MATH 021 - Calculus I, Fall 2022
Syllabus
Instructors
• Section 110-114: MW 10:45 AM - 12:00 PM
Prof. Donald Outing: dao417@lehigh.edu
• Section 210-214: TR 7:55 AM - 9:10 AM
Prof. Trisha Moller: trm500@lehigh.edu
• Section 310-314: MW 1:35 PM - 2:50 PM
Prof. Jiayuan Wang: jiw922@lehigh.edu
• Section 410-414: MW 9:20 AM - 10:35 AM
Prof. Jiayuan Wang: jiw922@lehigh.edu
• Section 510-514: TR 1:35 PM - 2:50 PM
Prof. Lei Wu: lew218@lehigh.edu
• Section 610: Remote
Prof. Daniel Conus: dac311@lehigh.edu
If you have any questions about the course, please feel free to contact the instructor of your
section.
Text
J. Stewart, Calculus, Early Transcendentals, ninth edition, Brooks/Cole.
ISBN: 978-1-337-61392-7
Attendance
You will attend two lectures per week, conducted by your instructor, and one recitation per
week, conducted by your TA (teaching assistant).
Attendance at all of these sessions is required.
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Prerequisites
All students in MATH 21 must have taken the ALEKS placement assessment and obtained
a score of 76 or above (*) It is recommended that students continue to practice their skills
using the individualized modules provided by ALEKS. Evidence shows that one of the main
reasons preventing students from performing well in Calculus is their lack of proficiency in
basic skills, such as algebra, pre-calculus, and trigonometry. Practicing these skills on ALEKS
before and throughout the course is an important step to help students succeed.
(*) The ALEKS score requirement for MATH 21 is waived for:
• students who received a 4 or 5 on the AP exam and chose to relinquish their credit to
take MATH 21;
• students who took MATH 0 - PreCalculus at Lehigh University;
• students who already took MATH 21 at Lehigh University in a previous semester.
Learning Objectives
• Students will learn the definitions and interpretations of limits and continuity, learn
how to verify the existence and value of a limit by using the precise definition and by
using limit theorems, and how to check for continuity using limits.
• Students will learn the definitions and interpretations of derivatives and integrals, and
learn how to evaluate them by using the definitions and by using the appropriate theorems and formulas.
• Students will understand and use the main theorems regarding the above, including the
extreme value theorem, the intermediate value theorem, the mean value theorem, and
the fundamental theorem of calculus. Students will gain an understanding of the proofs
of these theorems as well as thorough experience in applying them.
• Students will be able to solve applied problems (i.e., word problems) using techniques
from calculus. These include problems concerning motion, general rates of change curve
sketching, optimization, area of regions, volumes of solids, exponential growth and decay.
Course Site, Gradescope and Email
You will have two Course Site pages for this course, one for general course information and
announcements, and another for your specific lecture. You will automatically be enrolled in
Course Site but you need to enroll in Gradescope, via email from Gradescope.
Email messages will be sent to your Lehigh email address. In sending email to instructors
and TAs, please include the course (Math21) and your section number in the subject line.
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Students are responsible for checking Course Site and their Lehigh email regularly
for announcements regarding this course.
Also, all homework should be submitted and graded in an online service called Gradescope.
Students should upload the PDF of completed homework to Gradescope. If you cannot find
your name for MATH 021 on Gradescope (especially if you register for this course after August
20), please use the entry code G22XBP
Assignments
Homework You will be assigned homework problems for each section. The Hand-In Homework sets will be listed on Course Site with the due dates. You will hand in a homework
set approximately every week. Your solutions should be properly scanned and uploaded
to Gradescope. Each homework will contain five to ten problems, but only five of them
will be graded and count towards your homework grade.
In addition, there are suggested Practice Homework problems. You do not have to turn
in these Practice Homework problems.
Homework Presentation As you complete your homework, please keep in mind the following points. Failure to do so will result in a penalty to your homework grade.
• Your homework solutions should be handwritten and appropriate for a college-level
course.
• Your work must be NEAT. Do not hand in your scratch work!
Homework may take you several attempts and that practice is good work. After
solving the problem on rough drafts, rewrite the problem on a fresh sheet of paper.
• You must write the answers in order and use a single column format in your writing.
• You should SHOW ALL WORK, with all the steps to solve each problem. If you do
not show the reasoning that you use to arrive at your solution, you may not receive
full credit, even for a correct answer.
• Your homework pages should be properly scanned and uploaded to Gradescope.
• Each homework set will contain five to ten problems, but only five of them will be
graded and count towards your homework grade.
Late Assignments Late assignments will not be accepted.
Collaboration When faced with difficulty in mathematics, it helps to work through problem
with a colleague. We welcome and encourage you to work with classmates, friends,
tutors and myself. Feel free to exchange ideas as your work through the problems.
HOWEVER: when writing your homework response, you MUST work on your own.
The final response you write on your homework should be yours and yours alone. We
recommend that while you may complete the scratch work for all of your homework
with a classmate, you should write the final copy of your homework when you are alone.
Instances of plagiarism can result in a zero on the assignment, a failing grade in the
course, or University disciplinary action.
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Examinations
1. Common Hour Examinations There will be two common hour exams this semester.
More information will be provided later.
2. Final Examination The final examination will be comprehensive. Students should not
make any commitments for the examination period until the dates for their final exams
are announced by the Registrar. No early final exams will be given.
3. Note that use of any electronic devices on exams is strictly prohibited.
Grading
The various assignments and exams will be scaled to give the following possible points towards your final total.
Homework (twelve in total, lowest two dropped)
Common Hour Exams (two in total)
Final
Total
Points
100
100 (each)
200
500
If you earn at least 90% of the total possible points, 450, you will receive a grade of at least Ain the course, if you earn at least 80% of the total possible points, 400 total, you will receive at
least a B-; C-, 70%, 350 points; and if you earn at least 60% of the possible points, 300 points,
you will pass the course.
Accommodations for Students with Disabilities
Lehigh University is committed to maintaining an equitable and inclusive community and
welcomes students with disabilities into all of the University’s educational programs. In
order to receive consideration for reasonable accommodations, a student with a disability
must contact Disability Support Services (DSS), provide documentation, and participate in
an interactive review process. If the documentation supports a request for reasonable accommodations, DSS will provide students with a Letter of Accommodations. Students who are
approved for accommodations at Lehigh should share this letter and discuss their accommodations and learning needs with instructors as early in the semester as possible. For more
information or to request services, please contact Disability Support Services in person in
Williams Hall, Suite 301, via phone at 610-758-4152, via email at indss@lehigh.edu, or online
at studentaffairs.lehigh.edu/disabilities.
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Religious Accommodation Policy
The university policy is to support any member of the Lehigh community who requests an
absence due to the demands of religious holiday observance. Of course, nothing in this policy exempts a student from meeting course requirements or completing assignments, so the
student will have to negotiate with the instructor any make-up work.
The Principles of Our Equitable Community
Lehigh University endorses The Principles of Our Equitable Community
We expect each member of this class to acknowledge and practice these Principles. Respect
for each other and for differing viewpoints is a vital component of the learning environment
inside and outside the classroom.
Academic Honesty
Lehigh takes academic honesty very seriously, and you should, too. This applies to homework
as well as exams. Copying of homework solutions from other students, any other individual(s),
or any source, including the internet, is not allowed under any circumstance. Infringements
to the academic integrity policies will be prosecuted to the full extent of the Lehigh judicial
system. Lehigh University policies on academic integrity, including the Lehigh University
Undergraduate Student Senate Statement on Academic Integrity, can be found at:
studentaffairs.lehigh.edu/content/academic-integrity-resources
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Schedule
Week:
MW lectures
TR lectures
Week01:
(8/22-8/28)
2.1: The Tangent and Velocity Problems
2.2: The Limit of a Function
2.1: The Tangent and Velocity Problems
2.2: The Limit of a Function
Week02:
2.3: Calculating Limits Using the Limit
Laws
2.4: The Precise Definition of a Limit
2.5: Continuity
Homework 1 due
2.3: Calculating Limits Using the Limit
Laws
2.4: The Precise Definition of a Limit
2.5: Continuity
Homework 1 due
2.6: Limits at Infinity; Horizontal
Asymptotes
2.7: Derivatives and Rates of Change
Homework 2 due
2.6: Limits at Infinity; Horizontal
Asymptotes
2.7: Derivatives and Rates of Change
Homework 2 due
Week04:
(9/12-9/18)
2.8: The Derivative as a Function
3.1: Derivatives of Polynomials and Exponential Functions
Homework 3 due
2.8: The Derivative as a Function
3.1: Derivatives of Polynomials and Exponential Functions
Homework 3 due
Week05:
(9/19-9/25)
3.2: The Product and Quotient Rules
3.3: Derivatives of Trigonometric Functions
Homework 4 due
Exam1
3.2: The Product and Quotient Rules
3.3: Derivatives of Trigonometric Functions
Homework 4 due
Exam1
Week06:
(9/26-10/2)
3.4: The Chain Rule
3.5: Implicit Differentiation
Homework 5 due
3.4: The Chain Rule
3.5: Implicit Differentiation
Homework 5 due
Week07:
3.6: Derivatives of Logarithmic and Inverse Trigonometric Functions
3.8: Exponential Growth and Decay
Homework 6 due
3.6: Derivatives of Logarithmic and Inverse Trigonometric Functions
3.8: Exponential Growth and Decay
Homework 6 due
Mon 10/10 Pacing Break
3.9: Related Rates
3.9: Related Rates
3.10: Linear Approximations and Differentials
3.11: Hyperbolic Functions
Homework 7 due
(8/29-9/4)
Week03:
(9/5-9/11)
Thurs 9/22
(10/2-10/9)
Week08:
(10/10-10/16)
Homework 7 due
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Week:
MW lectures
TR lectures
Week09:
3.10: Linear Approximations and Differentials
3.11: Hyperbolic Functions
4.1: Maximum and Minimum Values
Homework 8 due
4.1: Maximum and Minimum Values
Week10:
4.2: The Mean Value Theorem
(10/24-10/30)
4.3: What Derivatives tell us about the
Shape of a Graph
Homework 9 due
Exam 2
4.3: What Derivatives tell us about the
Shape of a Graph
4.4:
Indeterminate Forms and
l’Hopital’s Rule
Homework 9 due
Exam2
(10/17-10/23)
Thurs 10/27
Week11:
4.2: The Mean Value Theorem
Homework 8 due
4.4:
Indeterminate Forms and
l’Hopital’s Rule
4.5: Summary of Curve Sketching
Homework 10 due
4.5: Summary of Curve Sketching
Week12:
(11/7-11/13)
4.7: Optimization Problems
4.8: Newton’s Method
4.9: Antiderivatives
Homework 11 due
Tues 11/8 Civic Engagement Day
4.8: Newton’s Method
4.9: Antiderivatives
Homework 11 due
Week13:
(11/14-11/20)
5.1: The Area and Distance Problems
5.2: The Definite Integral
5.3: Fundamental Theorem of Calculus
Homework 12 due
5.1: The Area and Distance Problems
5.2: The Definite Integral
5.3: Fundamental Theorem of Calculus
Homework 12 due
Week14:
(11/21-11/27)
5.3: Fundamental Theorem of Calculus
5.4: Indefinite Integrals and the Net
Change Theorem
W-F: Thanksgiving Break
5.3: Fundamental Theorem of Calculus
5.4: Indefinite Integrals and the Net
Change Theorem
W-F: Thanksgiving Break
Week15:
(11/28-12/4)
5.5: The Substitution Rule
6.1: Areas Between Curves
6.2: Volumes
5.5: The Substitution Rule
6.1: Areas Between Curves
6.2: Volumes
Final Exam
Week
See Registrar’s Schedule
See Registrar’s Schedule
(10/31-11/6)
11/23-11/25
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4.7: Optimization Problems
Homework 10 due
Practice Problems
Section
1.1-1.5; Review
2.1; Tangents & velocity
2.2; Limits
2.3; Limit rules
2.4; -δ
2.5; Continuity
2.6; Limits at ∞
2.7; Derivatives and Rates of Change
2.8; Derivatives
3.1; Polynomials and ex
3.2; Prod. and quot. rules
3.3, Appendix D; (sin(x))0
3.4; Chain rule
0
3.5; Implicit diff., sin−1 (x)
3.6; (ln(x))0
3.8; Exp. growth/decay
3.9; Related rates
3.10; Linear approx.
3.11; Hyperbolic functions
4.1; Max/min of functions
4.2; MVT
4.3; Graphing I
4.4; 00 , ∞
∞ , l’Hôpital
4.5; Curve sketching
4.7; max/min problems
4.8; RNewton’s method
4.9; f (x)dx
5.1, App. E; Areas, sums
5.2; The definite integral
5.3; FTC
5.4; Indef. integrals, change
5.5; Substitution
6.1; Areas, Review
6.2; Volumes
Practice Problems, NOT to be handed in.
§1.3 #2,17,18,33.
§1.4 #9,15.
§1.5 #7,15,17,21,53,65,73.
§2.1 #1,6.
§2.2 #5,7,9,11,13,19,31,35.
§2.3 #1,2,6,9,11,15,18,21,29,30,31,43,49.
§2.4 #1,3,11,13,14,21,29,31.
§2.5 #5,9,17,39,45,53.
§2.6 #3,5,19,23,27,39.
§2.7 #7,11,15.
§2.8 #1,3,25,27,41,50.
§3.1 #13,19,29,35,55.
§3.2 #21,25,27,53.
Appendix D #5,29,31,75,77,79.
§3.3 #1,3,9,33,39,53.
§3.4 #11,13,23,37,45.
§3.5 #5,17,23,27,29.
§3.6 #13,23,27,33.
§3.8 #3,9,11,17.
§3.9 #3,5,6,9,19,23,33.
§3.10 #3,7,13,17,25,43.
§3.11 #23,31,33,37.
§4.1 #7,27,35,39,47,53.
§4.2 #5,13,15,19,25.
§4.3 #5,9,15,19,27.
§4.4 #15,19,25,33,45,55.
§4.5 #1,7,10,11,19,33,39.
§4.7 #3,7,13,14,31,37.
§4.8 #9,17(two decimal places).
§4.9 #7,13,19,31,41.
Appendix E 15,25,31.
§5.1 #1,3,21.
§5.2 #7,29,33,47,73.
§5.3 #3,19,31,33,37,53.
§5.4 #5,9,11,13,27,35,37.
§5.5 #3,9,13,25,39,57,81.
§6.1 #4,9,13,21,35.
§6.2 #1,5,11,15,53.
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