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Southwestern College
2625 E. Cactus Road, Phoenix,
AZ 85032
Phone:
602-489-5300 Calculus I
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Course Information:
Course Name
Calculus I
Course Number
SM 130
Semester Offered - Fall 2009
Instructor Information:
Name - Dr. Warren Pettitt
Office location Second floor of
Doerksen Administration building
Office phone 602 489 5300 ext 119
email address warren.pettitt@swcaz.edu
Office hours Daily 8:30 to 9:10
and 3:00 to 3:45
Course meeting Days August 20th to December 11th
Course meeting Time M,W,F 10:00- 10:50
Course meeting Place A211
Course Description: Calculus is
about the relation between a quantity and its rate of change. For an example,
if the quantity is the distance travelled at a given time, then its rate of
change is velocity. If the velocity is constant, then calculus is not required:
the distance travelled is the product of the elapsed time and the velocity. But
when the velocity is not constant, then this formula doesn't apply.
Nonetheless, the distance and velocity are intimately related. If the distance
travelled at all times is known, then the velocity at any given time can be
determined; and if the velocity at all times is known, then
the distance travelled at any given time can be determined. These two
operations are called differentiation and integration.
Prerequisites: Acceptable score on the math placement exam
Course Student Learning Outcomes:
Functions, Graphs and
Limits
a.
Plot points on a coordinate plane and interpret data presented graphically
b.
Find the distance between two points in a coordinate plane
c.
Find the x- and y- intercepts of graphs of equations algebraically and
graphically using a graphing utility
d.
Find the points of intersection of two graphs algebraically and graphically
using a graphing utility
e.
Find the slope between two points and use the slope-intercept and point-slope
forms to graph equations
f.
Find equations of parallel and perpendicular lines
g.
Use vertical line test to determine functions
h.
Use function notation to evaluate functions
i.
Determine the domain and range of functions algebraically and graphically
j.
Combine functions to create other functions
k.
Determine whether limits exist. If they do, find the limits
l.
Find one-sided limits
m.
Use the definition of continuity to determine if a function is continuous at a
point, on an open or on a closed interval
II. Differentiation
a.
Approximate the slope of a tangent line to a graph at a point
b.
Interpret the slope of a graph
c.
Use the limit definition to find the derivative of a function and the slope of
a graph at a point
d.
Use the derivative to find the derivative of a function and the slope of a
graph at a point
e.
Use the graph of a function to recognize points at which the function is not
differentiable
f.
Find the derivative using the constant rule, the power rule, the constant
multiple rule, and sum and difference rules
g.
Find the average rate of change of a function over an interval and the
instantaneous rate of change at a point
h.
Find the velocity of an object that is moving in a straight line
i.
Find the derivative using the product rule, quotient rule and chain rule
j.
Find higher order derivatives
k.
Find and use the position function to determine the velocity and acceleration
of a moving object
l.
Find derivatives implicitly
m.
Solve related-rate problems
III. Applications of
Derivatives
a.
Find the critical numbers of a function
b.
Find the open intervals on which a function is increasing or decreasing
c.
Use the First Derivative Test to find the relative extrema of a function
d.
Find the absolute extrema of a continuous function on a closed interval
e.
Find the open intervals on which a function is concave upward or concave
downward
f.
Find the points of inflection of the graph of a function
g.
Use the Second Derivative Test to find the relative extrema of a function
h.
Find the vertical and horizontal asymptotes of a function and sketch its graph
i.
Solve applied optimization problems
k.
Find infinite limits and limits at infinity
l.
Analyze the graph of a function
IV. Integration
a.
Use the definition of the natural logarithm to write exponential equations in
logarithmic form, and vice versa
b.
Sketch the graphs of exponential and logarithmic functions
c.
Use the properties of logarithms to expand and condense logarithmic expressions
d.
Find the derivatives of natural exponential and natural logarithmic functions
e.
Use the basic integration rules to find indefinite integrals
f.
Use substitution to find indefinite integrals
g.
Use the Fundamental Theorem of Calculus to evaluate definite integral
h.
Use substitution to find definite integrals
i.
Find the area of regions bounded by the graph of a function and the x-axis
j.
Find areas of regions bounded by two or more graphs
Texts and Resources:
Calculus by Larson, Hostetler and Edwards (8th edition).
Text website http://college.cengage.com/mathematics/larson/calculus_analytic/8e/student_home.html.
Dr. Pettitts website www.swcit.org/warren.
One of the best websites for your text is Eduspace located at http://cengage.blackboard.com/webapps/portal/frameset.jsp. Of course this costs more (as if the book did not cost enough already, I would have to mortgage my house to buy that one).
Registration code for my class at Eduspace PROFP-42EB8B41F3D641
Course Schedule (including assignments and activities):
Aug. 21st Introduction Overview and Pre-calculus review
August 24th Introduction Pre-calculus review
August 26th Limits Part A
August 28th Limits Part B
August 31st Limits Part C
Sep. 2nd Evaluating Limits
Sep. 4th Derivatives
Sep. 7th Labor Day no class
Sep. 9th Using derivatives
Sep. 11th Special derivatives
Sep. 14th Power rule
Sep. 16th Product/Quotient rule
Sep. 18th Chain rule
Sep. 21st review for test
Sep. 23rd TEST
Sep. 25th Trig functions
Sep. 28th Exponential functions
Sep. 30th Log functions
Oct. 2nd Day of Outreach/No class
Oct. 5th Implicit differentiation
Oct. 7th Application of Implicit differentiation
Oct. 9th Application of derivative
Oct. 12th Linear approximation
Oct. 14th Optimization problems Part a
Oct. 16th Optimization problems Part b
Oct. 19th Related rate problems
Oct. 21st Intro to curve sketching
Oct. 23rd 1st derivative test
Oct. 26th 2nd derivative test part A
Oct. 28th 2nd derivative test part B
Oct. 30th Asymptotes
Nov. 2nd Putting it all together
Nov. 4th review for test
Nov. 6th TEST
Nov. 9th Antiderivatives
Nov. 11th Integration by substitution Part A
Nov. 13th Integration by substitution Part B
Nov. 16th Integration by substitution Part C
Nov. 18th Questions/homework help
Nov. 20th Fundamental theorem of calculus Part a
Nov. 23rd Fundamental theorem of calculus Part b
Nov. 25th Application of Integration
Nov. 27th Thanksgiving vacation
Nov. 30th Area between 2 curves Part a
Dec. 2nd Area between 2 curves Part b
Dec. 4th Integration with respect to y
Dec. 7th Review for test
Dec. 11th Final (8:00-10:00)
Homework for each section:
Introduction: P1 1-4,17,23,29,35,57
P2 1,4,11,19,57,69
P3 1,5,14,25,32,39,41,44
Limits: 1:1 3,4,5,6,9
1:2 2,9,11,15,19,23,33
1:3 5,9,23,27,29,39
1:4 7,13,17,35,37,43,61,71
1:5 1,9,13,27,33,41,51,63
Derivatives 2:1 1,3,13,17,25,37,38,81
2:2 5,7,27,35,41,57
2:3 1,9,15,21,29
Trig Functions 2:2 19,21,37
2:3 41,51
2:4 41,85
Exponential functions 5:4 3,11,33,37
Log functions 5:1 17,21,37,45,55,75
Implicit differentiation 2:5 1,7,15,23,29,41
Apply derivatives 2:2 95,96,97
Linear Approximation 3:8 9,15
3:9 3,5
Optimization 3:7 2,19,20,33,34,41,42
Related Rates 2:6 1,5,13,15,19,27,33
Curve sketching 3:1 1,5,11,13,19,33
3:2 1,3,5,13,19,29,33,35
3:3 3,7,13,19,35,63
3:4 3,13,39,67
3:5 3,5,15,23,27,59
Antiderivatives 4:1 5,9,17,23,35
Integration by substitution 4:5 1,9,19,21,23,45,51,57,60,65
5:4 85,87
Fundamental theorem 4:4 7,13,29,33,41
Apply integration 4:1 67,73,77
Area between 2 curves 7:1 3,7,19,25,35,45
Integrate with respect to y Take any question from 7:1 and integrate with respect to y
Assessment and
Grading:
Assignments and their weight
Tests 150 points
Final 200 points
Quizzes 15 points each
Homework 75 points for each test
Absence Absence from 5 or more lectures is sufficient reason for the instructor to drop the student from the course with a failing grade.
Late Work Work will not be accepted
after the due date. Please communicate
with me as soon as possible if circumstances arise that necessitate extensions
be granted.
Letter Grades:
A 90% to 100%
B 80% to 89.5%
C 70% to 79.5%
D 60% to 69.5%
F - < 60%
Expectations for
Students:
A. Attendance
· Students are responsible to arrive for lectures at the scheduled time. Tardiness is an interruption to instruction.
· It is the students responsibility to obtain pertinent information from other students or the instructor in the event of tardiness or absence.
· In anticipation of absence from a scheduled quiz, test, or lab it is the students
responsibility to make arrangements in advance to take a quiz, test or perform a lab exercise at an alternate time that is mutually convenient and agreeable. Missed assignments will be averaged in as a zero on the course grade unless prior arrangements have been made. There is no makeup for these. Excused missed tests must be made up within 1 week of the scheduled time they were taken. Arrangements to make up the test must be made as soon as the student returns to class.
· There is no late work, if you have an emergency concerning any assignment please contact me as soon as possible.
B. Reading
1. Most benefit will be derived from the course if the assigned reading is done prior to
arrival at the lectures. You will find scanning the text to be insufficient in your
preparation.
2. The instructor may assign additional reading.
C. Cell Phones and other electronic devices should not be on during class.
Accommodation and
Special Needs - Include the following statement: Your instructor is willing to make any reasonable adaptations for
limitations due to any disability, including a learning disability, in keeping
with SWC policies and the Student Handbook.
Any student with documented certifiable special needs should contact the
office of the Dean of Student Services on campus and they will inform me of the
proper accommodations you require. If
you have a special need, including a learning disability, it is your
responsibility to contact this office as soon as possible to discuss your
accommodation needs.
Retention of Examinations and
Assignments: Instructors will retain copies of student examinations and assignments
not returned to students for one semester in case of dispute between a faculty
member and a student in assigning or recording a grade. After that time, instructors
may discard course materials in a manner that preserves student
confidentiality.
E-mail Policy Include the following statement: Students are issued an official Southwestern College student email address when they are admitted to the College. These addresses all have the same form: firstname.lastname@swcaz.edu. This is the only electronic mailing address recognized by the college. Students are responsible for all official college communications, including attachments, transmitted to this address. SWC faculty and staff are not responsible for forwarding email to personal email accounts that are not assigned by the college. Students are required to check their SWC email on a daily basis.
Withdrawal:
Last day for withdrawal without
instructor signature September 4th
Last day for withdrawal with
instructor signature October 30th
Disclaimer note - Include: This syllabus is subject to modification. The instructor will communicate with students any changes.