MATH247: Calculus 3 (Advanced Level)
                                                       FALL 2022
                • Instructor: Spiro Karigiannis     • Email: karigiannis@uwaterloo.ca
                • Office: MC 5326                   • Office Hours: Monday/Wednesday 1:00pm–1:50pm
                • Lecture Room: RCH 305             • Lecture Times: Monday/Wednesday/Friday 8:30am–9:20am
               • Course Website: https://learn.uwaterloo.ca/
               • The course website is on UW-LEARN (D2L). All course material (assignments, solutions, supplementary
                 material) will be posted there. It is your responsibility to check the course website on a regular basis.
                 Ignorance is not an acceptable excuse for missing deadlines.
               • There will be an online discussion forum on Piazza for the course.
               • All assignments must be submitted via CrowdMark, and all graded work (assignments and midterm) will be
                 returned to students via CrowdMark.
            Course description: In this course we will give a rigorous treatment of the topology of Rn, and of the differential
            and integral calculus of functions from Rn to Rm. Some of the important results we will prove in detail are:
            the Bolzano-Weirstrass Theorem, the Heine-Borel Theorem, the characterization of differentiability in terms of
            the existence and continuity of all partial derivatives, the inverse and implicit function theorems, the rigorous
            definition of Riemann integration, Fubini’s Theorem, and the change of variables theorem.
            Prerequisites: ThecourseprerequisitesareMath146[LinearAlgebra1(AdvancedLevel)]andMath148[Calculus
            2 (Advanced Level)]. This course is for Honours Mathematics students only. You are expected to have had previous
            exposure to and be comfortable with rigourous mathematical proofs. We will cover a very large amount of
            difficult material at a very fast pace.
            Brief description of topics: The topology of Rn: completeness, open sets, closed sets, connectedness, com-
            pactness, continuity, uniform continuity. Differential calculus of multivariable functions: partial derivatives, differ-
            entiability, chain rule, Taylor’s theorem, extreme value problems. Local properties of continuously differentiable
            functions: open mapping theorem, inverse and implicit function theorems. Riemann integration: Jordan content,
            integrability criteria, Fubini’s theorem, change of variables theorem.
            Textbook: There is no required textbook for this course. Some useful references are the following:
               • W. Fleming, Functions of several variables, second edition, Undergraduate Texts in Mathematics, Springer-
                 Verlag, New York, 1977.
               • G. B. Folland, Advanced Calculus, Prentice Hall, 2002.
               • K. Hoffman, Analysis in Euclidean space, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1975.
               • L. H. Loomis and S. Sternberg, Advanced calculus, paperback edition of the 1990 revised edition of the 1968
                 original, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2014.
               • J. R. Munkres, Analysis on manifolds, Addison-Wesley Publishing Company, Advanced Book Program,
                 Redwood City, CA, 1991.
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           Marking scheme
           Your course mark will be determined as follows:
              • Assignments: 30% (twelve assignments, one every week, worth 2.5% each)
              • Midterm test: 15% (Tuesday 18 October 2022, 4:30pm–6:20pm, location TBD)
              • FINAL EXAM: 55% (date and time TBD)
           You may use calculators/computers to do the assignments, but you will not be permitted to use them for the
           midterm or the final exam. Please note that you are strongly encouraged to work together with your classmates on
           the assignment problems, but you must write up and turn in your own solutions to the problems. The assignments
           are an integral part of your evaluation in this course and I encourage everyone to take them very seriously. I will
           not be sympathetic to requests for leniency after the exam if you have not done the assignments. There is NO
           possibility to base your entire course mark on the final exam. This course will cover a large amount of
           difficult material at a fast pace. If you do not work hard in this course from day one, you will not do well.
           There will be no opportunity for a make-up midterm test. A student who misses the midterm test without a valid,
           acceptable excuse (accompanied by documented proof, such as a medical note) will receive a score of zero on the
           test. Students who miss the midterm for valid reasons will have the 15 points missed transferred to the final exam.
           Assignment due dates:
               • Assignment 01 due   Tuesday, September 13     • Assignment 07 due   Tuesday, November 1
               • Assignment 02 due   Tuesday, September 20     • Assignment 08 due   Tuesday, November 8
               • Assignment 03 due   Tuesday, September 27     • Assignment 09 due   Tuesday, November 15
               • Assignment 04 due   Tuesday, October 4        • Assignment 10 due   Tuesday, November 22
               • Assignment 05 due   Tuesday, October 18       • Assignment 11 due   Tuesday, November 29
               • Assignment 06 due   Tuesday, October 25       • Assignment 12 due   Tuesday, December 6
           NOTE: For information on academic offences and accessibility services, please see the detailed version of the
           course outline available at: https://outline.uwaterloo.ca/view/nhjv8s
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