The following is a chapter by chapter guide intended to help you organize the material we have covered in class as you study for your exam. It is only intended to serve as a guidline, and may not explicitly mention everything that you need to study. It is also important you are comfortable with the basics of differention and integration (as covered in Calculus I and Calculus II classes).
Please review all homework, quiz and workshop problems for the chapters given below. I have also compiled a list of additional practice problems.
12.1 & 12.2: These sections cover the basics of vectors and vector algebra. Make sure you understand them well, including how to find lengths of vectors, unit vectors pointing in a given direction, and sums of vectors. It is also very important to know how to find the parametric equation of a line and determine the intersection of two given lines.
12.3: Know how to find the dot product of two vectors, and how to determine the angle between them using their dot product. You should also know how to find the projection of a vector along another vector, and how to write a vector as a sum of two vectors, one of which is parallel to a given direction and the other perpendicular to that direction.
12.4: Know how to find the cross product of two vectors and its geometric interpretation. You should also know how to use cross products and triple products to find the area of a parallelogram and the volume of a parallelepiped.
12.5: You must know how to find the equation of a plane given a point on the plane and a normal vector, or a line and an additional point contained in the plane, or three points on the plane. You should also be able to determine the intersection of a line and a plane, or the intersection of two planes.
12.6: While it may be helpful to understand concepts in this chapter, you are not required to be able to classify quadric surfaces, and will not be explicitly examined on this chapter.
13.1 & 13.2: Make sure you understand what a vector valued function represents, and know how to find limits, derivatives and integrals involving such functions. You should also be able to find the tangent line at a point on the space curve traced out by a vector valued function.
13.3: You must know the formulas to find speed and arc length. You should also know the method for finding the arc length parametrization of a curve.
13.4: You should know the equations for the unit tangent and the unit normal to a curve at a given point. The curvature equations will be given to you on the exam, so you do not need to memorize them. However, you should feel comfortable computing with them. You should also know how to find the osculating circle through a point on a curve, characterized by its radius and center.
13.5: You should know what the velocity and acceleration functions mean in terms of derivatives of a vector valued function. You should also know how to find the tangential and normal components of the acceleration vectors using the methods of section 12.3. You do not need to memorize Equation 5 in Theorem 1 on p. 775, and I will give it to you if you require it. (Note that Equation 4 right above it is a restatement of the method of section 12.3.)
14.1 & 14.2: Make sure you understand what a function in several variables represents and what level curves (and surfaces) and contour lines are. You should know how to determine limits of several variable functions, and whether it is continuous or not. (Note that all problems relating to this should be possible to do without using the ε-δ definition given on p. 803.)
14.3: You must know how to find the partial derivatives of a several variable function, including higher order partial derivatives.
14.4: You should know what it means for a several variable function to be differentiable, although I will give you the equation in the definition of local linearity (Equation 1 on p. 821) if needed, so you do not need to memorize it. However, you are still required to know the equations for the linearization, linear approximation and tangent plane of the graph of a function at a given point.
13.4: Know how to find the gradient of a function, the derivative with respect to a given vector and the directional derivative. You should also know their geometric interpretations. Also make sure you how to use gradients to find the derivative of a function defined along a space curve, and to find the equation of a tangent place to a surface defined implicitly.
Maintained by ynaqvi and last modified 09/30/11