**MATH 252: NOTES FOR QUIZ 2**

TABLE OF CONTENTS (under construction)

**BIG FILE: **Chapter 15 and Sections 16.1-16.2 notes (handwritten);
see 15.4 improvements below

**SMALLER FILES (if you cant get the big file):**

**CHAPTER 15: VECTOR-VALUED FUNCTIONS**

Section 15.1 of Swokowski
: Vector-Valued Functions and Space Curves

**REVIEW: Section 13.1 covered plane curves: **Section 13.1 notes

**Applet for graphing parametric curves in the
plane:**

http://www.math.ucla.edu/~ronmiech/Java_Applets/index.html

(Click on "Graphing Parametric Curves.")

**Helix:**

http://math.bu.edu/people/paul/225/circular_helix.html

**Approximating Arc Length:**

http://math.bu.edu/people/paul/225/arc_length_animation.mov

Section 15.2 of Swokowski
: Limits, Derivatives, and Integrals

**Limit definition of tangent vector (derivative
VVF):**

http://math.bu.edu/people/paul/225/tangent_vec_animation.mov

**Tangent vectors along an elliptical helix
(based on derivative):**

http://math.bu.edu/people/paul/225/tangent_vec_animation2.html

Section 15.3 of Swokowski
: Motion

**Look under Section 14.4:**

http://www.grossmont.edu/jennyvandeneynden/archive/M281_links.htm

Section 15.4 of Swokowski
: Curvature

** Improvements to Notes on 15.4:**

On 15.4.13, since we assume *t* > 0, the expression for curvature can be
simplified to:

6 / [ *t *(9*t*^2 +
4)^(3/2)]

"Factoring" and canceling can help a
lot when normalizing a VVF, but it might not be as helpful when differentiating,
since you would need to use a product rule.

** Check out "Nested Circles Problem":** http://www.dansmath.com/
(Dan Bach's site has lots of great links.)

Section 15.5 of Swokowski
: Tangential and Normal Components of Acceleration (bonus)

(I'm mostly skipping this section, except for
curvature. I am assigning some homework problems, most of which are relevant to
curvature. The relevant curvature formula in this section is in my notes for
15.4. If you're curious about the rest of Section 15.5, check Section 14.4 of
the following:

http://www.grossmont.edu/jennyvandeneynden/archive/M281_links.htm)

Section 15.6 of Swokowski : Kepler's Laws (skip)

(The results are interesting, though. Read them.)

**CHAPTER 16:**

**(FOR QUIZ 2, WE WILL COVER AN INTRO TO FUNCTIONS
OF SEVERAL VARIABLES.)**

Section 16.1 of Swokowski
: Functions of Several Variables

**Look under Sections 13.6 and 15.1:**

http://www.grossmont.edu/jennyvandeneynden/archive/M281_links.htm

Section 16.2 of Swokowski
: Limits and Continuity (see Math 150, Chapter 2)

**GRAPHICS GALLERY:**

Math252Ch16Gallery.pdf
(there are some ideas from later in Ch.16)

**Look under Section 15.2 (use your mouse to
rotate!):**

http://www.grossmont.edu/jennyvandeneynden/archive/M281_links.htm

**A function without a limit, although limits
exist along all lines:**

http://www.math.tamu.edu/~tom.vogel/gallery/node15.html#SECTION00042000000000000000

Quiz 2 (Chapter 15, Sections 16.1-16.2) Notes: 52 pages total (2.8 MB)