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Math 115 (section 005)Calculus IWinter 2017Syllabus4 Credit HoursDearborn Discovery Core Category: Quantitative Thinking and Problem SolvingCourse Meeting Times:M 1:00 – 1:50 in 2063 CBTuTh 12:30 – 1:45 in 2046 CBFormat: Recitation / Classroom BasedInstructor:Frank MasseyOffice:2075 CASL BuildingPhone:313-593-5198E-Mail:fmassey@umich.eduOffice Hours:M 2:00 – 2:50TuTh 1:45 – 2:45 and by appointmentMy office hours are those times I will usually be in my office. However, occasionally I have to attend a meeting during one of my regularly scheduled office hours. In this case I will leave a note on my door indicating I am unavailable. In particular, if you know in advance that you are going to come see me at a particular time, it might not be a bad idea to tell me in class just in case one of those meetings arises. Please feel free to come by to see me at times other than my office hours. I will be happy to see you.Course Description (from Catalog):Functions and their graphs; limits and continuity of functions, differentiation, algebraic and trigonometric functions, applications of derivatives, definite and indefinite integrals, and applications of definite integral. This course includes computer labs. Students cannot receive credit for both MATH 113 and MATH 115.My Version of the Course Description:This course studies derivatives and integrals and the application of these concepts to a variety of problems such as those involving rates of change, graphing, optimization and area.Mathematics Program Goals:1.Increase students’ command of problem-solving tools and facility in using problem-solving strategies, through classroom exposure and through experience with problems within and outside mathematics.2.Increase students’ ability to communicate and work cooperatively.3.Increase students’ ability to use technology and to learn from the use of technology, including improving their ability to make calculations and appropriate decisions about the type of calculations to make.4.Increase students’ knowledge of the history and nature of mathematics. Provide students with an understanding of how mathematics is done and learned so that students become self-reliant learners and effective users of mathematics.Dearborn Discovery Core Goals - Quantitative Thinking and Problem Solving:1.Students are able to interpret information presented in mathematical form (e.g. with functions, equations, graphs, diagrams, tables, words, geometric figures).2.Students are able to represent information/data in mathematical form as appriate (e.g with functions, equations, graphs, diagrams, tables, words, geometric figures).3.Students are able to carry out mathematical (e.g. algebraic, geometric, logical, statistical) procedures flexibly, accurately and efficiently to solve problems.4.Students are able to evaluate the validity of logical or quantitative arguments.Math 115 Learning Goals:Each of the Department's classes emphasizes some learning goals more than others. In this class the basic concepts of calculus and the mathematical tools that derive from them are of fundamental importance along with recognizing when and how to apply them in various contexts; there is group work in the computer labs culminating in collaborative written reports; homework, graded and ungraded, also addresses the application of these tools in specific settings; technology in the form of computer labs, in-class computer demonstrations and the use of on-line resources is an important feature of the course.Text:Calculus, by James Stewart, published by Brooks/Cole Publishing Company. In the schedule below I have put in the appropriate sections and some suggested problems in both the 6th edition (2008) and the 7th edition (2011), so if you get either edition you should be able to follow along with the text ok. However, if you plan to take Math 116, the instructor might not have both editions in the course outline, so it may be some extra work for you if you have the 6th edition. In the schedule below the 6th edition is denoted by S6 and the 7th edition by S7. I suggest you check out or other on-line sources for a cheaper price on the text. The bookstore should have the 7th edition.Supplementary Materials:Student Solutions Manual for Single Variable Calculus. This has worked out solutions to the odd numbered problems in the text. It should be available in the bookstore.Coursepack for Mathematics 115, Calculus I. This has information on the mathematics software Mathematica. It should be available in the bookstore and also on-line at . This contains copies of this course outline, the assignments, exams that I gave in this course in the past and some Notes. Some of the Notes cover material from the lectures and some are concerned with using Mathematica to do some of the calculations that arise in the course. Some of the notes are written using Mathematica, and to read them you either need to use a computer on which Mathematica has been installed (many of the computers on campus have Mathematica on them) or you can use the "Mathematica Player" software that can be downloaded for free from products/player/. This software allows you to read Mathematica files, but does not allow you to execute the Mathematica operations in the file. See me if you have trouble accessing any of the items in the website.Assignment and Grading Distribution :4 Midterm Exams (100 points each)4003 Assignments (15 points each) 45Final Exam 100Total545The assignments can be found on CANVAS and at www-personal.umd.umich.edu/~fmassey/math115/Assignments/.The dates of the exams are on the schedule below. All exams are closed book, but a formula sheet will be provided. You may find that your calculator can do some of the problems on the exams. If this is so, you still need to show how to do the problem by hand, even if you use a calculator to check your work. In the schedule below are some suggested problems for you to work on. Some of these problems are representative of what will be on the exams, while others are simply to help you fix the concepts in your mind or prepare you to do other problems. Work as many problems as time permits and ask for help (in class or out) if you can’t do them.A copy of the formula sheet is at www-personal.umd.umich.edu/~fmassey/math115/Exams/Formulas.doc. No make-up exams unless you are sick.Grading Scale:On each exam and the assignments I will look at the distribution of scores and decide what scores constitute the lowest A-, B-, C-, D-. The lowest A- on each of these items will be added up and the same for B-, C-, D-. The lowest A, B+, B, C+, D+, D will be obtained by interpolation. For example, the lowest B is 1/3 of the way between the lowest B- and the lowest A-, etc. All your points will be added up and compared with the lowest scores necessary for each grade. For example, if your total points falls between the lowest B+ and the lowest A- you would get a B+ in the course. This information is in the file YourGrade which is located in the course website at www-personal.umd.umich.edu/~fmassey/math115/ . After each exam and assignment is graded this information will be updated and you should be able to see how you stand. You can find out what scores I have recorded for you by going to CANVAS, selecting Math 115 and clicking on Grades on the left. Check your grades after each exam and assignment to see that they were entered correctly.Withdrawal:Monday, March 20 is the last day to withdraw from the course.Tentative Course Outline:S7 = 7th edition of StewartS6 = 6th edition of StewartNotes = Notes in the websiteDatesSection(s)Topics and Suggested Problems1/9, 10S7: §1.1, 1.2, Appendix B.S6: §1.1, 1.2, Appendix B. Notes:?1.1, 1.2Mathematical modeling, functions, rates of change.Exam l, W 12 #l, 2Ex l, F 16 #l, 2S7: §1.1 #25, 27, 39 – 44 (just sketch graph), 47, 62 – 67 §1.2 #14 – 17 Appendix B: #25, 4l, 62S6: §1.1 #21, 23, 34 – 38 (just sketch graph), 41, 56 – 59 §1.2 #14 – 17 Appendix B: #25, 4l, 621/10Notes: 4.1,?4.2Using Mathematica.1/12, 17S7: §1.4, 2.l, 2.2. S6: §2.l, 3.l, 3.2. Notes:?1.3Instantaneous rates of change and derivatives, velocity, tangents to curves.Ex l, W 12, #3Ex l, F 16, #3S7: §1.4 #5 (also draw a graph of y vs t showing the four secant lines and the tangent line) 2.1 #3, 6-8, 13, 23, 32, 35, 37, 39, 45 §2.2 #1, 3, 5, 27, 43S6: §2.1 #5 (also draw a graph of y vs t showing the four secant lines and the tangent line) §3.1 #3, 5-7, 13, 21, 29, 33, 35, 37, 43 §3.2 #1, 3, 5, 25, 391/19S7: §1.5 – 1.6, 1.8.S6: §2.2 – 2.3, 2.5.Notes:?1.4Properties of limits, continuity.Ex l, W 12 #4Ex l, F 16 #4S7: §1.5 #5, 7 §1.6 #5, 7, 9, 11, 15, 17, 21, 27, 50 §1.8 #3, 41S6: §2.2 #4, 7 §2.3 #5, 7, 9, 11, 15, 17, 21, 23, 48 §2.5 #3, 371/24Notes:?1.4Assignment 1 due.1/23, 24, 26S7: §2.3S6: §3.3Notes: §2.1Algebraic rules for finding derivatives.Ex l, W 12 #5, 6Ex l, F 16 #5, 6Final Ex, F 16 #2Final Ex, W 12 #1S7: §2.3 #l-21 (odd), 25-43(odd), 67, 71, 76, 91S6: §3.3 #l-19 (odd), 23-41(odd), 63, 67, 72, 871/26S7: §2.3S6: §3.3Notes: §2.2Second and higher derivatives.Ex 2, W 12 #4Ex 2, F 16 #4S7: §2.3 #59, 61, 63, 87S6: §3.3 #57, 59, 61, 831/30Review.1/31Exam 1.1/30, 2/2,?6S7: §2.4S6: §3.4Notes: §2.3Derivatives of trigonometric functions.Ex 2, W 12 #1, 2Ex 2, F 16 #1, 2Final Ex, F 16 #2Final Ex, W 12 #1S7: §2.4 #l-l5 (odd), 37, 38, 39 – 47 (odd)S6: §3.4 #l-l5 (odd), 37, 38, 39 – 47 (odd)2/7S7: §2.5, 2.9S6: §3.5, 3.9Notes: §2.4The chain rule for differentiating composite functions, differentials.Ex 2, F 16, #lEx 2, W 12, #lFinal Ex, F 16 #2Final Ex, W 12 #1S7: §1.3 #35, 43 §2.5 #l3, 15, 23, 29-37 (odd), 77, 87 §2.9 #11aS6: §1.3 #35, 43 §3.5 #l3, 15, 23, 29-37 (odd), 77, 87 §3.9 #11a2/9S7: §2.6S6: §3.6Notes: §2.5Differentiating functions defined by equations (implicit differentiation).Ex 2, F 16, #5Ex 2, W 12, #5Final Ex, W 12 #2Final Ex, F 16 #3S7: §2.6 #9, 15, 17, 19S6: §3.6 #9, 15, 17, 192/14Notes §1.4Assignment 2 due.2/13, 14S7: §2.7S6: §3.7Notes: 2.6Rates of change arising in science, engineering and business. Ex 2, W 12 #3Ex 2, F 16 #3S7: §2.7 #l, 15, 17, 19, 23S6: §3.7 #l, 15, 17, 19, 212/14, 16S7: §2.8S6: §3.8Notes: 2.7Related rates of change. Ex 2, F 16, #6Ex 2, W 12, #6Final Ex, W 12 #3S7: §2.8 #11, 13, l5, 23, 30, 34 S6: p. 193 #77-80S6: §3.8 #11, 13, l5, 23, 30, 32 S6: p. 198 #77-802/20S7: §2.9, 3.2S6: §3.9, 4.2Linear approximations, the mean value theorem. (Some of the examples of linear approximations will be mixed in with other topics in Chapter 3.)Ex 3, F 16, #2Ex 3, W 12, #2S7: §2.9 #1, 7, 25, 27, 33 (In 25, 27 & 33, use the mean value theorem to get an upper bound for the error in the approximation.)S6: §3.9 #1, 7, 25, 27, 33 (In 25, 27 & 33, use the mean value theorem to get an upper bound for the error in the approximation.)2/21Review.2/23Exam 2.3/6, 7S7: §3.1, 3.3S6: §4.1, 4.3Maxima and minima of functions, increasing and decreasing behavior of functions. Ex 3, F 16, #1, 3Ex 3, W 12, #1, 3Final Ex, F 16 #1S7: §3.1 #3, 31, 35-41 (odd), 47, 55, 56 §3.3 #5, 27(a), (b), (e), 29(a), (b), 35(a), (b), 39(a), (b)S6: §4.1 #3, 31, 35-41 (odd), 47, 55, 56 §4.3 #5, 27(a), (b), (e), 29(a), (b), 35(a), (b), 39(a), (b)3/7S7: §3.4S6: §4.4Vertical asymptotes of functions and places where the derivative doesn’t exist.Ex 3, F 16, #1Ex 3, W 12 #1Final Ex, F 16 #1S7: §3.4 #9, 11, 19, 33, 37S6: §4.4 #9, 11, 19, 33, 373/9S7: §3.3S6: §4.3Convex and concave behavior of functions.Ex 3, F 16, #1Ex 3, W 12, #1Final Ex, F 16, #1S7: §3.3 #7, 27(c), (d), 29(c), (d), 35(c), (d), 39(c), (d)S6: §4.3 #7, 27(c), (d), 29(c), (d), 35(c), (d), 39(c), (d)3/15S6: §3.4, 3.5S6: §4.4, 4.5Behavior of functions as x . Determining properties of functions from their graphs and derivatives.Ex 3, F 16, #1Ex 3, W 12, #1Final Ex, F 16, #1S7: §3.4 #13, 17, 19, 25, 27 (on 25, 27 also describe behavior as x∞) §3.5 #9, 13, 27, 35, 39S6: §4.4 #11, 17, 19, 25, 27 (on 25, 27 also describe behavior as x∞) §4.5 #9, 11, 25, 33, 373/14, 16S7: §3.7S6: §4.7Maximum / minimum word problems.Ex 3, F 16 #4Ex 3, W 12 #4Ex 4, W 12 #1Final Ex, W 12, #4Final Ex, F 16 #5S7: §3.7 #11, 12, 15, 32, 37S6: §4.7 #9, 10, 13, 30, 353/16S7: §3.8S6: §4.8Notes: 1.8Newton's method.S7: §3.8 #5, 15S6: §4.8 #5, 153/20, 21S7: §3.9S6: §4.9Antiderivatives and indefinite integrals.Ex 4, F 16, #1, 2Ex 4, W 12, #2S7: §3.9 #3-17 (odd), 21, 29, 31, 39, 41, 43, 45, 53, 63-65, 71 S6: §4.9 #3-17 (odd), 21, 29, 31, 39, 41, 43, 45, 53, 63-65, 713/21S7: §4.1, Appendix ES6: §5.1, Appendix ENotes: 3.1Sums.Ex 4, F 16, #3Ex 4, W 12, #3S7: App E #5, 7, l3, l5, 2l, 23, 3l §4.1 #3, 17S6: App E #5, 7, l3, l5, 2l, 23, 3l §5.1 #3, 153/21Assignment 3 due.3/23S7: §4.2S6: §5.2Notes: 32, 3.5Areas and definite integrals. Ex 4, F 16, #4Ex 4, W 12, #4S7: §4.2 #9, 23, 33, 37S6: §5.2 #9, 23, 33, 373/27Review.3/28Exam 3.3/30, 4/3S7: §4.3, 4.4S6: §5.3, 5.4Notes: 3.3, 3.4Finding integrals using the fundamental theorem of calculus.Ex 4, F 16, #5, 6Ex 4, W 12, #5, 6S7: §4.3 #3, 7, 9, 11, 23, 25, 27, 29, 31 §4.4 #23, 25, 27, 29, 33, 35S6: §5.3 #3, 7, 9, 11, 23, 25, 27, 29, 31 §5.4 #23, 25, 27, 31, 35, 374/4, 6S7: §4.5S6: §5.5Integration using substitutions.Final Ex, F 16, #4Final Ex, W 12, #5S7: §4.5 #9, 11, 16, 17, 25, 39-47 (odd)S6: §5.5 #9, 11, 17, 19, 21, 39-47 (odd)4/10Review.4/11Exam 4.4/13S7: §5.1S6: §6.1Areas.S7: §5.1 #5, 17, 23Final Ex, F 16 #6S6: §6.1 #5, 17, 234/13, 17S7: §5.2S6: §6.2Volumes by slicing perpendicular to an axis.Final Ex, F 16, #7Final Ex, W 12, #6aS7: §5.2 #7, 9S6: §6.2 #7, 94/18S7: §5.3S6: §6.3Volumes by slicing by cylinders about an axis.Final Ex, W 12, #6bS7: §5.3 #5, 11S6: §6.3 #5, 114/18S7: §5.4S6: §6.4Work.Final Ex, W 12, #7Final Ex, F 16 #8S7: §5.4, #l, 3, 7S6: §6.4, #l, 3, 74/20Review.Friday, April 28 11:30 – 2:30 p.m. Final Exam.University Attendance Policy:A student is expected to attend every class and laboratory for which he or she has registered. Each instructor may make known to the student his or her policy with respect to absences in the course. It is the student’s responsibility to be aware of this policy. The instructor makes the final decision to excuse or not to excuse an absence. An instructor is entitled to give a failing grade (E) for excessive absences or an Unofficial Drop (UE) for a student who stops attending class at some point during the semester.Academic Integrity Policy:The University of Michigan-Dearborn values academic honesty and integrity. Each student has a responsibility to understand, accept, and comply with the University’s standards of academic conduct as set forth by the Code of Academic Conduct (), as well as policies established by each college. Cheating, collusion, misconduct, fabrication, and plagiarism are considered serious offenses and violations can result in penalties up to and including expulsion from the University. In this course, the penalty for a first violation will be a grade 0 on the related assignment. A second violation will result in a failing grade for the course. All violations will be reported to CASL and the student’s home unit.Disability Statement:The University will make reasonable accommodations for persons with documented disabilities. Students need to register with Disability Resource Services (DRS) every semester they are enrolled. DRS is located in Counseling & Support Services, 2157 UC ().?To be assured of having services when they are needed, students should register no later than the end of the add/drop deadline of each term. If you have a disability that necessitates an accommodation or adjustment to the academic requirements stated in this syllabus, you must register with DRS as described above and notify your professor. Safety:All students are encouraged to program 911 and UM-Dearborn’s University Police phone number (313) 593-5333 into personal cell phones. In case of emergency, first dial 911 and then if the situation allows call University Police.The Emergency Alert Notification (EAN) system is the official process for notifying the campus community for emergency events. All students are strongly encouraged to register in the campus EAN, for communications during an emergency. The following link includes information on registering as well as safety and emergency procedures information: . If you hear a fire alarm, class will be immediately suspended, and you must evacuate the building by using the nearest exit. Please proceed outdoors to the assembly area and away from the building. Do not use elevators. It is highly recommended that you do not head to your vehicle or leave campus since it is necessary to account for all persons and to ensure that first responders can access the campus.If the class is notified of a shelter-in-place requirement for a tornado warning or severe weather warning, your instructor will suspend class and shelter the class in the lowest level of this building away from windows and doors.If notified of an active threat (shooter) you will Run (get out), Hide (find a safe place to stay) or Fight (with anything available). Your response will be dictated by the specific circumstances of the encounter. ................
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