Date |
Topic |
Reading Assignment |
Homework Problems |
|
| Friday, August 26 |
Syllabus/Course procedures
Euler's method: introducing the method
Implementing Euler's Method on a computer: Introducing Loops |
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* |
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Monday, August 29 |
Introduction to Maple --- or a refresher
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Euler's method handout |
Euler's Method exercises, pt. 1
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Wednesday, August 31 |
Introducing Project and Paper #1: Euler's Method Project |
* |
Euler's Method Exercises, pt. 2 (Not to turn in.) |
| Friday, Sept. 2 |
Class work on Euler's Method Project |
* |
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Monday, Sept. 5 |
Euler's Method and Approximating Sums.
Approximating sums: Left, right, midpoint and trapezoidal sums
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Euler's Method Paper Due |
Wednesday, Sept. 7 |
Discussion: What is Area?
Summation notation; working with sums
Riemann Sums and sigma-notation
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Sect 5.6:
5, 6, 9, 16, 18, 21, 23, 24, 28, 32, 33, 34 |
Friday, Sept. 9 |
The Definition of the Integral.
Probing the Definition of the Integral
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Sect 5.7, pt 1:
1-4, 7, 9, 10, 12, 13ac, 14ad, 15ad, 18c, 24ad, 25, 26.
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Monday, Sept. 12 |
Computing Integrals Using Riemann Sums
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| Wednesday, Sept. 14 |
Error estimates, part I
Comparing errors in Left Sum/Right Sum approximations---part I
Comparing errors in Midpoint/Trapezoid approximations---Part I
Simpson's rule---a brief look |
Section 6.1 in OZ |
Worksheet: Computing Integrals Using Riemann Sums |
| Friday, Sept. 16 |
Error estimates part II
General error bounds for Approximating Sums
|
Section 6.2 in OZ |
Sect 6.1 pt 1:
1, 4, 5, 11, 15-18, 19a, 26, 28, 31, 33, 35, 36, 43, 46. |
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Monday, Sept. 19 |
Proofs of the Error Estimates |
* |
Sect 6.1 pt. 2
52, 54, 55, 56, 61-64.
Sect 6.2:
1, 2, 5, 6, 11, 13, 15, 17. |
| Wednesday, Sept. 21 |
Test # 1--- covers through Section 6.2 |
Friday, Sept. 23 |
Review of "Guess and Check" methods and Substitution. |
* |
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Monday, Sept. 26 |
Integration by Partial Fractions, part I. |
Section 8.2 in OZ |
Integral Worksheet #1---2, 7, 13, 14, 17, 19, 20, 24, 25, 26, 29, 30, 32, 35, 36, 37, 39, 40, 43, 46. |
Wednesday, Sept. 28 |
Integration by Parts |
Section 8.1 in OZ |
Integral Worksheet #2--- Partial Fractions |
Friday, Sept. 30 |
Practice: Integral Worksheet #4--- General techniques |
* |
Integral Worksheet #3--- Integration by Parts |
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Integration by Partial Fractions, part II. |
Section 8.2 in OZ |
* |
Wednesday, October 5 |
Gateway Exam |
Friday, October 7 |
No class---October Break! |
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Monday, October 10 |
Area between curves |
Section 7.1 (through top of page 417.) |
Sect 8.2:
2, 6cd, 7cd, 28c, 31, 33-40. |
Wednesday, October 12 |
Solids of revolution.
Introducing: The Goblet project. |
Section 7.2 in OZ |
Sect 7.1: 13, 14, 16, 17, 19, 23.
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Friday, October 14 |
Center of Mass of a solid of revolution.
Work on Goblet Project continued
|
* |
(Work on Problems for 7.2! Be prepared to see me in office hours if you have questions.)
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Monday, October 17 |
Various applications of integration.
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* |
Sect 7.2: 25, 26, 27, 28, 29, 31. |
Wednesday, October 19 |
Separation of variables |
Section 7.4 in OZ |
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Friday, October 21 |
Approximation with Polynomials
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Section 9.1 in OZ |
Sect 7.4: handouts and 18, 19, 21, 22. |
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Monday, October 24 |
Taylor Polynomials and Taylor's Theorem |
Section 9.2 in OZ |
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Wednesday, October 26 |
L'Hopital's Rule
Geometric series--a first look
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9.1: 3, 5, 7-10, 13, 16, 18, 21, 22, 25, 26, 27, 30, 31, and 32. |
Friday, October 28 |
Test # 2---through Section 9.1 |
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Monday, October 31 |
Improper integrals |
Section 10.1 in OZ |
Problems attached to handout on Taylor's Theorem. |
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Sequences of real numbers: definitions and convergence. |
Section 11.1 in OZ |
L'Hopital's Rule exercises (handout)
Sect. 10.1: 1, 3, 4, 5, 7-17 (odds only) and 33, 35, 39, 45. |
Friday, November 4 |
Geometric series---introducing paper/project #2 |
* |
Sect. 11.1:
1-17 (odds only), 18, 19-24, 27, 31, 33, 34. |
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Monday, November 7 |
Convergence and Divergence of Series |
Section 11.2 in OZ |
* |
Wednesday, November 9 |
Tests for convergence (not ratio) |
Section 11.3 in OZ |
Sect. 11.2:
1, 4, 7, 8, 11, 12, 13, 17, 20, 23, 24. |
Friday, November 11 |
The Ratio Test
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* |
* |
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Monday, November 14 |
Working with the convergence tests |
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Wednesday, November 16 |
Pulling it all together---recap and review |
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Friday, November 18 |
Test # 3 |
Thanksgiving Break |
Monday, Nov. 28 |
Absolute vs. conditional convergence
Alternating series |
Section 11.4 in OZ |
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Wednesday, Nov. 30 |
Power Series |
Section 11.5 in OZ |
Sect. 11.4: 1, 4, 6, 7, 9, 11, 14, 19, 20, 21, 24, 25. |
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Power Series--a work day |
* |
Geometric Series paper due. |
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Monday, December 5 |
Power series as functions |
Section 11.6 in OZ |
Sect. 11.5:
4-7, 9, 10 , 11, 13, 15, 16, 17, 23, 25, 26, 27-30, 33, 34, 36, 37, 43, 47. |
Wednesday, December 7 |
Finish Power Series
Taylor and MacClaurin Series |
Section 11.7 in OZ |
Sect. 11.6: 1-4, 7, 9,11,12, 20, 21. |
Friday, December 9 |
Recap/review of series |
* |
Sect. 11.6 (cont.): 35, 36, 37ab, 45, 47, 51-54. |
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Final Examination
Section 01 --- Monday, December 12, 2011 from 1:30 p.m. to 4:30 p.m.
Section 02 --- Thursday, December 15, 2011 from 1:30 p.m. to 4:30 p.m. |