MATH 133 Calculus I: Spring 2017 Limits, Continuity, Differentiation, Integration, and Applications

Size: px

Start display at page:

Download "MATH 133 Calculus I: Spring 2017 Limits, Continuity, Differentiation, Integration, and Applications"

Hector Clarke
5 years ago
Views:

1 MATH 133 Calculus I: Spring 2017 Limits, Continuity, Differentiation, Integration, and Applications Section 1 MTWF 9:00 9:50 am King 243 Instructor: Susan Jane Colley King (office) or (messages) (home please call before 10:00 pm) scolley@oberlin.edu sjcolley@math.oberlin.edu Web page: Office Hours: Monday 3:30 5:00 pm Tuesday 3:00 4:30 pm Wednesday 3:00 4:30 pm Thursday 4:30 5:30 pm Friday 2:30 3:30 pm Also by appointment Text: James Stewart, Single Variable Calculus, 8 th ed., Cengage. This text is required and is available at the Oberlin Bookstore. We will be studying Chapters 1 5. Goals: Homework: Exams: This is an introductory course in the differential and integral calculus of functions of a single variable. Ideas of function and limit will be used to define and understand the key concepts of derivative and integral. Various applications (e.g., to the sciences and economics) of the mathematical constructions and methods will also be explored. The attached syllabus contains problems for you to work in order to gain some familiarity with the material. These problems are not to be turned in (unless otherwise noted). You should do as many or as few of them as you need in order to feel comfortable with the topics discussed in class. In addition, there will be separately assigned, hand-in problem sets due weekly (usually Tuesdays). No late assignments will be accepted (emergencies excepted, of course), but you may submit incomplete assignments. Solutions to the handin problem sets will be available online through Blackboard. In addition, there will be a few special assignments for you to work on in small groups. There will be four fifty-minute, in-class, closed-book exams and a two-hour, closed-book, comprehensive final. Tentative dates for the midterm exams are February 22, March 17, April 12, and April 28. Please let me know as

2 soon as possible if there is a problem with any of these dates. The final exam will take place on Thursday, May 11 from 9:00 to 11:00 am. Participation: Class attendance is not a formal part of your grade for the course. Therefore, you need not explain if you must miss a class, but you are responsible for finding out what material was discussed. It is recommended that you attend as many classes as possible, and that you be an active participant in them. Please try to arrive on time; it can be quite disruptive to your classmates to have latecomers and, moreover, it can be much more difficult for you to get what you need from class if you are late. Grading: Midterm exams (100 points each) 400 Final exam 200 Homework 150 Total 750 Deadlines: Online: Help: Note: I will try to be as clear as I can about the nature of assignments, and I will provide fair warning about when they are due. Late assignments normally will not be accepted. At the same time, I do understand that emergencies arise, so if unforeseen circumstances are interfering with your ability to complete some work in the course (e.g., significant illness, but not assignments for other classes), please contact me immediately, preferably before the assignment is due. Copies of assignments, handouts, etc. will be posted on the course Blackboard site. Go to blackboard.oberlin.edu (and your Academic Hub ) to access these materials. You should always feel free to ask me questions about the material discussed in class, problems with the homework, life beyond calculus, etc. My office hours appear above, but if they are inconvenient, you are welcome to arrange another time to meet with me. Besides me, there are two other forms of support available to you: (1) Walk-in tutoring available 7:30 9:30 pm Monday through Thursday in King 237 (upperclass students will be available to answer questions and work problems), (2) Tutoring through Student Academic Services in Peters Hall, Room 118. (This is mainly for more extensive help. To obtain this service, you need to get a card from the SAS office in Peters and bring it to me. After I sign the card, you should return it to the SAS office and shortly thereafter you will be assigned a private undergraduate tutor.) Calculus has a reputation for being a difficult subject, but you needn t find it so if you work regularly and effectively. Allow yourself an average of 8 hours per week outside of class to devote to this course. Try to work on your calculus several times each week so that you keep up with the material presented in class and get your questions answered. Finally, if you have a 2

3 documented disability I am happy to discuss academic accommodations with you; please contact me as soon as possible so I can understand how to be of assistance. Outline of the Course Preliminaries ( , Appendices A D) Limits and continuous functions ( ) Differentiation (Chapter 2) Applications of differentiation (Chapter 3) Integration (Chapter 4, Appendix E) Applications of integration (Chapter 5) 1.5 weeks 1.5 weeks 3.5 weeks 2.5 weeks 2 weeks 2 weeks 3

4 Readings and problems below are from James Stewart, Single Variable Calculus, 8 th ed. Note that 19/1 means problem 1 on page 19 of Stewart. The problems listed below are not to be turned in (unless otherwise noted); they are intended for your own practice. As a result, you should feel free to work together on these questions, ask me about them, etc. Most of the problems have answers in the back of the text. A recommended routine is for you to do some relevant reading in the text before a topic is discussed in class, then to reread and work problems once that topic has been discussed. Finally, the dates listed should are only approximate; you can expect some give and take over the course of the semester. Date Topics Reading Problems M 1/30 Introduction Real numbers, intervals PRELIMINARIES App. A T 1/31 Inequalities, abs. value App. A A9/ 1,2,5,7,17,21,23,25,33,45,49 xxvi/ Diagnostic Test A W 2/1 Functions / 1,3,5,11,21,25,31,35,43,49 F 2/3 Functions (contd.) / 51,55,57,63,69, / 1,3,9,15,19,21 M 2/6 Review of Trigonometry App. D A32/ 1,9,15,23,25,29 T 2/7 Trig. Review (contd.) App. D A32/ 33,35,43,53,67,69,77 xxx/ Diagnostic Test D W 2/8 New functions from old / 1,3,5,11,13,15,23,33 xxix/ Diagnostic Test C In addition, you should read and review the following on your own: Equations of lines App. B A15/ 1,7,11,15,19,21,23,25,29,31,37, 45,51,57 Graphs of conics App. C A23/ 1,3,9,11,19,21,25 xxviii/ Diagnostic Test B LIMITS AND CONTINUOUS FUNCTIONS F 2/10 Tangent lines and / 1,3,5,7 rates of change M 2/13 Limits / 1,3,5,7,17,19,23,29,45 T 2/14 Computing limits / 1,7,10,11,15,17,19,21,23,27,35, 41,47,53,55,57 4

5 W 2/15 Formal def n of limit / 1,5,11,15,29,39 F 2/17 Continuous functions / 1,3,9,11,17,21,29,45,51,53,55,73 DIFFERENTIATION M 2/20 Derivatives and rates of change / 1,3,7,9,13,17,21,23,33,37, 41,47,51,53,59 T 2/21 Differentiability / 1,5,7,9,23,25,33,39,49,53,55,59,61 W 2/22 EXAM 1 F 2/24 Computations / 3,5,7,11,13,17,23,25,37,41,43,51, 55,71,79,83,93,97 M 2/27 Trigonometric derivatives / 3,5,7,9,15,23,25,35,37,39,41,43,57 T 2/28 The chain rule / 1,3,5,9,13,17,21,23,33,41 W 3/1 The chain rule (cont d) / 53,59,61,63,65,69,73,83,89 F 3/3 Implicit differentiation / 1,3,9,13,15,17,21,25,31,43, 49,51,57,61 M 3/6 Some applications / 1,5,11,13,21,23,29,31 T 3/7 Related rates / 1,3,7,9,11,13,19,21 W 3/8 Related rates (contd.) / 25,31,39,41,43 F 3/10 Approximations / 1,3,7,13,15,17,23,27 M 3/13 Approximations (contd.) / 31,33,35,41 APPLICATIONS OF DIFFERENTIATION T 3/14 Extrema of functions / 1,3,7,10,11,15,27,29,33,37,39,45, 49,53,55,63,65,67,69 W 3/15 The mean value theorem / 3,5,7,9,19,23,27,31,35 F 3/17 EXAM 2 M 3/27 Curve sketching / 1,3,7,9,11,13,17,19,23,31,37,39, 43,57,58,65,73 T 3/28 Limits at / 1,3,5,7,9,15,21,29,35,45,51,53, 57,61,63 W 3/29 More curve sketching / 3,15,17,31,37,39,45, / 5,7 F 3/31 Optimization / 3,11,15,21,23 M 4/3 Optimization (contd.) / 25,27,31,33,35 T 4/4 Optimization (contd.) / 47,53,63,73 5

6 W 4/5 Newton s method / 1,3,7,9,11,15,21,29 F 4/7 Antiderivatives / 1,3,5,7,15,19,31,33,35,43,49, 53,57,65,69 INTEGRATION M 4/10 notation; induction App. E A38/ 1,5,9,11,13,19,21,27,31,37 T 4/11 Area and distances / 1,5,13,17,21 W 4/12 EXAM 3 F 4/14 The definite integral / 1,5,9,17,19,21,25,33,35,39 M 4/17 Definite integral (contd.) / 43,45,49,57,65,70 T 4/18 Fundamental theorems / 1,3,5,7,11,17,19,23,25,27,29,31 W 4/19 Fund. thms. (contd.) / 37,53,65,67,75 F 4/21 Indefinite integrals / 1,3,7,11,13,23,33,35, 41,45,47,49,55,59,65 Method of substitution / 1,5,9,11,13,17,21,25 M 4/24 Substitutions (contd.) / 29,37,39,43,57,59 APPLICATIONS OF INTEGRATION T 4/25 Area between curves / 1,3,7,13,17,19,21,23,29,33,53,57 W 4/26 Volumes: disks and slices / 1,5,7,15,17,19,29,31,33,39 F 4/28 EXAM 4 M 5/1 Disks and slices (contd.) / 49,55,63,66,69,71 T 5/2 Volumes: shells / 1,3,9,13,15,19,23,25,31,37,41 W 5/3 Work / 1,3,5,7,21,33 F 5/5 Average value / 1,5,9,13,17,19 Review and Farewell Thursday, 5/11 9:00 11:00 am FINAL EXAM 6

7 Honor Code Policies Homework You are permitted, even encouraged, to collaborate on homework. For homework that is not graded, feel free to consult anyone at all: your classmates, me, other students, friends, relatives, Marvin Krislov (the last one not really). For homework that is to be handed in and graded, I expect you to be somewhat more careful. Specifically, you should continue to ask questions of me regarding homework problems and you may collaborate with one or two of your classmates (per assignment). Please do not undertake significant collaboration with more than two students without permission. If you do collaborate, you are expected to write your own solution to problems (i.e., not to copy) and to indicate the name(s) of any student(s) with whom you worked. You may consult any written sources for hand-in homework, provided that you give appropriate citations. Please write your homework solutions with care. From time to time, there will also be group assignments. In these instances you will be required to work with two or three other classmates and to hand in jointly written reports. Otherwise, the ground rules are the same as for regular hand-in homework as described above. Examinations Unless specifically indicated otherwise, in-class tests are assumed to be closed-book. Collaboration of any sort (other than to ask me questions) will not be permitted. Any time limits will be indicated with each test. Honor Pledge On every assignment that you submit for credit, you are expected to sign the Oberlin College Honor Pledge: I have adhered to the Honor Code on this assignment. If you need clarification of the policies above, please do not hesitate to ask. Should you require some variation in these rules, you must discuss the matter with me well in advance of any assignment. For general information about the Honor System at Oberlin, consult < >. 7

8 Guidelines for Written Work Mathematics is not only a means for understanding quantitative issues, but is also provides an effective and efficient notational and conceptual supplement to natural language. Good communication of mathematics requires thoughtful and precise prose writing, especially when trying to convey complex arguments and ideas. When you attempt any mathematical writing, you should bear the following in mind: Mathematical symbols provide an extremely compact and concise form of expression, so it is important that you surround your symbols with words, phrases, and sentences. It is expected that you will write your problem solutions in clear, grammatically correct prose consisting of complete sentences. Remember, you are providing a coherent solution, not just a list of answers. The reader should not have to guess about what you are thinking = 4 is a symbolic way of writing a sentence. In particular, the symbol = means equals and is a verb, equivalent to the verb to be. While we re on the subject, you should have the greatest respect and reverence for the equals sign. Use it only to indicate that two quantities are actually equal (to the best of your knowledge), not as punctuation or to fill space on the page. You should expect to revise and rewrite your solutions before submission. Do not hand in your rough scratch work. If you cannot solve a problem completely, then write an honest, coherent attempt and indicate where you ve had difficulties. Homework should be neatly and legibly written, the problems properly labeled (and in order), and the pages stapled. Final answers should be clearly marked as such. Presentation does make a difference and can even help you with your understanding. It takes time and practice to write mathematics well. If you make the effort, your written presentation is certain to improve. 8

Penn State University - University Park MATH 140 Instructor Syllabus, Calculus with Analytic Geometry I Fall 2010

Penn State University - University Park MATH 140 Instructor Syllabus, Calculus with Analytic Geometry I Fall 2010 There are two ways to live: you can live as if nothing is a miracle; you can live as if