MATH
141 - PRECALCULUS
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• NOTES FOR THE FINAL
• OUTLINE FOR THE FINAL:
Math141OutlineFinal.pdf
BIG FILES: Chapter 7 … Chapter 8 … Chapter 9 (see
Pascal Triangle Links below) … Chapter 10 (Part 1:
Conics) … Chapter 10 (Part 2:
Polar Curves) (partly handwritten)
• The handwritten notes on Chapter 10 are
more concise:
Chapter 10 (mostly handwritten)
• CORRECTIONS: Page 8.58 (top):
Pierre [not George] Sarrus. Page
8.60 (middle): “lower left [not right] corner.”
VIDEOS AND WEB LINKS: SEE BELOW
SMALLER FILES (if you can’t get the big files)
Chapter
7: Systems and Inequalities
Sections 7.1-7.3 in Larson:
Systems of Equations
Section
7.4 in Larson: Partial Fractions
Sections 7.5-7.6 in Larson:
Graphing Inequalities and Linear Programming
Chapter
8: Matrices and Determinants
Section 8.1 in Larson: Matrices
and Systems of Equations
Smaller
files for older computers:
Section 8.2 in Larson: Matrix
Operations
Section 8.3 in Larson: Matrix
Inverses
Section 8.4 in Larson:
Determinants
Section 8.5 in Larson:
Applications of Determinants
Chapter
9: Discrete Math
Sections 9.1 and 9.6 in Larson:
Sequences, Series, and Counting
• FIBONACCI SCULPTURE: http://sfglobe.com/2015/01/14/3d-printed-sculptures-look-alive-when-spun-under-a-strobe-light/
• FIBONACCI TED TALK BY PROF. ARTHUR BENJAMIN: https://www.youtube.com/watch?v=SjSHVDfXHQ4
Sections 9.2 and 9.3 in Larson:
Arithmetic and Geometric Sequences, Partial Sums, and Series
• QIX AND FILLING IN A BOX (GEOMETRIC SERIES TALK)
• Sample game: https://www.youtube.com/watch?v=Wvzyd0OZg1I
• Winner! (2x) https://www.youtube.com/watch?v=RGSPj3vlR6M
Section 9.4 in Larson: Mathematical
Induction
• THE HEART OF INDUCTION: https://www.youtube.com/watch?v=p_E3feHZtZM
• HANDSHAKE PROBLEM: https://www.youtube.com/watch?v=dIejOnMP20c
• KHAN ACADEMY ON INDUCTION: https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-induction/v/proof-by-induction
Section 9.5 in Larson: Binomial
Theorem
The
Beauty of Pascal's Triangle
•
http://www.mathsisfun.com/pascals-triangle.html
See
also Chaos and Fractals by Peitgen, et al.
http://en.wikipedia.org/wiki/Pascal's_triangle
The Magic of Pascal's
Triangle (Plinko from The Price is Right
and Word Jumbles)
QUINCUNX ("PLINKO") APPLETS AND SITES
•
The Price is Right / Plinko winner (the Plinko
board is in the second half): http://www.youtube.com/watch?v=vuMir11YFPs.
What does this have to do with Pascal’s triangle? See the links above!
http://www.jcu.edu/math/isep/Quincunx/Quincunx.html (This applet's better.)
http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html
http://en.wikipedia.org/wiki/Bean_machine (Wikipedia article)
http://en.wikipedia.org/wiki/Quincunx (Wikipedia article)
Chapter
10: Conics and Polar Coordinates
Chapter 10 (Part 1:
Conics) … Chapter 10 (Part 2:
Polar Curves) (partly handwritten)
• ANIMATION ON CONICS
https://www.youtube.com/watch?v=HO2zAU3Eppo
Corrections: (0:48-1:07) The
double-nappe cone (or simply “cone”) here should not be thought of as finite,
so there are no “bases” and there is no “base perimeter.” The term “directrix” is used elsewhere,
especially when describing parabolas.
OLDER NOTES
Chapter 10 in Larson: Ellipses
(handwritten) and Hyperbolas (typed)
Section 10.4 in Larson:
More on Hyperbolas (handwritten)
Sections 10.7 and 10.8 in Larson:
Polar Coordinates and Polar Graphs (handwritten)
CHAPTER 10:
TYPED NOTES ON PARABOLAS (OPTIONAL) AND POLAR CURVES (REQUIRED)