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:
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:
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 $a\leq x\leq b$
April 2 Section 6.7: 1, 2, 3, 6, 7 (a,c,e), 8, 10 (read the explanation above the problem), 11, 17
April 7 Section 6.7: 15, 19, 20, 24
Section 7.4: 1–5
April 15 Section 7.8: 1–4
Section 7.12: 1, 2, 5 (a,b,d)
April 23 Section 7.12: 3, 4, 5 (do several parts, including l)
April 28 Final Homework: surface integrals and the divergence theorem. (Answers are on the second page.)

Don't forget that the PDF of the course packet has answers for all the problems marked with green dots.
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: Stokes' Theorem