Chaos and Calculus syllabus block 2

CC MATHEMATICS CHAOS AND CALCULUS

Course Syllabus
Block 2 of
Chaos and Calculus

Instructors:

Jane McDougall	jmcdougall@coloradocollege.edu (Block 2)
	Palmer 134 x6275
	Office Hours: M-Th 1:30 - 3; Friday by appointment
Kathy Merrill	kmerrill@coloradocollege.edu (Block 1)

Paraprofessional:
      Yoko Shimizu: Palmer 130, x6727, mailto:yshimizu@coloradocollege.edu

Student Mentor:
     Katie Allison: mailto:k_allison@coloradocollege.edu

Class time:
     9:15 AM each morning, with occasional additional meetings in the afternoon.

Texts:
    Chaos Under Control: The Art and Science of Complexity by Peak and Frame
    Calculus (Schaum's Outline), by Ayres and Mendelson
    Arcadia, by Tom Stoppard (first block)
    Proof, by David Auburn

Grades:
During Block 2 you will be evaluated on the following: Quizzes (about twice per week) , Homeworks (also about twice per week), Lab assignments (as part of homework, or as more formal afternoon sessions), and Chaos under Control assignments. You will be reading some short stories, and participating in a library research project. You will also study the play Proof by David Auburn. At the end of block two you will receive a single grade for this course. The evaluation for the block two will be as follows:
    15% for calculus homework,
    15% for CUC and lab assignments
    20% for the quizzes / short writeups,
    10% for class participation,
    15% for the Proof assignment,
    10% for the library assignment,
    15% for the final test.

Quizzes vs Short Calculus Writeups:
There are six quizzes in all for the block. In lieu of at least one quiz, you should research and write a paragraph (about 300 - 400 words) on the appropriate topic. You can replace up to three quizzes in this manner.
Rules:
    You must take quiz one or quiz two
    You must take quiz three
    You must take quiz five
    You must replace at least one quiz with a write up


Honor Code:
    Each assignment will have specific instructions about how much collaboration is allowed with your classmates. No collaboration will be allowed on quizzes. On all assignments, you must give complete bibliographical references for all sources you consult, including online resources. Honor Code convictions will result in an automatic grade of No Credit for the course. For more information about the Colorado College Honor Code, see http://www2.coloradocollege.edu/Students/Pathfinder/Policies/Academic/HonorSystem.html

Schedule:

WEEK 1
Monday, Sept 30	9:15 AM: Review of calculus one. Area calculations, some predating the calculus. Discussion of infinity in calculus, and infinity in the "Book of Sand". Review of the exponential function.
Tuesday, Oct 1	CUC chapter 3 pp 75 - 92. Fractal Dimension. Calculus chapters 25 and 26. Calculus with the Logarithm and the Exponential function. Quiz One or Alternative: Available after class and due at 3 p.m. Integration by substitution. Algebraic properties of log and exp.
Weds., Oct 2	CUC Chapter 3 pp 92 - 112: The fractal dimension of a natural fractal. Diffusion limited aggregation. Calculus Chapters 28, 29, 30. Final examples on logarithms and exponentials. Arclength. Volumes. Overnight Trip to the CC cabin: departure at 3 p.m. Cabin activities: Fractal dimension exercises.
Thursday, Oct 3	Return to campus, departing the cabin at 11 a.m. Afternoon lab 1:30 in Palmer 14. Click here for a picture of Bryce Canyon. Homework One: Due by 5 p.m.
Friday, Oct 4	Calculus chapter 59 and 31: Volumes by shells. Differential Equations and Integration by parts. Quiz Two or Alternative: Available after class and due at 3 p.m. Calculus with exp and log. Arclength.
WEEK 2
Monday, Oct 7	Calculus Chapters 31 and 32: Differential Equations in physics. Trigonometric Substitution. For pictures of Diffusion Limited Aggregation, look here. Homework Two: Due by 5 p.m.
Tuesday, Oct 8	More practice with methods of integration Discussion of short story by Stanislaw Lem. Calculus Chapter 35: Improper integrals. Quiz Three: available after class and due by 3PM. Methods of integration.
Weds., Oct 9	Calculus Chapter 35: Improper Integrals. Discussion of short story by Stanislaw Lem. Infinity and countable sets.
Thursday, Oct 10	Calculus Chapter 44. Using the integral test and comparison tests to determine when a series converges. Chapter 45 and 46. Conditional Convergence. 10:45 a.m. Library Orientation Homework Three: Due by 5 p.m.
Friday, Oct 11	Calculus: Using the alternating sign test and ratio test to determine when a series converges. Introduction to infinite sums of functions: Power Series. Chapter 46: Sums which are functions, and their applications in physics: Power Series and Taylor Series. 10:45 a.m. Dan Johnson Talks about his REU experiences modelling the weather. Quiz Four or Alternative: Available after class and due by 3PM. Solve a separable differential equation. Convergence of integrals. (Covers chapter 59, 35).
WEEK 3
Monday Oct 14	Convergence of series. Taylor series and power series. Complex arithmetic (see handout to be provided). CUC chapter 7: Introduction to the Mandelbrot set. Library Assignment Write up is due in the morning. Homework Four:
Tuesday, Oct 15	CUC chapter 7: The Mandelbrot set and Julia sets. Connections with the logistic map. Quiz Five: available after class and due by 3PM. Convergence of series.
Weds., Oct 16	Calculus chapter 37 and 41. Parametric Curves and Polar Coordinates. Afternoon Lab Session. Homework Five:
Thursday, Oct 17	Polar integrals Calculus chapter 21. Newton's Method. CUC chapter 8. Newton's basins of attraction. Initial Reading of the play Proof. Quiz Six: available after class and due by 3PM. Parametric Curves (areas, lengths and derivatives) and polar coordinate conversions (no calculus yet). Alternative: write up about cycloids.
Friday, Oct 18	CUC chapter 8. Discussion of the play Proof - with Marlow.
WEEK 4
Monday, Oct 21	Calculus review and catch up. Homework Six:
Tuesday, Oct 22	Proof Assignment is due.
Weds., Oct 23	Final Test