Exam #1 Review

Scheduling Information:	Time: Friday, February 17, from 7:30-8:20am (EGAD!) Location: CUC McConomy. Review Session: Thursday, February 16, from 6:00-7:20 in DH 2210.

Topics Covered:	Three-Dimensional Coordinate Systems (12.1) Vectors (12.2) The Dot Product (12.3) The Cross Product (12.4) Equations of Lines and Planes (12.5) Cylinders and Quadratic Surfaces (12.6) Vector Functions and Space Curves (13.1-13.2) Arc Length and Curvature (13.3) Motion in Space: Velocity and Acceleration (13.4)

Review Questions:	What are the rectangular coordinates of a point in R^3? What is the right hand rule for coordinated systems? What is the first octant? What is the distance formula in R^3? In R^2? What is a vector? What are the components of a vector? [I didn't define this word so clearly in lecture today, so they may need some help with this one] What are "equivalent" vectors? What are the geometric rules for adding vectors? The algebraic rule? What is the geometric interpretation of scalar multiplication? The algebraic rule for scalar multiplication? What is the geometric interpretation of the difference between two vectors? How do you compute the length of a vector? What are the eight properties of vector addition and scalar multiplication? What is the dot product of two vectors? How can you find the angle between two vectors? What is meant by "orthogonal" vectors? How can you tell if vectors are orthogonal? What is the scalar projection of one vector onto another? How is it computed? What is the vector projection of one vector onto another? How is it computed? What is the cross product of two vectors? How can you compute the cross product of two vectors? Why does the cross product exist only in three dimensions? How does the result of the cross product relate to the two vectors being multiplied? [orthogonal] What does the cross product have to do with areas? What is the scalar triple product? What does it have to do with volumes? What is a vector equation for a line? What are parametric equations for a line? What are symmetric equations for a line? What is a normal vector to a plane? What is a vector equation for a plane? What is a scalar equation for a plane? What is the angle between two planes? What is a cylinder? What is a quadric surface? What is a trace of a surface (aka cross section) How can traces be used to help visualize a surface? What is a vector valued function? What is one way we can interpret vector valued functions? [parametrized curves] What is the limit of a vector valued function? What does it mean to say a vector valued function is continuous? What is the derivative of a vector valued function? How is it computed? How can we interpret the derivative of a vector valued function? [velocity vector of parametrized curve] What is the integral of a vector valued function? What does the Fundamental THeorem of Calculus for vector valued functions say? How can we interpret the integral of a vector valued function? [Integral of velocity vector is displacement vector] What is the arc length of a parametrized curve? What is the arc length function for a parametrized curve? What does it mean to parametrize a curve by arclength? What is the tangent vector of a parametrized curve? What is the curvature of a parametrized curve.

Exercises:	Section 12.1 #3, 5, 7, 9, 13, 19, 23, 29, 35, 41. Section 12.2 #1, 5, 7, 9, 13, 15, 1, 21, 25, 29, 39, 51. Section 12.3 #1, 3, 5, 9, 11, 13, 17, 19, 25, 27, 33, 39, 41, 53, 55, 63. Section 12.4 #1, 3, 9, 11, 15, 21, 23, 25, 31, 33, 35, 37, 43. Section 12.5 #1, 5, 7, 11, 15, 19, 21, 23, 25, 27, 31, 35, 41, 45, 51, 57. Section 12.6 #5, 7, 9, 11, 13, 19, 21,23,25, 27, 43. Section 13.1 #1, 3, 7, 11, 13, 15, 21, 23, 25, 27, 31, 47. Section 13.2 #3, 7, 9, 11, 17, 19, 21, 23, 35, 37, 43, 47, 49, 51, 53, 57. Section 13.3 #3, 5, 11, 13, 15, 17, 19, 21, 25, 27, 47, 49. Section 13.4 #3, 5, 9, 11, 15, 19, 25, 33, 41.

Reference Tables:	I'll give you this reference sheet to use with your exam.