MATH 0120 Business Calculus
Spring Term 2009 (2094)
INSTRUCTOR
Elayne Arrington, PhD
Office: 608 Thackeray Hall
Office Hours: MWF 2:00 – 3:30 (or by appointment )
Telephone: 412-624-8337 or 8375 (Math Office)
fax: 412-624-8397
e-mail: earr@pitt.edu
http://www.math.pitt.edu/~earr
TEACHING
ASSISTANTS
TEXTBOOK
eme11@pitt.edu
Brief Applied Calculus, Fourth Edition, by Geoffrey C. Berresford and Andrew M.
Rockett; Houghton Mifflin Company, 2007.
COURSE
PREREQUISITES
Math 0031 (College Algebra) or equivalent, Math 0100 (Preparation for Business
Calculus), or an appropriate score on the mathematics placement test.
COURSE
DESCRIPTION
This course is designed for students in business, economics, and other social
sciences. It introduces the basic concept of limit and its application to continuity,
differentiation, integration, maximization, minimization and partial derivatives.
Applications to the social sciences, especially business and economics, are
stressed. The calculus of trigonometric functions is not covered.
COURSE GOALS
The course will provide students with the opportunity to:
 Learn the elements of business calculus in an environment that recognizes
the diverse population of the course and the University.
 Explore mathematical concepts in more depth by collaboration in small
diverse groups.
 Improve communication skills by speaking and writing about
mathematics in small groups.
LEARNING
OUTCOMES
Students of the course will be able to:
 Find limits of functions presented as graphs, tables, or algebraic
expressions.
 Use the concept of limit to define the derivative of a function.
 Differentiate functions involving powers, exponentials, and logarithms.
 Apply the concepts of differentiation to solve optimization problems.
 Use the derivative to hand sketch the graphs of functions involving
powers, exponentials, and logarithms.
 Find indefinite integrals of functions involving powers, exponentials, and
logarithms.
 Find definite integrals of appropriate functions.
 Apply the definite integral to solve problems.
 Find partial derivatives of functions of two variables.
 Apply the method of Lagrange multipliers to solve constrained
optimization problems.
ArringtonMath0120Diverse(W)2094
COURSE
ORGANIZATION
The course consists of lecture and recitation components. Each student must
register for a recitation that is associated with the lecture that he or she is attending.
Lectures are M, W, F. Recitations are scheduled on W and F of each week. The
Wednesday recitation will be a collaborative one in which students work in small
diverse groups to complete worksheets. These worksheets will cover problems
similar to the practice problems, but in more depth. Students will assemble
individually in the Friday recitation. A quiz will be given in the Friday recitation
almost every week of the term. Students should read each section before the lecture
on that section.
CALCULATOR
POLICY
A graphing calculator such as a TI-83 or above will be useful in doing many of the
practice problems and visualizing solutions, but only fully written solutions
showing all work will receive full credit. Because of the nature of the tested
material, calculators will not be permitted on the 50-minute examinations or on
the Departmental Final Examination.
MAKE-UP POLICY
There will be no make-up* for exams, worksheets, or quizzes.
*The instructor will make arrangements with affected students when an
examination or quiz is scheduled on a religious holiday or a date on which the
student must represent the University. There is no make-up for worksheets.
FINAL
EXAMINATION
POLICY
The one-letter-grade rule applies: A student’s course grade in Math 0120 will not
exceed her/his grade on the Math 0120 Departmental Final Examination by more
than one letter grade.
GRADING POLICY
The student’s course grade will be based solely on her/his performance on the
worksheets, the quizzes, and the examinations as follows:
 Worksheets
10%
 Quizzes
15%
 Exam #1
15%
 Exam #2
15%
 Exam #3
15%
 Departmental Final Exam
30%
Worksheet and quiz grades will be based on the best 10 scores.
STUDENTS WITH
DISABILITIES
A student with a disability for which he or she is requesting an accommodation,
should contact both the instructor and the Office of Disability Resources and
Services, 216 William Pitt Union (412) 648-7890 as early in the term as possible.
ACADEMIC
INTEGRITY
Cheating/plagiarism will not be tolerated. Students suspected of violating the
University of Pittsburgh Policy on Academic Integrity will incur a minimum
sanction of a zero score for the quiz, exam or paper in question. Additional
sanctions may be imposed, depending on the severity of the infraction. Students may
work together or use library resources to do homework, but each student must write his or
her own solutions independently. Copying solutions from other students will be considered
cheating, and handled accordingly.
CLASSROOM
CONDUCT
DEADLINES
All students are expected to report to class on time, refrain from individual
conversation during class, turn cell phones and pagers off or to “vibrate”, and show
respect for fellow students and faculty.
Add/drop: Friday, January 16. Monitored withdrawal: Friday, March 6.
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ArringtonMath0120Diverse(W)2094
MATH 0120 Business Calculus
Class Schedule
Spring Term 2009 (2094)
Monday
(Lecture)
Jan. 5
Sec. 1.1
Jan. 12
Sec. 1.4
Jan. 19
Holiday, No Class
Jan. 26
Sec. 2.5
Feb. 2
Sec. 3.1
Feb. 9
Sec. 3.2
Feb. 16
Sec. 3.5
Feb. 23
Sec. 4.2
Mar. 2
Sec. 5.1
Mar. 9
Spring Recess
Mar. 16
Sec. 5.2
Mar. 23
Sec. 5.5
Mar. 30
Sec. 6.2
Apr. 6
Review
Apr. 13
Sec. 7.5
Wednesday
(Collaborative
Recitation)
Jan. 6
Jan. 13
Worksheet #1
Jan. 20
Worksheet #2
Jan. 27
Worksheet #3
Feb. 3
Worksheet #4
Feb. 10
Worksheet #5
Feb. 17
Worksheet #6
Feb. 24
Worksheet #7
Mar. 3
Worksheet #8
Mar. 10
Spring Recess
Mar. 17
Worksheet #9
Mar. 24
Worksheet # 10
Mar. 31
Worksheet #11
Apr. 7
Worksheet #12
Apr. 14
Review
Wednesday
(Lecture)
Jan. 7
Sec. 1.2
Jan.14
Sec. 2.1
Jan. 21
Sec. 2.3
Jan. 28
Sec. 2.6
Feb. 4
Review
Feb. 11
Sec. 3.3
Feb. 18
Sec. 3.6
Feb. 25
Sec. 4.3
Mar. 4
Review
Mar. 11
Spring Recess
Mar. 18
Sec. 5.3
Mar. 25
Sec. 5.6
Apr. 1
Sec. 7.1
Apr. 8
EXAM #3
Apr. 15
Review
Friday
(Recitation)
Jan. 8
Jan. 15
Quiz #1
Jan. 22
Quiz #2
Jan. 29
Quiz #3
Feb. 5
Quiz #4
Feb. 12
Quiz #5
Feb. 19
Quiz #6
Feb. 26
Quiz #7
Mar. 5
Quiz #8
Mar. 12
Spring Recess
Mar. 19
Quiz #9
Mar. 26
Quiz #10
Apr. 2
Quiz #11
Apr. 9
Quiz #12
Apr. 16
Review
Friday
(Lecture)
Jan. 9
Sec. 1.3
Jan. 16
Sec. 2.2
Jan. 23
Sec. 2.4
Jan. 30
Sec. 2.7
Feb. 6
EXAM #1
Feb. 13
Sec. 3.4
Feb. 20
Sec. 4.1
Feb. 27
Sec. 4.4
Mar. 6
EXAM #2
Mar. 13
Spring Recess
Mar. 20
Sec. 5.4
Mar. 27
Sec. 6.1
Apr. 3
Sec. 7.2
Apr. 10
Sec. 7.3
Apr. 17
Review
Final Examination: Wednesday, April 22: 12:00 – 1:50 p.m.
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ArringtonMath0120Diverse(W)2094
Math 0120
PRACTICE PROBLEMS
1.1
REAL NUMBERS, INEQUALITIES,
AND LINES
PAGE 15
#7,10,14,17,23,24,28,32,40,42,46,48,63,69
1.2
EXPONENTS
PAGE 28
#5, 16,25,28,34,38, 54,66,73,74,85,91
1.3
FUNCTIONS
PAGE 43
#1,7,10,16,21,25,30,34,38,45,51,58,65,68,72,77
1.4
FUNCTIONS, CONTINUED
PAGE 60
#1,4,8,14,20,26,32,36,45,50,57,61,68,77,80,89,94
2.1
LIMITS AND CONTINUITY
PAGE 83
#2,14,17,23,26,32,35,40,43,47,50,55,57,67,71
2.2
RATES OF CHANGE, SLOPES, AND
DERIVATIVES
PAGE 98
#1,7,10,20,22,28,30,42,44,55,58
2.3
SOME DIFFERENTIATION FORMULAS
PAGE 113
#6,12,16,20,24,26,30,32,35,38,46,51,55,61
2.4
THE PRODUCT AND QUOTIENT
RULES
PAGE 127
#1,9,12,21,25,28,33,34,40,47,50,53,56,62
2.5
HIGHER-ORDER DERIVATIVES
PAGE 141
#2,5,8,10,14,20,24,34,39,47,56,58
2.6
THE CHAIN RULE AND THE
GENERALIZED POWER RULE
PAGE 152
#1,7,11,16,19,24,30,34,36,42,47,52,53,58,62,78
2.7
NONDIFFERENTIABLE FUNCTIONS
PAGE 160
#1,2,3,4,6,11
3.1
GRAPHING USING THE FIRST
DERIVATIVE
PAGE 178
#1,4,10,12,15,20,24,29,35,43,48,54,60,65,66
3.2
GRAPHING USING THE FIRST AND
SECOND DERIVATIVES
PAGE 192
#3,8,10,15,18,20,22,26,29,42,51,52,54
3.3
OPTIMIZATION
PAGE 205
#1,4,6,12,18,23,27,36,38,39,45,51
3.4
FURTHER APPLICATIONS OF
OPTIMIZATION
PAGE 216
#2,5,6,8,10,12,16,18,21
3.5
OPTIMIZING LOT SIZE AND
HARVEST SIZE
PAGE 225
#2,3,4,6,7,8,10,15
3.6
IMPLICIT DIFFERENTIATION AND
RELATED RATES
PAGE 235
#4,8,10,12,16,18,20,22,24,27,31,36,38,43,50,56,59
4.1
EXPONENTIAL FUNCTIONS
PAGE 257
#10,12,13,16,18,20,22,24,27,35,36,39,40,42
4.2
LOGARITHMIC FUNCTIONS
PAGE 274
#2,3,9,12,16,18,20,21,29,35,37,43,60
4.3
DIFFERENTIATION OF EXPONENTIAL
AND LOGARITHMIC FUNCTIONS
PAGE 289
#2,4,8,10,13,18,22,26,28,30,34,37,42,43,54,57,58,
65,74
4.4
RELATIVE RATES AND ELASTICITY
OF DEMAND
PAGE 302
#5,10,16,18,22,26,28,30,32,34
4
5.1
ANTIDERIVATIVES AND
INDEFINITE INTEGRALS
PAGE 322
#6,8,10,16,20,22,29,32,34,44,46,48,52
5.2
INTEGRATION USING
LOGARITHMIC AND
EXPONENTIAL FUNCTIONS
PAGE 333
#2,4,7,10,12,18,23,26,28,37,40,42,46,50
5.3
DEFINITE INTEGRALS AND
AREA
PAGE 348
#2,13,19,20,26,29,34,38,45,50,56,60,66,68,75,
81,84,88, 103,109
5.4
AVERAGE VALUE AND AREA
BETWEEN CURVES
PAGE 363
#3,6,10,22,29,33,38,42,48,57,63,64,66,68
5.5
CONSUMERS’ SURPLUS AND
INCOME DISTRIBUTION
PAGE 374
#4,6,10,12,13,14,16,21
5.6
INTEGRATION BY
SUBSTITUTION
PAGE 386
#1,6,14,17,23,28,32,34,36,40,43,50,54,56,
60,66,69,73
6.1
INTEGRATION BY PARTS
PAGE 406
#4,10,12,18,21,26,29,34,39,46,4 7,54,56,59
6.2
INTEGRATION USING TABLES
PAGE 417
#4,10,16,26,34,36,63,67
7.1
FUNCTIONS OF SEVERAL
VARIABLES
PAGE 493
#6,8,14,20,24,27,30,33,34,35
7.2
PARTIAL DERIVATIVES
PAGE 507
#3,8,11,14,16,22,23,26,29,34,36,42,45,49
7.3
OPTIMIZING FUNCTIONS OF
SEVERAL VARIABLES
PAGE 519
#4,6,11,16,20,22,24,26,30,34
7.5
LAGRANGE MULTIPLIERS AND
CONSTRAINED OPTIMIZATION
PAGE 545
#5,8,10,12,16,24,28,31,38
5