Math 550, Spring 2012
Syllabus for Math 550 Section 001 & 510.
Honors and Graduate Student Project Due before 5pm, Friday 4-27-12.
Description of the Project. Updated 4-21-12!
Necessary comments on the Lorentz scalar product and the Hodge * operator
Suggested References Updated 4-17-12!
Section 3 of the Paper.
Extra Credit Homeworks All of these are not required, but can be used as
reference material. Anyone who wants extra credit can complete any of them
and turn them in any time on or before 5pm, Friday 4-27-12.
Sections covered and Homework assigned:
section 1.1, p. 21, #22,26,30. Vectors in 2D and 3D space. Due 1-18 in class.
Scan from text.
Scan from text.
section 1.2, p. 36, #14,18,20. Inner Product, Length, Distance. Due 1-18 in class.
Scan from text.
Scan from text.
Solutions
Based on the 2nd lecture. Homework set #2 Due 1-20 in class.
Solutions
Extra Credit: Theory Homework #3 (linear mappings and Bases).
Practice Homework #3. Due 1-27 in class.
Further explanation for Theory and Practice Homework #3.
Solutions
Extra Credit: Theory Homework #3.5 (Subspaces).
Extra Credit: Theory Homework #4 (Bilinear mappings, dot products).
Based on the 5th lecture: Practice Homework #5. Due 1-30 in class.
Further explanation of Practice Homework #5.
Solutions
Extra Credit: Theory Homework #6 (Orientations).
Based on the 6th & 7th lectures: Practice Homework #7. Due 2-1 in class.
Solutions
section 1.3, p. 61, #2a,3,4,5,6,7. Areas, volumes, cross-products, triple products. Due 2-6 in class.
Extra Credit: Theory Homework #8 (Wedge product, Hodge *, Volume, Cross Product).
Exam 1, Wednesday Feb. 8, 10 problems from above material. Bring blue books!
Exam 1 Review.
Addendum to Exam 1, due Friday February 17.
Sections covered:
section 2.2, p. 125, #3,4,20,26. (open sets, continuous functions) Due 2-20 in class.
Solutions
Extra Credit: Practice Homework #9 (Wedge products, Hodge *).
Highly recommended for all students
because it is much easier than earlier extra credit homeworks.
section 2.3, p. 139, #2,6,8,12,16,20. (partial derivatives, differentiability) Due 2-24 in class.
Solutions
section 2.4, p. 149, #8,14,16,18. (tangent vectors to curves) Due 2-27 in class.
Solutions
section 2.5, p. 159, #4,8,10,14,20. (Chain rule) Due 2-29 in class.
Solutions
Proof Step Lists. Updated 3-3-2012.
section 4.4, p. 310, #4,12,14,16,18,20. (Divergence, Curl) Due 3-12 in class.
section 8.6, p. 603, #1,2,3. (wedge product, exterior derivative) Due 3-12 in class. Note the book's notation
for dx /\ dy is dx dy.
Practice Homework #12 (Exterior Derivation, Gradient, Divergence, Curl).
Due 3-14 in class.
Solutions
Exam 2, Friday Mar. 16. Ten problems from above sections. Bring Blue Books!
Exam 2 Review.
Sections covered:
Practice Homework #13 (Forms, Parameterizations).
Due 3-26 in class.
section 5.3, p. 347, #2,7,11. (Double Integrals) Due 3-28 in class.
section 5.4, p. 353, #1,2. (Iterated integrals) Due 3-28 in class.
section 7.2, p. 447, #2,3,6,8,12(the vertices are in the xy-plane: z=0),16. (Line integrals) Due 4-4 in class.
section 6.2, p. 390, #2,8,14,20,26. (Change of variables in type 1 integrals) Due 4-11 in class.
section 7.3, p. 459, #2,6,8,10,14. (Parameterized surfaces) Due 4-13 in class.
Exam 3, Monday Apr. 16. Bring Blue books! Ten questions from the above sections.
Exam 3 Review.
Solutions of selected HW problems.
The proof required in problem #7 of exam #3.
Sections covered:
section 7.6, p. 497, #2,4,6,10,16,18. (Type 2 integrals over surfaces) Due 4-18 in class.
Comments about surface integrals.
section 8.1, p. 528, #2,4,10,12. (Green's Theorem) Due 4-20 in class.
Comments about Green's Theorem.
section 8.2, p. 547, #6,8,10. (Stokes' Theorem) Due 4-20 in class.
Final Exam: Wednesday, April. 25, 2-5 pm, in usual
classroom. 20 or so problems from any of the above sections. Bring Blue Books.
The semester and the final exam breaks into four blocks:
Vector Algebra, 12 lectures, 6 questions, 3 from Exam 1.
Differentiation, 12 lectures, 6 questions, 3 from Exam 2.
Integration, 12 lectures, 6 questions, 3 from Exam 3.
Generalized Stokes' Theorem, 3 lectures, 2 questions. Final Exam Review.
Solutions to some HW problems.
Any of the earlier material which contributes in any way to the last (4th) block of material
is clearly of greater importance than something that does not.