138 Course Outline W20 PDF

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Download 138 Course Outline W20 PDF

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University of Waterloo

MATH 138

Calculus II for Honours Mathematics

Winter 2020

Course objectives. The goal of this course is to further expand your knowledge of calculus and its applications for one-variable functions. The course can broadly be split into three parts. First, we will explore areas under curves and the Fundamental Theorem of Calculus, integration techniques, and applications of integration including finding the area between two curves, volumes of solids of revolution, and the average value of a function. Secondly, we will examine differential equations. We will study how to solve separable differential equations and linear differential equations as well as their applications to population growth and Newton’s Law of Cooling. Finally, we investigate infinite series. Various tests of convergence will be introduced for series of numbers. Then, we study power series with a focus on Taylor series and look at their applications. Tentative Course Schedule Week 1 2 3 4 5 MT RW 6 7 8 9 10 FE

Dates Jan 6–10 Jan 13–17 Jan 20–24* Jan 27–31 Feb 3–7 Feb 10–14** Feb 17–21 Feb 24• –28 Mar 2–6 Mar 9–13 Mar 16–20† Mar 23–27 Mar 30–Apr 3

Text Sections 1.2–1.4 1.5–1.7 2.1–2.3 2.4, 3.1 3.2, 3.3, 4.1, 4.5.1 4.2, 4.3, 4.5–4.8 5.1–5.4 5.5–5.7 5.8–5.10 6.1, 6.2, 6.3 6.4, 6.5, 6.6, 6.7 6.8, 6.9, 6.10

Topics Events Riemann Sums, Definite Integrals, Average Value FTC I, FTC II, Change of Variable Quiz 1 Trig. Sub., Integration By Parts, Partial Fractions Quiz 2 Improper Integrals, Areas Between Curves Quiz 3 Volumes, Intro to DEs, Direction Fields Quiz 4 Separable DEs, Linear DEs, Applications Quiz 5 READING WEEK Intro to Series, Geo. Series, Div. Test midterm Positive Series, Integral Test, Alternating Series Quiz 6 Types of Convergence, Ratio & Root Tests Quiz 7 Intro. to Power Series, Functions, Differentiation Quiz 8 Integration, Review of Taylor Polys., Taylor Series Quiz 9 Convergence, Binomial Series, Applications Quiz 10

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* 100% tuition refund deadline Jan 24th ** 50% tuition refund deadline Feb 14th † Drop, with WD ends March 20th • Midterm Exam: Monday February 24th , 100 minutes, 7:10-8:50 pm. (location TBA) Course Text: MATH 138 Calculus II for Honours Mathematics Course Notes by Barbara A. Forrest and Brian E. Forrest, available online and in print at the bookstore. Online version available at http://www.math.uwaterloo.ca/~baforres/UCM138/Lectures/BarbsM138Lectures. html Course Website: https://learn.uwaterloo.ca/d2l/home/509246 Calculators: Calculators (and other devices) are not allowed during the quizzes, midterm, or final exam. Grades: Your final grade consists of: Quizzes (Best 8): 20%; Midterm Exam: 30%; Final Exam: 50%.

Quizzes: There will be 10 quizzes during the tutorials (starting January 15th) Your best 8 quiz marks will count for 20% of your final grade. Missed quizzes for ANY REASON will receive a grade of zero. Note that there are no tutorials on January 8th or February 26th. Practice problem sets will be posted on Learn 1-2 weeks before the quiz. Solutions will also be posted on Learn. At least one problem from the practice problem set each week will appear on the quiz! Getting help. Your instructor will have office hours: the times and location will be included in the module for their section in the course website. Additionally, the tutorial centre will be available to all students, the schedule will be posted on Learn. Although help for completing practice questions is available (from instructors, TA’s, or colleagues in the course) keep in mind that you will be on your own during the quizzes, midterm, and final exam: seeking help should be in the scope of clarifying the material taught rather than in having the problems completed. Instructors and contact info by section: LEC 001 & 002 LEC 003 & 004 LEC 005 (PHYS and MATHPHYS) LEC 006 LEC 008 LEC 009

Jennifer Nelson [email protected] Jordan Hamilton [email protected] Michael Waite [email protected] Diana Castaneda Santos [email protected] Lilia Krivodonova [email protected] Jun Liu [email protected]

Piazza: A Piazza page for this class will be created at the start of term and students will be given the link. This is a great place to ask and answer questions about the course. Midterm: The midterm is scheduled on Monday February 24th , it will be 100 minutes long between 7:10pm and 8:50pm. The material covered in the midterm together with the location of the midterm will be posted on Learn before Reading Week. The midterm will be graded and returned electronically via Crowdmark. Missed Midterm: If you are unable to write the midterm (for example, you are sick) then valid documentation (such as a University of Waterloo Verification of Illness form) should be submitted to the Math Undergraduate Office (MC 4022) and to your instructor. In this case, the weight of the midterm may shift to your final exam. There will be NO make-up midterm. Final Exam: There will be a registrar-scheduled final exam for the course. Details will be posted on Learn. Missed Final Exam: As with the midterm, you must have a valid reason and provide appropriate supporting documentation to the Math Undergraduate Office and to your instructor if you miss the final exam. Absence from the final exam may result in a grade of INC at the discretion of your instructor. To be considered for an INC, you must have a passing grade on the midterm test and an overall average of at least 50% on the quizzes. (See http://ugradcalendar.uwaterloo.ca/page/Regulations-Accommodations.) Extra Resources: MATH 137 Notes: http://www.math.uwaterloo.ca/~baforres/UCM137/CourseNotes/Forrest_M137CN.pdf MATH 138 Online Lectures: http://www.math.uwaterloo.ca/~baforres/UCM138/Lectures/BarbsM138Lectures. html CEMC courseware: Integral Calculus (11 lessons) https://courseware.cemc.uwaterloo.ca/11?gid=26 Applications of Integral Calculus (8 lessons) https://courseware.cemc.uwaterloo.ca/11?gid=27

Learning Outcomes: by the end of this course, students will be able to: • Write clear and well-organized mathematical solutions and proofs. • Solve problems in Calculus through logical thinking and careful analysis. • Set up and evaluate Riemann integrals for simple functions • Utilize the Fundamental Theorem of Calculus to evaluate definte integrals. • Apply various integration techniques including change of variable, integration by parts, trigonometric substitution, and partial fractions. • Solve problems with integration including improper integrals, areas between curves, and volumes of revolution. • Solve separable and first-order linear differential equations. • Model real-world problems with differential equations. • Understand infinite series and convergence (both absolute and conditional). • Apply various series convergence tests. • Compute the radius and interval of convergence for power series. • Compute the Taylor series for many elementary functions. • Use Taylor series to solve application problems.

Mental Health Support: The Faculty of Math encourages students to seek out mental health support if needed. On-campus Resources: • Campus Wellness https://uwaterloo.ca/campus-wellness/ • Counselling Services: [email protected] / 519-888-4567 ext 32655 / Needles Hall North 2nd floor, (NH 2401) • MATES: one-to-one peer support program offered by Federation of Students (FEDS) and Counselling Services: [email protected] • Health Services: located across the creek from the Student Life Centre, 519-888-4096. Off-campus Resources: • Good2Talk (24/7): Free confidential help line for post-secondary students. Phone: 1-866-925-5454 • Here 24/7: Mental Health and Crisis Service Team. Phone: 1-844-437-3247 • OK2BME: set of support services for lesbian, gay, bisexual, transgender or questioning teens in Waterloo. Phone: 519-884-0000 extension 213 Academic Integrity: In order to maintain a culture of academic integrity, members of the University of Waterloo community are expected to promote honesty, trust, fairness, respect and responsibility. [Check www.uwaterloo.ca/academicintegrity/ for more information.] Grievance: A student who believes that a decision affecting some aspect of his/her university life has been unfair or unreasonable may have grounds for initiating a grievance. Read Policy 70, Student Petitions and Grievances, Section 4, http://www.adm.uwaterloo.ca/infosec/Policies/policy70.htm. When in doubt please be certain to contact the department’s administrative assistant who will provide further assistance. Discipline: A student is expected to know what constitutes academic integrity to avoid committing academic offenses and to take responsibility for his/her actions. A student who is unsure whether an action constitutes an offense, or who needs help in learning how to avoid offenses (e.g., plagiarism, cheating) or about ”rules” for group work/collaboration should seek guidance from the course professor, academic advisor, or the undergraduate associate dean. For information on categories of offenses and types of penalties, students should refer to Policy 71, Student Discipline, http://www.adm.uwaterloo.ca/infosec/Policies/policy71.htm. For typical penalties check Guidelines for the Assessment of Penalties, http://www.adm.uwaterloo.ca/infosec/guidelines/penaltyguidelines.htm. Appeals: A decision made or penalty imposed under Policy 70, Student Petitions and Grievances (other than a petition) or Policy 71, Student Discipline may be appealed if there is a ground. A student who believes he/she has a ground for an appeal should refer to Policy 72, Student Appeals, http://www.adm.uwaterloo.ca/infosec/Policies/policy72.htm. Note for students with disabilities: Access Ability Services, located in Needles Hall, Room 1401, collaborates with all academic departments to arrange appropriate accommodations for students with disabilities without compromising the academic integrity of the curriculum. If you require academic accommodations to lessen the impact of your disability, please register with the Access Ability Services at the beginning of each academic term....