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 can’t 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 (9t^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 Review

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

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