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. 1 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. 2 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. 3 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. 4 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 5 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 6 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 7 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. 8