Math 5C - Vector Calculus II - Winter 2007

Instructor: Alex Dugas my homepage
Office: 6510 South Hall
Office Hours: T 2 - 4, Th 1 - 3

Prerequisites: Math 5B (with a grade of C or better).

Text: Wilfred Kaplan. Advanced Calculus. Fifth edition, Addison-Wesley.

Lecture: T Th 9:30 - 10:45 am in 1006 North Hall.

Section: You must sign up for and attend a discussion section as well.  The section times and locations for this course are as follows: 

• W   8:00-8:50,  Girv 1115
• W   5:00-5:50,  Phelp 3519
• W   6:00-6:50,  Phelp 3519
• W   7:00-7:50,  Phelp 1444
• F    12:00-12:50, Trail 940

The GSI for this course is Garrett Johnson.  His office hours are:

•  M 4-5,  SH 6431C
•  F 2-4,   MathLab SH 1607

Announcements:

• Solutions to the Final.  Final Grades should be available online by next Tuesday.  You can pick up your exams in my office beginning next Monday.
  
• I will have office hours next Tuesday from 12:00 – 2:00 pm.
• Here is an old 5C Final Exam.
• The Wave Equation problem on the review is harder than it’s supposed to be. A corrected version will appear in the solutions.
• The Final Exam is Wednesday, March 21, from 8-11am in NH 1006.  It will be around 10 problems, and will be based on material from the entire quarter.  Roughly half the problems will be based on material covered since the last midterm.  You are allowed one page (2-sided) of handwritten notes.  Here are some Review Problems, and Solutions.
• Midterm 2 Solutions.
• Midterm 2 is next Thursday, March 1, in lecture: 9:30 – 10:45 am.  It will be 5 problems, based on the material in chapter 6 that we have covered since the first midterm.  You are allowed a cheat sheet as for the first midterm (1 side of one page, hand-written). Here are some Review Problems.  Solutions to  Review Problems.
• To receive credit for the extra-credit part of  HW 5, please turn in just the extra-credit question to me in lecture this Thursday (2/15).
• Midterm 1 Solutions.
• Solutions to Review Problems are now available.
• Some notes for Tuesday's (1/30) lecture on Path Independence and Gauss's Law are posted below.
• You must bring a student ID to the midterm exam.
• The first midterm exam is next Tuesday, Feb. 6, in lecture: 9:30 – 10:45 am.  It will be 5 problems, and you are allowed a cheat sheet (see below) but no other notes, books or calculators.  Here are some Review Problems (solutions will be posted later), and two old exams with solutions:  Sample Exam 1,  Sample Exam 2. (note: some problems on these exams are on material we have not covered.)
• Cheat Sheet:  You will be allowed to bring one side of one 8.5'' x 11'' (or smaller) page of hand-written notes to the first midterm exam.    
• Please write your perm #'s on each homework assignment.
• Homework Solutions will be posted below.

Course Timetable (subject to change)
Date	Topics	Reading	Homework (in Kaplan)	Due Date
Tu 1/9	Line Integrals in 2D and 3D, Path Independence	Ch. 5.8 (review 5.1-5.6)	p. 312:  Ex. 1	Solutions
Th 1/11	Triple Integrals, Cylindrical & Spherical Coordinates.	Lecture  Notes	p. 121: Ex. 6a 2 additional prob.s
Tu 1/16	Parametrized Surfaces, Orientability, Surface Area	Ch. 5.9, 4.7	p. 248: Ex. 3	Solutions
Th 1/18	Surface Integrals of Functions and Vector Fields, Flux	Ch. 5.10	p. 313: Ex. 6a,b,d, 7a,b
Tu 1/23	Divergence Theorem	Ch. 5.11	p. 319:  Ex. 1a-e,  2a,c	Solutions
Th 1/25	Stokes' Theorem	Ch. 5.12	p. 330:  Ex. 1, 3
Tu 1/30	Path Independence	Ch. 5.13 Lecture Notes	p. 330-1:  Ex. 2, 4	Solutions
Th 2/1	Physical Applications	Ch. 5.15	Prob.s from Lecture
Tu 2/6	First Midterm	Ch. 5.8-5.13		Solutions
Th 2/8	Infinite Sequences and Series, Limits.  Convergence, Divergence.	Ch. 6.1, 6.2, 6.5 Lecture Notes	Homework 5
Tu 2/13	Convergence & Divergence Tests: Geometric Series, nth Term Test, Integral Test, p-Series, Comparison Test.	Ch. 6.5-6.7 Lecture Notes	p. 396:  Ex. 1-4, 5a, 9b	Solutions
Th 2/15	Alternating Series Test.  Absolute Convergence.  Ratio and Root Tests, Operations on Series.	Ch. 6.6, 6.7, 6.10 Lecture Notes	p. 396-7:  Ex. 6a, 7a, 8,  12a-f
Tu 2/20	Power Series.  Taylor & Maclaurin Series.	Ch. 6.11,  6.15-6.16 Lecture Notes	p. 417:  Ex. 1a,b,g,i	Solutions
Th 2/22	Operations on Power Series.  Taylor Series for ArcTan x, sin x, cos x, (1+x)^.5	Ch. 6.15,6.17 Lecture Notes	p. 429:  Ex. 1, 3a,c,d, 4
Tu 2/27	Taylor's Formula with Remainder.  Series of Functions.  Uniform Convergence, M-Test.	Ch. 6.11-6.14 Lecture Notes	p. 417-8:  Ex. 1c,e,f, 2a,c,d,f	Solutions
Th 3/1	Second Midterm	Ch. 6.1, 6.2, 6.4-6.7, 6.11, 6.15-6.17
Tu 3/6	Trigonometric & Fourier Series.  Fourier Coefficients.  Convergence Theorem.	Ch. 7.1 - 7.4 Lecture Notes	p. 478-9:  Ex. 1a,b,e,f, 5, 6	Solutions
Th 3/8	(Differentiation &) Integration of Fourier Series.  Complex Form of Fourier Series.	Ch. 7.5, 7.17 Lecture Notes
Tu 3/13	Wave Equation.  General Solution.  Fourier Sine Series.	Ch. 10.7, 7.5 Lecture Notes
Th 3/15	Wave Equation (cont.).  Review.	Ch. 10.8 Lecture Notes
W 3/21	Final Exam - 8:00 - 11:00 am

Homework:  Homework exercises will be assigned in lecture and listed on the course webpage (sometimes in advance).  All homework problems assigned in a given week are due on the following Wednesday in section.  You may work together on homework problems; however, you must write up your answers individually.  You must show all your work in order to recieve full credit.  Late homeworks will not be accepted.  However, your lowest homework score will be automatically dropped.

Exams: There will be two in-class midterm exams on Tuesday February 6 and on Thursday March 1 from 9:30 to 10:45 am.  Please arrive promptly.  The final exam will be Wednesday March 21, 8:00 - 11:00 am.  The problems on the exams will closely resemble those on the homeworks.   No make-up exams will be given, except in extaordinary circumstances.  If you have a serious conflict with any of these exams or miss one for any reason, it is your responsibility to notify me immediately so that other arrangements may be made.

Grades:  Grades will be computed from your scores on homeworks and exams as follows: Homework = 20%, Each Midterm = 20%, Final = 40%.  No letter grades will be assigned until the end of the semester, and the exact grading scale will depend on the difficulty of the exams.  However,  a 90% or above will guarantee you at least an A, an 80% will be at least a B, and 70% will be at least a C.