Preparation for the first exam in 251:1, 2, and 3

The exam will cover the material in lectures 1 through 9 of the syllabus. This is also the material covered in lectures 1 through 10 of the diary (but note, please, exclusions such as torsion). This is, roughly, the textbook material in chapters 12 and 13, and chapter 14 up to but not including optimization.
The exam is scheduled for 80 minutes, from noon to 1:20 PM on Thursday, February 25, in our usual classroom for Thursdays.

No formula sheets and no calculators may be used on the exam.

More specifically, the cover sheet for your exam will state:

Show your work. An answer alone may not receive full credit.
No texts, notes, or calculators may be used on this exam.
"Simplification" of answers is not necessary, but find exact values of standard functions such as e⁰ and sin(Π/2).

Here are some previous exams and review material that I've given in this course, going backwards in time (most recent is first).

A My first exam in fall 2008
This was given for a course using the same textbook and covering the almost the same material as the first exam here (optimization was not included, so problem 11 would not be eligible for this exam). Here are answers to that exam.
B My first exam in spring 2006
This was given for a course using a different textbook and a slightly different syllabus. Here are answers to that exam.
C A set of old review problems suitable for this first exam
And here are answers to most of these problems.

Old problems in relation to our syllabus
Here is a list of problems from those old exams "keyed" to each section of the syllabus. This may be useful to you.

Lecture Sections and Topics My exam problems

1 12.1 Vectors in the Plane
12.2 Vectors in Three Dimensions A2

2 12.3 Dot Product and the Angle Between Two Vectors
12.4 The Cross Product A4 A5 B1 B2 CG&H

3 12.5 Planes in Three-Space B3 CS

4 13.1 Vector-Valued Functions
13.2 Calculus of Vector-Valued Functions A1 CM CN CV

5 13.3 Arc Length and Speed
13.4 Curvature
13.5 Motion in Three-Space A3 B4 B5 CF CO&P CL

6 14.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables A7 CA CQ CT

7 14.3 Partial Derivatives
14.4 Differentiability, Linear Approximation and Tangent Planes A8 B6 CI CW&X

8 14.5 The Gradient and Directional Derivatives A10 B8 B9 CB CE CJ CW&X

9 14.6 The Chain Rule A9 B7 CC CD CE CK CR CU CW&X

Lecture	Sections and Topics	My exam problems
1	12.1 Vectors in the Plane 12.2 Vectors in Three Dimensions	A2
2	12.3 Dot Product and the Angle Between Two Vectors 12.4 The Cross Product	A4 A5 B1 B2 CG&H
3	12.5 Planes in Three-Space	B3 CS
4	13.1 Vector-Valued Functions 13.2 Calculus of Vector-Valued Functions	A1 CM CN CV
5	13.3 Arc Length and Speed 13.4 Curvature 13.5 Motion in Three-Space	A3 B4 B5 CF CO&P CL
6	14.1 Functions of Two or More Variables 14.2 Limits and Continuity in Several Variables	A7 CA CQ CT
7	14.3 Partial Derivatives 14.4 Differentiability, Linear Approximation and Tangent Planes	A8 B6 CI CW&X
8	14.5 The Gradient and Directional Derivatives	A10 B8 B9 CB CE CJ CW&X
9	14.6 The Chain Rule	A9 B7 CC CD CE CK CR CU CW&X

My design criteria for calculus exams
I try to ask questions about most (hopefully all) important topics which were covered in the period to be tested. I try to avoid asking problems which require special "finicky" tricks, and do try to inquire about techniques which are broadly applicable.

I want to give, on any calculus exam, questions which require reading and writing graphical information, reading and writing symbolic information, reading and writing quantitative information ("numbers"), and, finally, some question(s) requiring students to exhibit some reasoning and explanation, appropriate to the level of the course and also recognizing the limited time of an exam. I certainly don't always "hit" this target but that's my aim.

Maintained by greenfie@math.rutgers.edu and last modified 2/12/2010.