Final review subjects(1)

# Final review subjects(1) - Final review topics This list is...

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Final review topics This list is meant to give you an overview of the concepts and techniques that could be on the ﬁnal (Thursday 5/5 at 9am or (alternative) Saturday 4/30 at 12pm). Questions on the test may combine material from two or more of the sections listed. Background - Basic diﬀerentiation techniques: in particular, the product rule and the chain rule. - Basic integration techniques: in particular, integration by parts and inte- gration by substitution. - Graphing ellipses, circles, hyperbolas and parabolas in simple cases (e.g. when taking traces of a surface). Section 13.1 - Distances in two and three dimensions. - The equation of a sphere, and completing the square to ﬁnd center and radius. Section 13.2 - ‘ h a,b,c i ’ and ‘ a ~ i + b ~ j + c ~ k ’ notation for vectors. - Adding and subtracting vectors, and multiplying a vector by a scalar, and the geometric interpretation of these operations. - Basic properties of these operations on vectors (page 810). - The vector ~ PQ from a point P to a point Q . Section 13.3 - Taking dot products in two and three dimensions, and geometric interpre- tation. - Using dot products to check for orthogonality. - The formula relating the dot product of two vectors to the angle between them. Section 13.4 - Taking cross products, and geometric interpretation (including the ‘right- hand-rule’). - The formula relating the length of the cross product of two vectors to the angle between them. 1

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- Relation of the dot product to parallelism. - The formula for the volume of a parallelepiped in terms of the dot and cross products. Section 13.5 - Vector, parametric, and symmetric forms for the equation of a line (in- cluding the ‘direction vector’). - Finding whether two lines are parallel, skew, or intersect in a unique point (and ﬁnding the point if it exists). - The relationship of a normal vector to a plane with the scalar equation of a plane, and the geometric interpretation of the normal vector. - Using geometric information about points on a plane, and lines in or par- allel to a plane to ﬁnd its scalar equation. - Finding the angle between two planes.
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Final review subjects(1) - Final review topics This list is...

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