MAC 2313



MAC 2313

Review - Exam 2

June 10, 2010

When: June 25, 12:40-2:50, in the Math Department Computer Lab (same room as first exam)

What Material: Sections 12.1-12.5, 13.1-13.9 (excluding 13.4 and 13.7).

Procedure: You will have the entire class period. The exam will be closed book. You will be allowed one sheet of notes, 8-1/2 by 11 inch, front and back. A graphing calculator will be expected, though TI-89's and TI-92's will not be allowed.

How to Study: You have seen my exam, so you know what to expect. Most of the problems will be straightforward, but I do have get to put some word problems on this exam. Make sure you understand the material, and make sure you know how to convert the words into the math.

As usual, practice your buttocks off. Do as many problems as you can, and get yourself feeling good about the material. Make sure you can do derivatives, because it would really stink if you lost lots of points on a material you learned two courses ago. Also, you might want to practice with the solving system of equations (for 13.8 and 13.9). This can get tricky.

Since all the material is from chapters 12 and 13, it would be a good idea to go over the review problems for those two chapters.

Specific Topics:

• Vector Valued Functions: You should know what they are, how to take their derivatives, dot products, cross products, etc. You should be able to determine the velocity vector, speed, and acceleration of a vector function. No limits, no continuity, no domains. I have better things to torture you with. Practice Problems: 12.1, 9-16; 12.2, 11-26, 39-42, 57-68.

• Ballistics: Word problems! Know the formulas, plug everything into the right slots, get the right answer. You should be able to use the ballistics equations to determine any missing information: angle, initial velocity, distance, whatever. Practice Problems: 12.3, 1-16, 26-30, 32-34.

• Unit Tangent, Unit Normal, Acceleration Components, Arclength, and Curvature: Eh, it’s a bunch of formulas. Know the formulas, apply them, life is good. Of course, the formulas are annoying, but it will work. Be sure to use the shortcut if you are working out the unit normal vector to a plane curve. Be able to use the appropriate formula for curvature depending on how the curve is being described. Practice Problems: 12.4, 5-16, 23-44; 12.5, 1-6, 9-14, 21-40.

• Multivariable Functions: You won’t be asked to graph functions, but I may ask you to graph a level curve. If I do, it will be something you can figure out in an exam environment. I would be willing to give you domain questions here, and if I’m inspired enough I would may give you matching problems (matching the graph to the level curves). Practice Problems: 13.1, 5-28, 45-56.

• Limits and Continuity: The only limit/continuity question I would give you is one where you have to show that the limit does not exist because you get different values when you approach the point in different directions. Practice Problems: 13.2, 71-72.

• Partials: Know how to take partials. I might give you a “show it satisfies this differential equation” type question. Practice Problems: 13.3, 5-26, 33-40, 61-68, 77-86.

• Chain Rule: Messy way to take a derivative. You’d be most apt to see this problem in a related rates type problem, or something like on Quiz 5. Practice Problems: 13.5, 1-30, 43-57, 59-62.

• Directional Derivatives and Gradient: Know what they are and how to evaluate them. Also know what they are good for, and you should know all the cool gradient properties (normal to level curves, zero at critical points, direction of steepest ascent). Practice Problems: 13.6, 1-50, 55-64.

• Min/Max: Be able to find relative min, max, and saddle points of a function, and be able to identify the type of critical point by the second derivative test. You will need to be able to solve two equations, two unknowns. Practice Problems: 13.8, 7-14, 21-28.

• Min/Max Word Problems: Word problems galore. Practice Problems: 13.9, 1-20, 27-34.

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