Analytic Geometry and Calculus with Review
Course Goals:
The students will
• review mathematical concepts and techniques needed to successfully study
calculus.
• be introduced to the concept of a function.
• work with functions algebraically, numerically and graphically .
• be introduced to the concepts of limits and continuity of functions.
• develop the concept of a derivative as both a rate of change and as the slope
of a tangent to a curve.
• learn techniques for finding derivatives of algebraic and exponential
functions
• relate all concepts studied to real world problems
• use the graphing calculator as a tool for visualizing calculus concepts
Course Materials:
Texts: Calculus, 6E ( Single Variable, Early
Transcendantals) by Stewart
A Companion to Calculus, 2nd ed. by Ebersole, Schattschneider, Sevilla, Somers
Calculator: The TI 83+ or TI 84+ calculator is recommended
and will be used for presentations, but any comparable graphing calculator with
which the
student is familiar with is acceptable.
Attendance:
• Regular attendance is necessary in order to be most successful. Poor
attendance will affect a student’s classwork grade.
• There will be no make-up for missed quizzes due to absences
• Make-ups for tests due to absences will be given only in pre-approved cases.
It is the student’s responsibility to contact me before the test is
administered unless an emergency situation can be verified.
Academic Honesty:
Please refer to Moravian’s “Policy on Academic Honesty”
that is outlined in the current Student Handbook.
Specifically, for this class
• you may use any notes, books or library sources for homework assignments
(graded or non-graded). You may also work with other students on these
assignments, but, you must indicate those with whom you conferred as well as be
responsible to explain all solutions by yourself .
• all tests and quizzes are to be completed by you alone, without the aid of
books, notes or formula sheets unless specifically permitted by the instructor.
• graphing calculators will be required as indicated by the instructor for
answering questions on assignments, tests and quizzes. However, a complete
discussion as to how they were used may be required.
Special Considerations:
Accommodations can be made for those students who have
disabilities or special needs.
These conditions must be verified by the appropriate college office.
Evaluation and Grading:
Practice is vital for developing the required Calculus
skills. It is expected that the student does all homework problems assigned.
Some will be graded while the rest could be checked for completion.
The student will be evaluated on the basis of three exams,
best four (out of five) quizzes, graded homework assignments, class
participation, and a cumulative final exam. Late assignments will be graded
with a 20% penalty for each day that they are late.
The percent breakdown of the Final Grade is as follows.
Tests |
45% |
Quizzes |
15% |
Graded Homeworks and Class
Participation |
15% |
Final Exam |
25% |
The Final Grade will be computed according to the
following guideline.
AVERAGE |
GRADE |
AVERAGE |
GRADE |
92-100% |
A |
72-77% |
C |
90-91% |
A- |
70-71% |
C- |
88-89% |
B+ |
68-69% |
D+ |
82-87% |
B |
62-67% |
D |
80-81% |
B- |
60-61% |
D- |
78-79% |
C+ |
0-59% |
F |
Math 106 Course Outline--Fall 2008
|
Stewart |
CTC |
Daily Assignments (Tentative) |
Symbols and Notation |
|
0-A |
|
Modes of Communication |
|
0-B |
Pg 6 # 1,3 |
The Cartesian Coordinate Plane |
|
1-A |
Pg 13 # 4,5 |
Graphs |
|
1-B |
Pg 18 #3 |
Lines and Their Equations |
|
1-C |
Pg 25 # 1,3 |
Parallel and Intersecting Lines |
|
1-D |
Pg 29 # 1,3,4 |
Distance Between Two Points |
|
1-E |
Pg 32 # 1,2 |
The Circle |
|
1-F |
Pg 34-35 # 1,3,5 |
Review and Extension |
|
Exercises |
Pg 36-37 # 1,3,7,13 |
Function Notation |
|
2-A |
Pg 44 # 2,4 |
Domain and Range of a Function |
|
2-B |
Pg 48-49 # 2,3,4 |
Four Ways to Represent Functions |
1.1 |
|
Pg 20-22 # 1,5,7,27,29,31 |
The Graph of a Function |
|
2-D |
Pg 59-61 # 1,4,5 |
Special Classes of Functions |
|
2-E |
Pg 72 # 1,3,5 |
Graphing Calculators and Computers |
1.4 |
|
Pg 51# 1,3,5,17,19 |
Transformations of Graphs |
2-F |
|
Pg 82 # 3,4 |
Combinations of Functions |
|
3-A |
Pg 96-97 # 1-6 |
New Functions from Old Functions |
1.3 |
|
Pg 43 #1,3.9,11, 29,35,39,51,55 |
|
|
|
|
Negative and Rational Exponents |
|
7-A |
Pg 219-220 # 1,5a-d |
Rules of Exponents |
|
13-A |
Pg 343-345 #1,3,5,8ab |
The Natural Exponential Function |
13-B |
|
Pg 349--350 # 1,2,4,5,6 |
Exponential Functions |
1.5 |
|
Pg 58 # 3,13,19,25 |
TEST 1 (Tentatively September 24) |
The Tangent and Velocity Problem |
2.1 |
|
Pg 87 # 3,5 |
The Limit of a Function |
2.2 |
|
Pg 97-98 # 5,7,9,15,19,21,25,27 |
Algebraic Simplification of Functions |
|
3-B |
Pg 110-111 # 1a,d,e, 5,7,8 |
Calculating Limits Using the Limit Laws |
2.3 |
|
Pg 106 -107 # 3,11-25 odds, 35, 39 |
Inequalities |
|
3-C |
Pg 116 # 1 Pg 122-123 # 2a-c,5 |
The Precise Definition of Limits |
2.4 |
|
Pg 117-118 # 1,3,7,15,19 |
Continuity |
2.5 |
|
Pg 128-129 # 3,5,7,17,35,37,41,43,47 |
Polynomials |
|
4-A |
Pg 141-42 # 3,4 |
Domains of Functions |
|
4-C |
Pg 156 # 1,2,3 |
Graphical Interpretation |
|
5-A |
Page 179 #4 |
Algebraic Manipulations |
|
5-B |
Pg 183 # 3,4 |
Limits at Infinity: Horizontal Asymptotes |
2.6 |
|
Pg 140-142 # 1,3,7,9,15,19,23,25,39,41,43 |
TEST 2 (Tentatively October 24) |
Applications |
|
6B |
Page 205-206 #4,6,8a,b |
Derivatives and Rates of Change |
2.7 |
|
Pg 150-151 # 3,7,9,13,25 |
The Derivative as a Function |
2.8 |
|
Pg 162-174 # 23,27,35,37 |
Derivatives of Polynomials and Exponential
Functions |
3.1 |
|
Pg 180-181 # 3-10,11-35odd, 39,41,45,49 |
The Product and Quotient Rules |
3.2 |
|
Pg 187-188 # 3-19 odd,27-33 odd |
The Chain Rule |
3.4 |
|
Pg 203-204 # 3-11odd,
17,19,21,25,47,51 |
Simplifying Derivatives |
|
7-C |
Page 227 # 1,3,4 Page 229 #6,7 |
Iteration |
|
10-A |
Pg 297 # 1a,d,2b, |
TEST 3 (Tentatively November 19) |
Implicitly Defined Functions |
|
9-A |
Pg 288 # 2 a-d,3a-d |
Solving Equations that Contain dy/dx |
|
9-B |
Page 292 # 2a-c,3a-c |
|
|
|
|
Implicit Differentiation |
3.5 |
|
Pg 213 # 1,5,7,25,33,35 |
Rate of Change of Rate of Change |
|
10-B |
Pg 303-305 # 1,2,4 |
Rates of Change in the Natural and Social
Sciences |
3.7 |
|
Pg 230-231 # 1,9,15,29 |
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