MA242 Review IV
Line Integrals
First type: Scalar -> scalar. It is independent of the direction of the curve.
Second type : Vector -> scalar. When we change the direction of the curve, the result differ by
a sign.
Parametric form of curves in 2D and 3D
Sample Quiz 1
1. Given four points in an O XY Z coordinates: A (0, 0, 0), C (0, 1, 1) (a) Find the distance between A and D. (b) Find the area of the parallelogram formed by the vectors AB and AC. Are A, B, and C are in a same line? (c) Find a unit vector
MA242 Review II
Functions of two or more variables (f(x,y), f(x,y,z) . )
Domain: All possible (x,y)
Range: All possible function values
Graph of f(x,y), z = f(x,y)
Level curves of f(x,y) (surfaces if f(x,y,z). Curves where f(x,y) has the same values.
Final Review
Analytic Geometry
Points: (x,y), (x,y,z)
Distance between two points
mid-point
vectors in 2D and 3D: <x,y>, <x,y,z>
vector formed from two points, direction
vector operations and geometric and physical meanings:
a + b, a - b, a dot b,
Review Problems for Quiz 1 (9.1-10.3)
1. Given four points in an XYZ coordinates: A(0,0,0), B(1, -1, 0), C(0, 1, 1), and D(-1, 0, 1):
1. Find the distance between A and D.
2. Find triple product of AB, BC, and AB.
3. Find the area of the parallelogram for
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