given in the left-hand column below, you will receive a final grade in this course NO WORSE than the letter grade in the right-hand column on the next page:
Grade Conversion Table
>=90 : A = 4.0
85-<90 : B+ = 3.5
80-<85 : B = 3.0
72-<80 : C+ = 2.5
60-<72 : C = 2.0
55-<60 : C- = 1.5
50-<55 : D = 1.0
<50 : F = 0.0
I will adhere to the university's course withdrawal policy (see the Wilkes Student Handbook).
TENTATIVE LECTURE SCHEDULE - MATH 111
FALL 2003
1. Week of 8/25: What is calculus?; Introduction to the notions of the area problem, the tangent problem, the velocity problem, and finding limiting values of sequences, sums, and functions; review on basic terminology involving functions (including domain, co-domain, range, and invertibility of functions); review of exponential and logarithmic functions (parts of preview section, section 1.5, and 1.6 of textbook: Quiz #1: Friday, August 29th).
2. Week of 9/2: Completion of review on exponential and logarithmic functions; slopes of secant lines; the notion of limit and slopes of tangent lines; calculating average velocities; the notion of limit and instantaneous velocity (parts of sections 1.6 and 2.1 of textbook: Quiz #2: Friday, September 5th).
3. Week of 9/8: Techniques for understanding and computing limits of functions including the following: intuitive notion of a limit of a function of one variable; calculating limits algebraically; estimating limits using the graphing calculator; calculating one-sided limits; general rules for computing limits of functions; the notion of continuity of a function at a single point and on a domain D (parts of sections 2.1-2.4 of the textbook: Quiz #3: Friday, September 12th).
4. Week of 9/15: Computing limits via "pinching"; Rules for constructing continuous functions out of other continuous functions; limits at infinity; review for exam #1(parts of sections 2.3 - 2.5 of the text: EXAM #1: Friday, September 19th).
5. Week of 9/22: Go over exam #1; more on limits at infinity and horizontal asymptotes; more on average vs. instantaneous rates of change; the tangent-line problem and the definition of a derivative of a function at a real-number; the relationship between differentiability and "smoothness"; calculating derivatives of functions using the definition of derivative (parts of sections 2.5 - 2.8 of the text: Quiz #4: Friday, September 26th).
6. Week of 9/29: More on computing derivatives using the definition; the relationship between derivatives and linear approximations of functions at a given value; higher-order derivatives; learning "global" information about a function using the derivative; introduction to basic techniques for computing derivatives formulas(parts of sections 2.8, 2.9, 2.10, and 3.1 of the text: Quiz #5: Friday, October 3rd).
7. Week of 10/6: Methods for computing derivatives of functions including: Derivatives of polynomials, exponential, and trigonometric functions; the sum, product, and quotient rules; compositions of functions and the Chain Rule (parts of sections 3.1, 3.2, 3.4, and 3.5 of the textbook: Quiz #6: Wednesday, October 8th or Thursday, October 9th; OUT OF TOWN: Tuesday, October 7th – Wednesday, October 8th; FALL BREAK – Friday, October 10th ).
8. Week of 10/13: More on the Chain Rule; selected applications of the derivative; review for exam #2; go over exam #2 (parts of sections 3.3 and 3.5 of the textbook: EXAM #2: Wednesday, October 15th or Friday, October 17th; UNIVERSITY COURSE WITHDRAWAL DATE: Friday, October 17th).
9. Week of 10/20: Differentiating relations and implicit differentiation; differentiation of logarithmic functions, approximations and differentials; introduction to related rate problems (parts of sections 3.6, 3.7,3.8, and 4.1 of textbook: Quiz #7: Friday, October 24th).
10. Week of 10/27: More on related rates problems; absolute vs relative extrema of functions and the extreme-value theorem; where is a function increasing/decreasing; concavity of functions; the first and second derivative tests (parts of sections 4.1 - 4.3 of textbook: Quiz #8: Friday, October 31st).
11. Week of 11/3: Techniques for analyzing and graphing functions; optimization problems; computing limits of indeterminate forms using L'Hopital's Rule (parts 4.4, 4.5, and 4.6 of textbook: Quiz #9: Friday, November 7th).
12. Week of 11/10: More on L'Hopital's Rule; what is an antiderivative; rules for computing antiderivatives; review for exam #3 (parts of sections 4.6 and 4.9 of the textbook: EXAM #3: Friday, November 14th).
13. Week of 11/17: Go over exam number 3; more on finding antiderivatives including substitution and solving IVP's; finding areas under curves; the distance problem; Riemann Sums and definite integrals; the Fundamental Theorem of Calculus (FTOC) (parts of sections 4.9, 5.1, 5.2, and 5.3 of the textbook: Quiz #10: Friday, November 21st).
14. Week of 11/24: Computing definite integrals using the FTOC; techniques for calculating antiderivatives including simple substitution (parts of sections 5.3, 5.4 and 5.5 of the textbook: NO QUIZ).
15. Week of 12/1: More on simple substitution and applications of the Fundamental Theorem of Calculus; integration by parts (time permitting); review for final examination (parts of sections 5.5 and 5.6 of the textbook: Quiz #11: Thursday, December 4th).