M2E: MIDTERM 2 INFORMATION


DATE OF THE EXAM: Friday, March 2, 2018

TOPICS COVERED: Sections 16.1 up to 16.4, included. The focus will be on
-- Line integrals: both line integrals with recpect to arc length, and line integrals of a vector field, both in dimension 2 and 3. Calculating mass and center of mass of objects in the shape of a wire or similar, given the density function. Also calculating of work done by a force field.
-- Determining whether a given vector field is conservative and calculating potential functions. Calculations of work done by conservative vector fields.
-- Applications of the fundamental theorem for line integrals.
-- Green's theorm and its applications:
    -- evaluating line integrals of vector fields in terms of double integrals of functions,
    -- calculating the area of the region surrounded by a closed curve in terms of line integrals of suitable vector fields,
    -- calculation of line integrals along closed curves for vector fields the domain of which is not simply connected.

SAMPLE WRITING FOR THE EXAM: Following the suggestion of some of you, please look at the sample solutions at this link. Try to write in a similar way at the exam: That is, the explanations should be close to how it is done in this samle sheet. You should include all relevent information in your writing: Explain how you obtained your integrated formula and bouds, and write down all steps which are relevant. In order to give you all points you deserve, I need to see how you obtained the relevant conclusions, so please show as much of your work as you can.

FORMAT OF THE EXAM: Similar to Midterm 1. There will be four problems, each worth 10 points. The level of difficulty will be the same as in Midterm~1.

EXAM RULES: Please refer to the general exam rules under ``Course information and policies" on the course exam. In particular, no book, notes and no electronic devices of any kind will be allowed.

GRADING: I will be grading the midterm, so please all questions should be addressed to me (= the instructor). Otherwise, for general information concerning grading, see again ``Course information and policies" on the course website.

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Last Modified: March 1, 2018