Math 14
Fall Term 2003
Course Schedule
This schedule will be updated as the term progresses. Check for changes before starting your homework!
Date |
Read before that
date |
Problems due
that date |
Class discussion
that date |
Sept. 24 |
|
|
Geometry and transformations of n-space |
Sept. 26 |
1.1-1.5 |
1.1 #6 1.2 #12, 19, 32, 37bc 1.3 #15, 26 1.4 #9, 21 1.5 #10, 16, 30 |
Matrix Algebra |
Sept. 29 |
1.6 |
1.6 #2, 6 (You only need the def of || ||, not the Pythagorean Theorem stuff on p 54), 10, 11, 14. Supplementary problems from here |
Curvilinear coordinates |
Oct. 1 |
1.7 |
1.7 #8, 11, 12, 17, 18, 19, 20, 23, 24, 26, 33 (You may use Maple to help you, but make your sketches to turn in by hand.) |
Systems of Equations: Row Operations |
Oct.3 |
2.1,2.2 |
2.1 #12, 27, 35, and 37. Supplementary problems from here. |
Limits and Continuity Differentiability |
Oct.6 |
2.3 |
2.2 #1,2,3,8,10, 33, 36 2.3# 3, 6, 12, 16, 25 |
Differentiability |
Oct. 8 |
2.4, 2.5 |
2.2 # 39, 42 2.3 #26, 27, 29, 32, 48, 49 |
Chain Rule |
Oct.10 |
2.5 |
2.4 # 14, 18, 20 (don't give a trivial answer for part b), 21ab, 22 2.5 # 6, 9, 18, 20 (hint, start with right hand side), 26 |
Inverse Matrices |
Oct. 13 |
2.6 to p 166, 3.1 (through Ex. 6) 3.2 (through Ex. 8) |
2.6 # 6, 10, 12, 15 3.1 # 4, 20, 21 3.2 #3, 7, 12. Prove or give a counter example: the transpose of an invertible matrix is invertible and its inverse is the transpose of the inverse of the original matrix. |
Determinants I |
Oct 14 X-hour |
|
No
problems due but class meets today |
Determinants II |
Oct. 15 |
3.3, 3.4 |
3.3#3, 18, 24, 27 3.4 # 3, 8, 12ab, 16 Supplementary problems from here. |
Inverse and Implicit function theorems |
Oct. 17 |
4.1 |
4.1 #8, 17, 27a, 28, 31 2.6 #34, 39, 40, 42 2.5 # 24, 25 Supplementary problem from here. |
No Class |
Oct.20 |
4.2, 4.3 |
4.2 # 2, 22, 28, 35 4.3 # 1, 10, 18 |
Area, Volume, and double integrals |
Oct. 20 |
|
Review Session for Exam in Choate House Seminar Room, 6PM-8PM |
|
Oct 21 X-hour |
|
Test
1 in X-hour Take-home exam passed out; due Thursday Oct. 23. |
|
Oct. 22 |
5.1, 5.2 |
5.1 #6, 7 5.2 #1, 5, 6, 17 |
Double integrals |
Oct. 24 |
5.2 |
5.2 # 10, 11, 18, 22, 29 |
Order of Integration |
Oct. 27 |
5.3 |
5.3 # 4, 9, 11, 14 |
Triple Integrals |
Oct. 29 |
5.4 |
5.4 #4, 7, 8b, 10 (Hint: put the vertex at the origin and orient the cone upwards symmetrically with the z-axis), 14, 15, 19, 22, 5.3 #16 |
Change of Variables |
Oct. 31 |
5.5 through Example 9 |
5.5 #2, 3, 4, 5, 7, 9, 10, 12. |
Change of Variables |
Nov. 3 |
5.5 |
5.5 # 15, 19, 20, 22, 26, 27, 28 |
Applications |
Nov. 5 |
5.6 |
5.6 #2, 5, 8, 12 (Draw a picture), 14, 15, 16 (Use maple [plot3d] to draw a sketch of the region in 16. Experiment with dragging the sketch with the mouse to get a better view.) |
Line Integrals |
Nov. 7 |
6.1 |
6.1#3, 4, 6, 11, 16, 21 |
Line Integrals |
Nov. 10 |
6.1 |
6.1 #14, 15, 17, 18, 19, 22 |
Green's Theorem |
Nov. 11 X-hour |
|
Test
2 in X-hour. Take-home exam
passed out; due Thursday Nov. 13. |
|
Nov. 12 |
6.2 |
6.2 #5. 7, 10, 11, 17, 20 |
Conservative Vector Fields |
Nov. 13 |
|
Prosser Lecture: Sync: The Emerging Science of Spontaneous Order |
Steven Strogatz Cook Auditorium 7PM |
Nov. 14 |
6.3 |
6.3 #1, 2, 3 (Hint: Check out Th. 3.5 and Equation 1), 4, 12, 17 |
Parameterized Surfaces |
Nov. 17 |
7.1 |
7.1 # 2, 4, 10, 11 (also d. By considering the derivative matrix of the parameterization), 14, 18, 24 |
Surface Integrals |
Nov. 19 |
7.2 through Thm. 2.5 |
7.2 #4, 5, 7, 8,9 7.1 # 8, 21 |
Surface Integrals |
Nov. 21 |
7.2 |
7.2 12, 13, 18, 19, 21, 22 |
Stokes's Theorem |
Nov. 24 |
7.3 |
7.3 # 2, 3, 5, 11 (see Example 2), 15 |
Gauss's Theorem |
Nov. 26 |
Holiday |
Holiday |
Holiday |
Dec. 1 |
7.3 |
7.3 #6. 7. 12, 14, 16, 18 |
Stokes, Gauss, Divergence and Curl |
Dec. 3 |
7.3 |
7.3 #17, 19, 20, 23, Integrating around a circle in the x-y plane isn't quite correct at the bottom of p457. We should actually be integrating around an ellipse. Explain how Problem 23 fixes this. 26 (An intuitive explanation involving integrals, perhaps around interestingly shaped regions is sufficient as an explanation.) |
Wrap up and course evaluation Take home portion of Final exam passed out. It will be sealed so you can ask questions until you unseal it. |
Dec. 7 |
Final Exam |
Take
home exam due |
Classroom portion today |