Mathematics

Material on Test 1

9.1 Three-dimensional coordinate systems: distance, equation of sphere, regions in 3-space defined by an equation or by inequalities.

9.2 Vectors: vector algebra, unit vectors.

9.3 Dot product: angle between vectors, orthogonal and parallel vectors, scalar and vector projection, work.

9.4 Cross product and determinant: geometric interpretation of cross product, use of cross product and determinant to find areas and volumes, use of determinant to check whether three vectors are coplanar.

9.5 Planes and lines: normal vector of a plane, equation of plane, plane through three points, parallel planes; direction vector of a line, vector and parametric equations of a line, parallel lines, point of intersection of two lines or of a line and a plane, plane through two lines or through a point and a line. Omit distance from a point to a plane.

9.6 Functions of two variables and surfaces: domain and graph of a function, traces in planes, graphing quadric surfaces.

10.1 Vector functions and space curves: domain, match equation with sketch, sketch simple curves.

10.2 Derivatives of vector functions: derivative, find and sketch unit tangent vector, angle between curves. Omit integrals.

10.3 Arc length and curvature: arc length, unit tangent and normal vectors, curvature. I will give you Formula 9, p. 719, for curvature.

10.4 Motion in space: velocity, acceleration, speed, sketch of velocity and acceleration vectors, tangential and normal components of acceleration.I suggest you remember the formulas from lecture for tangential and normal components of acceleration.

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