DEPARTMENT OF MATHEMATICS TRENT UNIVERSITY MATH 2110H: Several Variables Calculus 2017 FALL Peterborough

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1 DEPARTMENT OF MATHEMATICS TRENT UNIVERSITY MATH 2110H: Several Variables Calculus 2017 FALL Peterborough Instructor: Dr. Haile Gessesse Trent Telephone: (705) x 7925 Campus: Peterborough Office Location: GCS 332 Office Hours: Tuesday and Thursday 12:00-13:00 Academic Administrative Assistant: Gina Collins Office Location: SC math@trentu.ca Telephone: x7715 Tutorial Assistant: TBA Course Description: This is a first course in multivariable calculus. Topics covered include functions of several variables, curves and surfaces in two and three dimensions, spherical and cylindrical coordinates, vectors in the plane and space. Differentiation in several variables including partial derivatives, directional derivative, gradient, chain rule, extreme values and optimization. Integration in several variables including double and triple integrals and change of variables. Course Pre-requisites: MATH 1100Y or MATH 1120Y and MATH 1350H (MATH 1350H may be taken as co-requisite). Required Text: University Calculus, Early Transcendental, J. Haas, M. Weir, G. Thomas Jr, Pearson (third or second edition). learningsystem/blackboard: Relevant course material and homework will be made available on LearningSystem/Blackboard. Important dates or sudden announcements will also be made via the course main page and announcements section. It is important to visit the course page regularly. Math Resource Center: The Math Resource Center (MRC) is available for students taking a course in calculus, differential equations, statistics, and linear algebra. The MRC is located in Peter Gzowski College 338 and schedule will be announced. Course Format: Peterborough Campus: Please check to confirm times and locations.

2 Type Day Time Location Lecture Tue 11:00 11:50 GCS 103 Lecture Wed 10:00 10:50 GCS 103 Lecture Thu 9:00 9:50 GCS 103 Workshop / Tutorial Fri 12:00 12:50 GCS 103 Students will be assigned to a Workshop / Tutorial time, and are encouraged to attend for additional assistance with course work. Learning Outcomes/Objectives/Goals/Expectations: The course is developed to address several learning outcomes. By the end of the course a successful student should be able to: (1) Demonstrate knowledge of vector operations including dot product, cross product and vector applications. (2) Draw quadratic surfaces. (3) Demonstrate knowledge of polar, cylindrical and spherical coordinates. (4) Find equations of lines and equations of planes in multi-dimensional settings. (5) Find partial derivatives, directional derivatives, and gradient vectors. (6) Solve optimization problems of two or more variables using various techniques including Lagrange Multipliers. (7) Evaluate double and triple integrals in various coordinates including Cartesian, Polar, Cylindrical and Spherical Coordinates. (8) Understand substitution rule in multiple integrals. Course Evaluation: Type of Work Weighting Due Date Six Written Assignments (Write solutions for assigned questions showing each step towards the answer) One Written Midterm (Closed book, show your work type questions; covers contents from the first lecture to the latest lecture.) 30% Tentatively due: Fri, September 29, 13:00 Fri, October 6, 13:00 Fri, October 13, 13:00 Fri, November 3, 13:00 Fri, November 17, 13:00 Fri, December 1, 13:00 30% Wednesday, Oct 18, in-class Written Final Examination (Type of questions similar to Midterm. Three our comprehensive Exam where higher proportion given on Topics after Midterm.) 40% In the exam period, as scheduled by the university. Calculators are not allowed on the midterm or final exam. Both the midterm and final exam are closed book.!2

3 Course Grading Policies: The final date to withdraw from this course without academic penalty is November 7th, 2017 for the Fall (FA) term. By this date at 30% of the course grade will have been completed, graded and returned. After this date students remain registered will receive final grades. Assignments: Assignments will be posted on Blackboard. Solutions are to be submitted to the correct dropbox labeled Haile Gessesse before the due date. Drop boxes are located at room GCS 336. Be sure to double check that you are submitting to the correct dropbox because assignments submitted to the wrong box (and late assignments) will be given a grade of 0. Assignment solutions will be posted by Mondays 9AM. Late assignments will NOT be accepted. The first assignment will be due on September 29. You may discuss the assignment problems with your classmates, but you are expected to write up your solutions independently. Copying assignment solutions and/or presenting someone else s work as your own is a serious academic offence and will be treated accordingly. See the ACADEMIC INTEGRITY section below for more information. Seminars: Seminars will be primarily used for asking for help on the assignments. Students are strongly encouraged to try the assignment questions before coming to seminars. Date to remember: Tuesday, November 7, 2017 is the final date for withdrawal from the course without academic penalty. After this date students remain registered will receive final grades. Department Policy: Final date to appeal marks for assignments, quizzes or projects for Fall half courses is March 5th, Course Policies: Please read carefully (1) s: You must use your Trent to contact the Instructors. s from non-trentu.ca addresses (e.g. hotmail.com, gmail.com) will be ignored. The subject line of each must contain MATH 2110H. (2) Workshops will be used for solving some textbook questions, help on assignments. (3) Missed and late assignments will receive a grade of zero. (4) Discussions with others on assignments are allowed. But you are required to do them by your own; copying is not allowed. (5) There are no makeup tests and exam. Week-by-week schedule (Tentative): The schedule of topics is listed below. It is important that you attend class and use the Blackboard system regularly to remain informed about the material being covered. Week of Term Section A Dates Topics Textbook Sections 1 Sept 7 Introduction, Vectors 11.1!3

4 2 Sept 12, 13, 14 Vectors in the Plane and Three Dimensions, Dot Product, Cross Product 3 Sept 19, 20, 21 Planes in Space, Quadratic Surfaces, Curves in Space and Their Tangents 11.1, 11.2, , 11.5, 4 Sept 26, 27, 28 Curves in Space and Their Tangents, Functions of Several Variables 5 Oct 3,4,5 Limits and Continuity in Higher Dimensions, Partial Derivatives, Jacobian 6 Oct 10, 11, 12 Chain Rule, Directional Derivative and Gradient 7 Oct 17, 18, 19 MIDTERM TEST, Tangent planes and Differentials 11.6, , , Reading Week Break 9 Oct 31, Nov 1, 2 Second Derivative Test, Optimization Problems 10 Nov 7, 8, 9 Lagrange Multipliers, Double Integrals and Iterated Integrals over Rectangles , Nov 14, 15, 16 Double Integrals over General Regions, Area, Double Integrals in Polar Coordinates 12 Nov 21, 22, 23 Triple Integrals in Rectangular Coordinates, Moments and Center of Mass 13 Nov 28, 29, 30 Triple integrals in Cylindrical and spherical coordinates, Substitution in Multiple Integrals 14.2, 14.3, , , Dec 5, 6 Review (if time permits) Academic Integrity: University Policies!4

5 Academic dishonesty, which includes plagiarism and cheating, is an extremely serious academic offence and carries penalties varying from failure on an assignment to expulsion from the University. Definitions, penalties, and procedures for dealing with plagiarism and cheating are set out in Trent University s Academic Integrity Policy. You have a responsibility to educate yourself unfamiliarity with the policy is not an excuse. You are strongly encouraged to visit Trent s Academic Integrity website to learn more: Please note that some assignments for this course may allow for team work. However, all examinations (and certain assignments where noted) will be sole work, and evidence of collaboration on the same will be treated very seriously. Access to Instruction: It is Trent University's intent to create an inclusive learning environment. If a student has a disability and documentation from a regulated health care practitioner and feels that he/ she may need accommodations to succeed in a course, the student should contact the Student Accessibility Services Office (SAS) at the respective campus as soon as possible.!5

Math 181, Calculus I

Math 181, Calculus I [Semester] [Class meeting days/times] [Location] INSTRUCTOR INFORMATION: Name: Office location: Office hours: Mailbox: Phone: Email: Required Material and Access: Textbook: Stewart,