Date |
Topic |
Reading Assignment |
Homework Problems |
| |
| Monday, January 18 |
Syllabus/Course procedures
Euler's method: introducing the method
Implementing Euler's Method on a computer: Introducing Loops
|
|
|
| Wednesday, January 20 |
Introducing Project and Paper #1: Euler's Method Project |
|
Euler's Method Exercises |
| Friday, January 22 |
Introduction to Maple--or a refresher. |
|
|
| * |
| Monday, January 25 |
Class work on Euler's Method Project |
|
|
| Wednesday, January 27 |
Approximating sums: Left, right, midpoint and trapezoidal sums
|
|
|
| Friday, January 29 |
No class---Carol Schumacher at a conference
|
| * |
| Monday, February 1 |
Summation notation; working with sums
The definition of the integral.
Computing integrals using Riemann Sums |
Section 5.7 |
Euler's Method Project Due
Sect 5.6: 5, 6, 9, 16, 21, 23, 24, 28, 29, 32, 33, 34. (Well-labeled diagrams are required!) |
| Wednesday, February 3 |
Approximating Integrals numerically
Comparing errors in left, right, midpoint. trapezoidal Riemann sums---Simpson's rule |
Section 6.1 |
Sect 5.7: 1,3, 7, 10, 12, 15ad, 18c, 24ad.
Worksheet: Computing Integrals Using Riemann Sums |
| Friday, February 5 |
Group Quiz #1
Comparing errors continued. |
|
Sect 6.1, part 1:
1, 4, 5, 11, 15-18, 19a, 26, 28, 31, 35. |
| * |
| Monday, February 8 |
Error Bounds for Approximating Sums: general cases:
Proofs of the error estimates |
Section 6.2 |
Sect 6.1, part 2: 29, 30, 38, 40, 43, 46, 52, 54, 55, 56, 61, 62, 63, 64. |
| Wednesday, February 10 |
Back to the FTC: Integrals and antiderivatives. Review of "guess and check" methods and substitution. |
|
Sect 6.2:
1, 2, 5, 6, 11, 13, 15, 17. |
| Friday, February 12 |
Integration by partial fractions, part I |
Section 8.2 |
Integral Worksheet #1 due----not to turn in. |
| * |
| Monday, February 15 |
Test #1 (through section 6.2) |
| Wednesday, February 17 |
Integration by parts |
Section 8.1 |
Integral Worksheet #2--- Partial Fractions |
| Friday, February 19 |
Integration by Partial Fractions, part II. |
|
Integral Worksheet #3--- Integration by Parts |
| * |
| Monday, February 22 |
Practice: Integral Worksheet # 4--- General techniques |
|
Sect 8.2:
2, 6cd, 7cd, 28c, 31, 33-40. |
| Wednesday, February 24 |
Gateway exam |
|
|
| Friday, February 26 |
Areas between curves |
Section 7.1 (through top of page 417) |
|
| * |
| Monday, March 1 |
Finding volumes by parallel cross section
Introducing the goblet project |
|
Sect 7.1: 13, 14, 16, 17, 19, 23. |
| Wednesday, March 3 |
Center of Mass of a solid of revolution---work on the goblet project |
|
Sect 7.1: 39, 40, 42, 43.
Sect 7.2: 25, 26, 27, 28, 29, 31. |
| Friday, March 5 |
Work on the goblet project. |
|
|
Spring Break
|
| Monday, March 22 |
Separation of variables
|
Section 7.4 |
|
| Wednesday, March 24 |
Solving the logistic equation |
|
Sect 7.4: 1, 2, 3, 4, 9, 12, 13, 18, 19, 21, 22. |
| Friday, March 26 |
Group quiz #2---techniques and applications of integration |
|
Goblet project due |
| * |
| Monday, March 29 |
Approximations by polynomials: Taylor polynomials. |
Section 9.1 |
|
| Wednesday, March 31 |
Taylor Polynomials and Taylor's theorem |
Section 9.2 |
Sect. 9.1: 3, 5, 7-10, 13, 16, 18, 21, 22, 25, 26, 27, 30, 31, and 32. |
| Friday, April 2 |
Geometric series---a first look. |
|
|
| * |
| Monday, April 5 |
L'Hopital's Rule
Introducing Improper integrals |
L'Hopital's Rule handout |
Sect. 9.2: 5, 7, 8, 10. |
| Wednesday, April 7 |
Improper integrals |
Section 10.1 |
L'Hopital's Rule exercises (handout) |
| Friday, April 9 |
Sequences of real numbers: definitions and convergence. |
Section 11.1 |
Sect. 10.1, part I: 1, 3, 4, 5, 7, 8, 12. |
| * |
| Monday, April 12 |
Sequences of real numbers---getting more precise.
Geometric series---ideas to consider and write about. |
|
Sect. 10.1, part II: 9-17 (odds only) and 33, 35, 39, 45.
Sect. 11.1:
1-17 (odds only), 18.
|
| Wednesday, April 14 |
Convergence and divergence of series |
Section 11.2 |
Sect. 11.1: 19-24, 27, 31, 33, 34, 50, 51, 52, 54. |
| Friday, April 16 |
Tests for convergence of series--pt 1 |
Section 11.3 |
Sect. 11.2:
4, 7, 8, 11, 12, 13, 17, 20, 23, 24.
(Hint: on the last two. Compute a few partial sums for the series. Find a pattern so you can get a limit.) |
| * |
| Monday, April 19 |
Tests for convergence of series---pt 2 |
|
|
| Wednesday, April 21 |
Working with the convergence tests |
|
Geometric series paper due. |
| Friday, April 23 |
Absolute vs. conditional convergence; Alternating series |
Section 11.4 |
Testing for convergence---worksheet |
| * |
| Monday, April 26 |
Test #2 |
| Wednesday, April 28 |
Power Series |
Section 11.5 |
|
| Friday, April 30 |
Power Series---a work day. |
|
Sect. 11.4: 1, 3, 4, 6, 7, 9, 11, 14, 19, 20, 21, 23, 24, 25. |
| * |
| Monday, May 3 |
Finish power series
Taylor and Maclaurin Series |
Section 11.6 |
Sect. 11.5:
4-7, 9, 10 , 11, 13, 23, 25, 26, 43, 47. |
| Wednesday, May 5 |
Taylor's theorem, revisited
Course evaluations |
Section 11.7 |
Sect. 11.6: 1-4, 5,6,7,10, 11, 20, 35, 36, 37. |
| Friday, May 7 |
Recap/review of series |
|
Sect. 11.7: 2-5, 7, 9, 12. |
| |
Final Examination
6:30 p.m. on Wednesday, May 12
|