Block Two Syllabus
In this block we’ll be continuing with our review of
Calculus I and II in the Schaum’s outlines book, and also reflecting on the mathematical
and philosophical nature of infinity, as reflected in supplementary material in
class, and our readings of the stories of Jorge Luis Borges. You’ll have
regular homework assignments to do, two papers to write, a final group project
to work on, and two exams during the course of the block to take. A detailed
class shedule is below.
Your grade for this block will be based on 15% each for the two essays, 20% each for the two exams, and 10% each for the Homework, group project and class participation.
|
Date |
Class Activity |
Assignment for after class |
|
Monday, October 3 |
Discussion: “Why is Calculus the Science of Infinity?” What does “infinite” mean? Mythological Theory of the integral; Shells |
Read Lem’s “Extraordinary Hotel” Begin Reading Borges stories Begin Homework #1 Start thinking about Essay #1 |
|
Tuesday, October 4 |
Countable infinity; discussion of Lem’s “Extraordinary Hotel” Prime numbers: there are infinitely many What methods of integration are there, anyway? Integration by Parts: Schaum, Chapter 31 |
Continue on Homework #1 Read Schaum, Chapter 31 |
|
Wednesday, October 5 |
A trigonometric interlude: Schaum, Chapter 32 Real Numbers: rational and irrational, decimal & binary expansions |
Homework #1 due by 4 p.m. Begin Homework #2 Read Schaum, Chapter 32, pp. 289-292 and solved problems 1-23 |
|
Thursday, October 6 |
Trig substitutions: Schaum, Chapter 32: 292-294. Hippocrates’ quadrature of the lune: Simmons, B4 The Catenary: Simmons, B11 |
Read Schaum, Chapter 32, pp. 292-294 and solved problems 24-29; Read B4, B11 Work on Homework #2 |
|
Friday, October 7 |
An algebraic interlude (partial fractions): Schaum, Chapter 33 The Big Theorem about integration |
Read Schaum, Chapter 33 Homework #2 due by 3 p.m. Read more Borges! Work on Essay #1 |
|
Monday, October 10 |
Improper Integrals: Schaum, Chapter 35 Uncountable infinite sets; the Cantor dust |
Essay #1 due by 4 p.m. Read Schaum, Chapter 34 Start Homework #3 Review first group of Borges stories |
|
Tuesday, October 11 |
Discussion of Borges stories about creating a rich continuous world |
Work on Homework #3 |
|
Wednesday, October 12 |
Hardcore applications: Surface areas, centers of mass; Schaum 36, handout |
Homework #3 due by 4 p.m. Get ready for midterm (Schaum Chapters 31, 32, 33, 35 plus ideas about infinity) |
|
Thursday, October 13 |
AM: Review; PM Midterm J Here are solutions to the midterm! |
Read Schaum 36 & handout Start Homework #4 Review second group of Borges stories |
|
Friday, October 14 |
Discussion of Borges stories about bifurcations and iteration |
Continue Homework #4 Think about Essay #2 |
|
Monday, October 17 |
Infinite sequences and series: Schaum 42-43 Bernoulli brothers: Simmons A20 |
Homework #4 due by 4 p.m. Read Schaum 42-43, A20 Start Homework #5 Work on Essay #2 |
|
Tuesday, October 18 |
Convergence Tests: Integral, Comparison, & Alternating Series: Schaum 44-45 |
Read Schaum 44; Schaum 45 pp. 410-411 Continue Homework #5 |
|
Wednesday, October 19 |
Conditional & Absolute Convergence; the Ratio Test: Schaum 45 |
Homework #5 due by 4 p.m. Read the rest of Schaum 45 Start Homework #6 |
|
Thursday, October 20 |
Power Series: Schaum 46 Pi is irrational: Simmons B17 |
Read Schaum 46, B17 Continue Homework #6 |
|
Friday, October 21 |
Taylor’s Theorem: Schaum 47 |
Essay #2 due at 9 a.m. Continue Homework #6 Read Schaum 47 pp.432-434 Work on Final Project! |
|
Monday, October 22 |
More about Taylor’s Theorem |
Read the rest of Schaum 47 Homework #6 due by 4 p.m. |
|
Tuesday, October 23 |
Final Project Presentations |
Review for the Final Exam |
|
Wednesday, October 24 |
Final Exam |
BLOCK BREAK! |