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