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