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StudyGuideMidTerm1

# StudyGuideMidTerm1 - – ﬁnd the particular solution of...

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SHORT CALCULUS Math 16C Sec 1 Fall 2008 Mid-term exam 1 Study Guide Peter Malkin The structure of the first mid-term exam is as follows. Below is a list of the sections covered by each question together with an exhaustive list of types of questions that I might ask on the mid-term exam for each question. The list of types of questions are not given in any order. 1. Sections C.1 - C.4. Verify that an equation satisfies a differential equation. Find the general solution of a differential equation using either straight-forward integra- tion, the separation of variables technique, or the linear first order differential equation technique. Find a particular solution of a differential equation given initial conditions. Given a verbal description of an application of differential equations write down the differential equation, find the general solution of the differential equation,
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Unformatted text preview: – ﬁnd the particular solution of the diﬀerential equation using intial conditions, – and answer questions about the application using the solution of the diﬀerential equation. 2. Sections 7.1 - 7.2. • Find the midpoint of two points. • Find the distance between two points. • Find the equation of a sphere given suﬃcient information (e.g. center and radius or two endpoints of a diameter). • Find the center and radius of a sphere from the equation of the sphere. • Sketch the trace of a surface (i.e. the intersection of a surface with a plane). • Sketch a plane given by an equation. • Sketch and or identify a quadric surface from the equation of the surface (ellipsoid, ellip-tic parabloid, hyperbolic parabloid, elliptic cone, hyperboloid of one sheet, hyperboloid of two sheets). 1...
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