![]() ![]() (You should be able to see how this gives us 2-dimensional analogue to the Fundamental Theorem of Calculus.) This theorem is especially useful for finding the line integral of a (possibly non-conservative) vector field by treating the curve over which you are integrating as part of a boundary of a region in the plane. You should also know how to find a potential function for such vector fields, and be able to identify situations where this is useful for evaluating an integral.ġ6.4:You must know the statement of Green's Theorem, and be able to use it to obtain the value of a given integral. You should also be able to interpret the vector line integrals physically and geometrically.ġ6.3 You must know the Fundamental Theorem for Line Integrals, and how to identify when a given vector field is conservative. You should be able to find the line integral of a scalar function and of a vector field over a given space curve. ![]() It is really important to understand this section since all subsequent sections build on this material.ġ6.2 This section generalizes arc length integrals from Section 13.3. (It is also helpful to be able to calculate the Jacobian determinant in 3 dimensions for the change of variables to polar coordinates.)ġ6.1: This section deals with the basics of vector fields, and what they represent. The change of variables formula for double integrals. Know how to find the Jacobian determinant and use it to calculate (or approximate) the change in area of a domain. It is also still important you are comfortable with the basics of differentiation and integration (as covered in Calculus I and Calculus II classes).ġ5.10: Practise finding the appropriate change of co-ordinates to simplify your integral, by either simplifying the domain or the function. The final exam is cumulative, so it is important that you study the material from earlier chapters as well. ![]() Intended to serve as a guideline, and may not explicitly mention everything that The material we have covered in class as you study for your exam. The following is a chapter by chapter guide intended to help you organize The Q-Center will continue to hold afternoon and evening Calculus drop-in hours this week, but please be sure to consult the updated schedule. Reading period office hours are WTh 10:00am-11:50pm and F 2:30-3:30pm. The final exam is on Sunday, December 20, from 2:00pm to 5:00pm, in Chapin 201. ![]()
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