MATH 222 SYLLABUS - FALL 2016 CALCULUS AND ANALYTIC GEOMETRY II Lecture 002 M-W-F 1:20-2:10 (Bascom Hall 272) Lecture 004 M-W-F 12:05-12:55 (Van Vleck B102) Instructor: Rachel Davis Email: rachel.davis@wisc.edu Office: 517 Van Vleck Office hours: s 2:25-3:15pm s 4-5pm s 10-11am s 2:25-3:15pm Textbook: Math 222 notes, which can be purchased in B227 Van Vleck Hall during the first week of class, or at the reception desk on the 2nd floor for the remainder of the semester (See https://www.math.wisc.edu/calculuscourse-materials for more details on purchasing calculus notes). Website: All announcements and homework assignments will be posted on the Canvas site. Log in at: https://canvas.wisc.edu (Here is some additional information about the use of Canvas as the University of Wisconsin-Madison: https://canvasinfo.wisc.edu/ ). COURSE CONTENT 1. Techniques of integration (a) substitution (b) integration by parts (c) trigonometric integrals (d) trigonometric substitutions (e) partial fraction decompositions (f) improper integrals 2. Applications of integration (a) arc length (b) moments and center of mass (c) pressure and force 3. Differential equations (a) linear first order 4. Definitions and relations between infinite sequences and series, algebraic and geometric series 1
5. Series Convergence (a) convergence tests: integral, comparison and ratio tests (b) absolute convergence and alternating series 6. Power series and radius of convergence 7. Taylor series (a) Taylor s formula (b) exponential, cosine and sine expansions (c) error bounds for Taylor approximations 8. Analytic Geometry (a) vectors and parametric equations (b) lines and planes (c) dot and cross products EXAMS AND GRADES: 1. Homework quizzes: There will be weekly homework assignments for a total of around 12 assignments. Homework will be posted on the Canvas site every. Written work will be held to a high standard. You will be expected to show all of your work and will be graded based on what is on the page. Homework will be collected at the beginning of discussion section on. Homework will be worth 5% of your final grade. For each homework set, there will be a 20 minute quiz in discussion section with 2 problems on s. The first problem on the quiz will be identical to a homework problem. The second problem will be similar to a homework problem (possibly with some numbers changed). You may not use any notes or calculators during quizzes or exams. Quizzes will be worth 15% of your final grade. Only the best 10 homework and the best 10 quiz scores will be kept. There will be NO makeup quizzes. Please save dropped quizzes for emergencies. Homework and quizzes will count for 20% of your final grade. 2. Exams: There will be two midterms and a final for this course. Each midterm exam will be worth 25% of your final grade. The final exam will be worth 30% of your final grade. The questions on the midterms and final will be a combination of computational problems and word problems, similar to those you will see in lecture and on homework. The dates for these exams are Midterm 1:, October 13 7:30pm Midterm 2:, December 1 7:30pm Final exam:, December 21 10:05am There will be two midterm exams. If you have another UW course that conflicts with the exam, send an email to your TA with subject Math 222 Exam 1 Conflict or Math 222 Exam 2 Conflict no later than September 16. Other classes are the only conflicts that will be considered, and conflicts will not be considered after February September 16. (Send two emails if you have two conflicts.) Arrive early and bring your ID to each exam. Expectations: We expect each student and each instructor to be respect of all of the students and instructors involved in this course. For instance, we expect students to refrain from behaviors that are 2
disruptive to your instructors and your fellow students, including: showing up late to lecture or section on time, playing with electronic devices during lecture or section, or leaving early. ACADEMIC HONESTY POLICY The highest standards of academic honesty are expected of all students. Academic misconduct (including passing the work of someone else as your own or tampering with an exam) will not be tolerated. If you are not sure whether a certain behavior is considered academic misconduct, do not hesitate to contact your instructor or TA to inquire about it. You are expected to work individually in both midterms, the final, and the quizzes. However, group work is allowed, and even encouraged, for homework assignments. If you do decide to work with other people in your homework, you must still submit your own HW assignment to your TA. Listed on the top of your homework please list the names of all the students you collaborated with. You are not allowed to copy homework problems from other students, but your answer can match that of another student if you both actively collaborated to obtain the answer to that particular problem. You are also allowed to consult books and other sources while working on your HW assignment, but any external aid must be cited as such at the beginning of your HW. Reference materials of any kind are NOT allowed for the quizzes, midterms and final exam. PARTICIPATION POLICY Please feel free to ask questions during lecture. Even though it can be intimidating to stop a large lecture to ask a question, you should note that if there s anything that you don t understand, there s probably many other students who have the same question and lack the confidence to ask. You can also ask me questions right after class, during my office hours, during discussion section and during any of the TAs office hours. However, please DO NOT use email to ask me math questions. It is much easier and more efficient to answer math questions in person. Only email me for administrative purposes (i.e., if you have a conflict with the exam date, etc.) If you email me a question whose answer is relevant to other students, I might post an announcement on the Canvas page rather than answering your email personally. If the answer to your email is in this syllabus (i.e, if you email me to ask when the midterms are, etc.), then I might not answer the email at all. 3
Lecture Schedule and Assignment Sheet Date Lesson Section/Topic Tuesday September 6 Review I.1: Definite and indefinte; 1 September 7 September 8 Homework #1 and Quiz #1 today I.3: The double 2 September 9 angle formulas I.5, I.6: Integration by parts 3 September 12 Reduction formulas September 14 4 I.8: Partial fractions September 15 Homework #2 and Quiz #2 today September 16 5 I.8: Partial fractions September 19 6 I.10: Trig substitution September 21 7 I.11: Advanced substitution September 22 Homework #3 and Quiz #3 today September 23 8 I.12: Advanced substitution II September 26 9 II.1: Improper integrals II.2: Computing improper 10 September 27 integrals September 28 Homework #4 and Quiz #4 today S II.3: Improper integrals 11 September 30 Examples October 3 12 II.5: Estimating Improper III.1: Differential Equations 13 October 5 Definitions October 6 Homework #5 and Quiz #5 today III.2: Differential equations 14 October 7 Basic examples 4
Date Lesson Section/Topic I.14, I.15: Chapter Summary 15 October 10 Mixed Integration Problems October 12 16 Chapter II Review October 13 MIDTERM EXAMINATION #1 (No homework and no quiz today.) III.3: First Order 17 October 14 Separable Equations III.5: First Order Linear; 18 October 17 III.7: Direction fields; 19 October 19 October 20 Homework #6 and Quiz #6 today October 21 20 III.8: Euler s Method III.10: Applications I; 21 October 24 III.10: Applications II; 22 October 26 October 27 Homework #7 and Quiz #7 today October 28 23 IV.1: Taylor Polynomials I IV.2: Taylors Polynomials II; 24 October 31 IV.3: Taylor Polynomials III; 25 November 2 November 3 Homework #8 and Quiz #8 today November 4 26 IV.5: The Remainder Term IV.6: Lagrange s Formula for the Remainder Term; 27 November 7 IV.8: Taylor polynomial 28 November 9 Little o November 10 Homework #9 and Quiz #9 today November 11 29 IV.10: More on Taylor polynomials 5
Date Lesson Section/Topic V.1: Sequences and 30 November 14 Series November 16 31 V.2: Sequences November 17 Homework #10 and Quiz #10 today November 18 32 V.4: Series V.5: Convergence of 33 November 21 Taylor Series November 23 34 V.7: Leibniz formulas Thanksgiving November 24 recess No class. No HW. Thanksgiving November 25 recess No class November 28 35 VI.1, VI.2: Vectors November 30 36 Review for Exam 2 December 1 MIDTERM EXAMINATION #2 (No homework and no quiz today.) December 2 37 VI.3: Lines December 5 38 VI.4: Vector Bases December 7 39 VI.5: Dot Product December 8 Homework #11 and Quiz #11 today December 9 40 VI.6: Cross Product VI.7, VI.8: Applications 41 December 12 of the Cross Product December 14 42 REVIEW for FINAL EXAM December 15 Homework #12 and Quiz #12 today Study December 16 day No class December 21 10:05AM-12:05PM FINAL EXAMINATION 6
STUDENT RESOURCES 1. See your professor or TA during their office hours or after class. 2. Other office hours. If you are unable to attend, you can also attend the office hours of another TA for Lecture 002 or 004. 3. Mathlab: Drop-in tutoring staffed by TAs and advanced undergraduates. There are usually a lot more students than TAs, so it s not individualized attention. Location: B 227 VV. Open - 3:30-8:30 and Sundays 3:30-6:50. More info can be found: http://www.math.wisc.edu/undergraduate/mathlab. 4. Math department tutorial program: free program, you can meet weekly with a math TA in a small group. You can ask your TA for more details if interested in applying. This program has limited vacancies and requires a semester long commitment. http://www.math.wisc.edu/undergraduate/tprogram/contact 5. Greater University Tutoring Service (GUTS) It s a student organization offering free volunteer tutoring (in many subjects) ran by more advanced students. There are two formats, drop-in and regular meetings. More info on this program can be found http://guts.studentorg.wisc.edu/programs/info.html 6. College of engineering tutoring: Offers free drop-in tutoring at Wendt library for any student taking core math classes. They also offer scheduled tutoring for authorized students. http://wendt.engr.wisc.edu/spacesn-places/tutoring/ 7. Residence hall tutoring: Free drop-in tutoring at different residence hall locations. Hours and locations can be found http://www.housing.wisc.edu/residencehalls-academics-tutoring.htm 8. The Math Library has a collection of old exams. They can be found here: http://math.library.wisc.edu/reserve/ 9. UHS counseling services: Mental health and wellness counseling and workshops for students. More info can be found https://www.uhs.wisc.edu/mental-health/getting-started/ 10. Private tutors: a list of math graduate students and their tutoring rates: http://www.math.wisc.edu/tutors 7