(Sections 13.1-14.4)
13.1 Be able to do the HW assignments.
13.2 Know the properties of vectors (addition, multiplication by a scalar, length, unit vector, position vector).
13.3 Know the definition of the dot product.
Know the geometric properties of the dot product.
Know the properties of the vector projection.
13.4 Know the definition of the cross product.
Know the geometric properties of the cross product.
Know the properties collected in Theorem 8 on p. 854.
13.5 Know and UNDERSTAND the equation of a line.
Know and UNDERSTAND the equation of a plane.
Know how to parameterize a line segment connecting two given points.
Be able to do the HW assignments.
13.6 Know and understand how to use traces in order to sketch surfaces.
You donŐt need to know or to memorize Table 1 on p. 872.
13.7 Know the definition and the geometric meaning of cylindrical and spherical coordinates.
Be able to change coordinates.
14.1 Be able to draw space curves.
Be able to determine the direction in which a curve is traced.
Be able to match parametric equations with given graphs.
Know the parametric equations of a circle (in the xy-plane, for instance).
14.2 Know the differentiation rules on page 895.
Know and understand Example 5 on page 896.
Be able to find tangent vectors and unit tangent vectors.
Be able to find the equation of a tangent line.
14.3 Know how to compute the length of a curve.
Know how to reparametrize a curve with respect to arc length.
Know how to find the unit tangent, unit normal, and the binormal vector of a curve.
No questions about curvature will be asked.
14.4 Know how to compute the velocity and the acceleration.
Know how to find the position vector if the acceleration is given.
Know how to find the tangential and normal components of acceleration.
Be able to prove that a planet around the sun moves in a plane.
Make
statements on your test. (For instance: Write equal signs whenever you think
two expressions are equal.) Use a pencil and write legibly.