Math 234 (Lecture 3) — Spring 2017
Calculus—Functions of Several Variables
Lecturer: Joe Miller
Email: ude.csiw.htam@rellimj
Office: 521 Van Vleck
Office Hours:
  • Monday 1:00–2:00PM,
  • Thursday 9:30–10:30AM.
Lecture: MWF 12:05–12:55PM in B102 Van Vleck

Textbook:
Grade Breakdown
  • Discussion: 20%
  • Exam I: 25%
  • Exam II: 25%
  • Final exam: 30%
Discussion grades are based on quizzes. These grades will be adjusted at the end of the semester so that, even if your TA is a tough grader or gives hard quizzes, your course grade will not suffer. You should expect to have a quiz in discussion section (essentially) ever Thursday.

Make-up quizzes will not be offered, but we will drop the lowest quiz score.

Homework
Homework will not be collected.

Assigned on Exercises
January 20 Section 1.12: 1–15
January 29 Section 2.17: 2–6
February 6 Section 2.17: 1, 7
Section 3.Problems: 1–4, 10–12
February 13 Section 3.Problems: 5, 6, 7, 14
Section 4.3: 1(a), 2, 3, 4, 6
February 17 Section 4.7: 1–6, 8–10
Section 4.Problems (pages 72–73): 1–8, 10, 13
February 25 Section 4.Problems (pages 72–73): 9, 11, 14
Section 4.12: 1–6, 8, 10–12
March 4 Section 4.15: 2, 3, 7, 9, 12, 13 (find the function)
Section 5.3: 1, 2, 3
Section 5.6: 1 (do a few parts), 2, 5, 6, 7
March 10 Section 5.10: 2 (a,c,e), 5 (do a few parts), 7 (a,c), 8, 9
Section 5.13: 1, 2, 3, 5, 10, 12, 13, 14
March 26 Section 6.3: 1, 2, 3, 5 (do a few, including k), 6 (do a few), 8, 9. Note the typo in 8: $a\leq c\leq b$ should be $a\leq x\leq b$

Don't forget that the PDF of the course packet has answers for all the problems marked with green dots.
Exams
There will be two evening exams and a final. Make-up exams are possible only in very specific circumstances. It is your responsibility to avoid unnecessary conflicts.

Exam Dates:
  • Exam 1: Thursday, March 2 from 7:15–8:45PM (EVENING)
  • Exam 2: Thursday, April 13 from 7:15–8:45PM (EVENING)
  • Final: Monday, May 8 from 5:05–7:05PM (EVENING)
Tentative Syllabus
Note that this schedule is only an approximation!

Week Topics
1 Vector Geometry in 3-D space: review of vectors, dot and cross products, determinants, lines and planes
2 Parametric curves and vector functions: vector functions, parametric equations, derivatives, velocity and acceleration
3 Parametric curves and vector functions: Arc length, tangent, normal and binormal vectors, curvature
4 Functions of several variables: functions of two variables, level sets, linear functions, quadratic forms, polar coordinates
5 Derivatives: interior points and continuous functions, partial derivatives, linear approximations, tangent plane
6 Derivatives: Chain Rule, gradients, functions of three variables, implicit functions, higher order partial derivatives
7 Maxima and minima: Local and global extrema, continuous functions on closed bdd sets, critical points, linear regression
8 Maxima and minima: second derivative test, optimization
9 Integrals: double and triple integrals
10 Integrals: triple integrals, cylindrical coordinates, spherical coordinates
11 Vector Calculus: vector fields, line integrals
12 Vector Calculus: Fundamental Theorem of Calculus, conservative vector fields
13 Vector Calculus: Flux integrals, Green's Theorem
14 Vector Calculus: Surfaces and surface integrals, Divergence Theorem
15 Vector Calculus: Stoke's Theorem