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 guideline, and may not explicitly mention everything that you need to study. It is also important you are comfortable with the basics of differentiation and integration (as covered in Calculus I and Calculus II classes).
Please review all homework, WeBWorK and worksheet problems for the chapters given below. I have also compiled a list of additional practice problems.
11.1: Look over the examples 1-6 from Section 11.1 and make sure you can under- stand all the steps. You should also know how to find a parametrization for a given curve, how to eliminate the parameter, and how to find tangent lines without eliminating the parameter.
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 to find the area of a parallelogram.
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.
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 should know how to find the speed of a particle whose motion is given by parametric equations and the arc length of a given a space curve. However, you do not need to know about arc length parametrizations.
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 the formulas for the coefficients aT and aN given in Equation 2 on p. 759.
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 the functions are continuous or not. (Note that all problems relating to this should be possible to do without using the ε-δ definition given on p. 787, which you are not required to know.)
14.3: You must know how to find the partial derivatives of a several variable function, including higher order partial derivatives. Clairaut's Theorem is especially helpful for these higher order derivatives.
14.4: You should know what it means for a several variable function to be differentiable in terms of being well approximated by a tangent plane. (You do not need to know the equation in the definition of local linearity: Equation 1 on p. 806.) 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.
Maintained by ynaqvi and last modified 02/11/15