137 Course Outline.pdf - University of Waterloo MATH 137...

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University of WaterlooMATH 137Calculus I for honours mathematicsWinter 2020Course summary.Absolute values and inequalities.Sequences and their limits.Introduction to series.Limitsof functions and continuity. The Intermediate Value Theorem and approximate solutions to equations. Derivatives,linear approximation and Newton’s method. The Mean Value Theorem and error bounds. Applications of the MeanValue Theorem, Taylor polynomials and Taylor’s Theorem, Big-O Notation.Tentative Course ScheduleThe text sections refer to the course notes.WeekDatesText SectionsTopicsEvents1Jan 6–101.2Introduction. Sequences and convergence2Jan 13–171.2-1.4Limit rules. Implicit sequences, monotone convergence thm3Jan 20–24*1.5Contraction mapping. Series - geometric series, ratio testA1 due4Jan 27–312.8-2.10Limits & continuity. 3 theorems, piece-wise functions5Feb 3–72.1-2.5, 2.7, 3.2Limits of functions, asymptotes. Intro to derivative6Feb 10–14**3.3, 3.7-3.12, 4.2.1Derivative (cont). Rules of differentiation. AntiderivativesA2 due7Feb 17–21READING WEEK8Feb 24–283.5, 3.6Linear approximation, Newton’s method.midterm9Mar 2–64.1, 4.2.2-4.2.6Mean value theorem, Concavity10Mar 9–134.2.7, 4.2.8, 2.11/4.4Optimization, Curve sketchingA3 due11Mar 16–205.1Newton’s interpolation, Maclaurin polynomial12Mar 23–275.2Example Taylor polynomials, Remainder theorem13Mar 30–Apr 35.3Big-O notation, using Big-O, Approximation methodsA4 due* 100% tuition refund deadline Jan 24th** 50% tuition refund deadline Feb 14thDrop, penalty 1 period ends March 22nd(note that drop, penalty 2 period ends April 7th)Midterm Test:Monday February24th, 7:00-8:50 pm(location TBA).Course Text:MATH 137 Calculus I 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~baforres/UCM137/Lectures/BarbsM137Lectures.htmlCourse Website:~mscott/cauchy.htmCalculators:Calculators (and other devices) are not allowed during the midterm or final exam.Grades:Your final grade consists of:Assignments (Best 3 of 4): 10%;Midterm Exam: 30%;Final Exam: 60%.Note that your overall combined average on the Midterm and Final Exams must be over 50% to use this scheme (inother words, you must obtain at least 45/90 of those marks). If you do not, then your final grade will instead be yourcombined average on your Midterm and Final Exams.
Assignments:The weekly assignments aredue Fridays at 5:00 pmas indicated upon the assignment. These aresubmitted via Crowdmark.Late assignments for ANY REASON will receive a grade of zero. If you are unable tocomplete an assignment (for example, you were sick in the days leading up to the due time) then you should submitvalid documentation that details this incapacitation as soon as possible. In this case, the weight of that assignmentmay shift to the rest of your assignments.

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