Math 234 (Fall 2014) Calculus III: Functions of Several Variables

Lectures
Lectures are by Jeff Viaclovsky:
- Section 234-001 meets on Mondays, Wednesday and Fridays at 07:45-08:35 AM in Van Vleck B102.
- Section 234-002 meets on Mondays, Wednesday and Fridays at 09:55-10:45 AM in Van Vleck B102.
I will have office hours on Mondays and Wednesdays in Van Vleck 803 from 08:45-09:45 AM.

NOTE: If anyone is spotted browsing the internet or sending text messages during lectures, their computer or cell phone will be confiscated for the remainder of the lecture (the TAs *do* attend the lectures, and they will be watching carefully). However, taking notes on a tablet PC, or briefly using a computer to look up a formula is acceptable (except on an exam of course).
Textbook
Math 234 Third Semester Calculus by Sigurd Angenent. Copies are available from the Mathematics Department.
Student Resources
There are several additional resources available for those students needing some extra help: GUTS, MathLab, Math Tutorial Program, and Private Tutors. For detailed information, click here: Student Resources, or here: Alternate Link.

Discussion Sections and TAs

You must attend your assigned section, you are not allowed to attend other sections.

SECTION	LECTURE	TIME	LOCATION	TEACHING ASSISTANT

301	1	TR 07:45-08:35	Van Vleck B211	DONG, Yihe
302	1	TR 07:45-08:45	Van Vleck B131	HAN, Jiyuan
303	1	TR 08:50-09:40	Van Vleck B317	ROSS, Daniel
304	1	TR 08:50-09:40	Mech. Eng. 1156	LI, Lei
305	1	TR 11:00-11:50	Van Vleck B131	KIM, Jongchon
306	1	TR 11:00-11:50	Van Vleck B309	LIU, Yuan
307	1	TR 13:20-14:10	Sterling 2335	HAN, Jiyuan
308	1	TR 13:20-14:10	Van Vleck B305	KIM, Jongchon
309	1	TR 14:25-15:15	Van Hise 119	LI, Lei
310	1	TR 14:25-15:15	Babcock 121	TRIPP, Nathan
311	1	TR 07:45-08:50	Van Vleck B105	ROSS, Daniel
312	1	TR 07:45-08:50	Van Vleck B215	LIU, Yuan
321	2	TR 08:50-09:40	Ingraham 123	KIM, Yoosik
322	2	TR 08:50-09:40	Social Work 114	ALBERTIN, Anthony
323	2	TR 09:55-10:45	Humanities 2131	KIM, Yoosik
324	2	TR 09:55-10:45	Van Vleck B129	ALBERTIN, Anthony
325	2	TR 11:00-11:50	Van Vleck B317	DONG, Yihe
326	2	TR 11:00-11:50	Van Vleck B313	ALBERTS, Brandon
327	2	TR 12:05-12:55	Van Vleck B317	ALBERTS, Brandon
328	2	TR 12:05-12:55	Social Work 110	CHEN, Xianghong
329	2	TR 13:20-14:10	Humanities 2131	CHEN, Xianghong
330	2	TR 13:20-14:10	Van Vleck B313	TRIPP, Nathan

ALBERTIN, Anthony be reached at ajalbertin "at" gmail.com His office hours are T 11:00-12:20, W 12:00 - 1:00, and TR 11:00-12:20, at 101-22 Van Vleck, Phone: (920)342-2464.

ALBERTS, Brandon may be reached at blalberts "at" math.wisc.edu. His office hours are M 12:00 - 1:00 PM and W 1:00 - 2:00 PM at 522 Van Vleck, Phone: NA. Discussion webpage.

CHEN, Xianghong may be reached at xchen "at" math.wisc.edu. His office hours are M 3:30 - 4:30 PM and Th 2:30 - 3:30 PM at 822 Van Vleck, Phone: 262-0537. Discussion webpage.

DONG, Yihe may be reached at ydong "at" math.wisc.edu. Her office hours are M 3:30 - 6:00 PM at 820 Van Vleck, Phone: 262-7398.

HAN, Jiyuan may be reached at jiyuan "at" math.wisc.edu. His office hours are W 1:00-2:00 PM and W 5:00-6:00 PM at 522 Van Vleck, Phone: 263-7939. Discussion webpage.

KIM, Jongchon may be reached at jkim "at" math.wisc.edu. His office hours are T 14:30 - 15:30 PM and W 11:00 - 12:00 at 316 Van Vleck, Phone: NA. Discussion webpage.

KIM, Yoosik may be reached at ykim "at" math.wisc.edu. His office hours are M 12:00 - 1:00 PM and Th 3:00 - 4:00 PM at 718 Van Vleck, Phone: 262-0079. Discussion webpage.

LI, Lei may be reached at leili "at" math.wisc.edu. His office hours are M 3:30 - 4:30 PM and Th 10:00 - 11:00 AM at 520 Van Vleck, Phone: 262-3601. Discussion webpage.

LIU, Yuan may be reached at yliu "at" math.wisc.edu. Her office hours are M 4:00 - 5:00 PM and W 4:00 - 5:00 PM at 818 Van Vleck, Phone: 262-1425. Discussion webpage.

ROSS, Daniel may be reached at ross "at" math.wisc.edu. His office hours are M 12:00 - 1:00 PM and F 1:00 - 2:00 PM at 318 Van Vleck, Phone: NA. Discussion webpage.

TRIPP, Nathan may be reached at ntripp "at" wisc.edu. His office hours are T 3:30 - 5:00 PM and TR 3:30 - 5:00 PM at 101-24 Van Vleck, Phone: 263-1350.

Examinations and Homework
There will be weekly homework assignments, which do not have to be handed in. However, there will be weekly quizzes in your discussion sections which will account for 20% of your final grade. There will be 2 in-class exams, and a final exam. The final grade will be roughly 25% for each in-class exam, and 30% for the final (plus 20% for the discussion quizzes). The in-class exams are scheduled for October 8 and November 12. The final exam is scheduled for Tuesday, December 16 from 17:05-19:05 PM.
- Week 1 HW: Chapter 1 (pages 16-18) 1, 3, 5, 8, 9, 12, 13, 15, 16, 17.
- Week 2 HW: Chapter 2 (pages 31-33) 1, 2, 3, 4, 5, 7.
- Week 3 HW: Chapter 3 (pages 46-48) 2, 3, 5, 6, 7, 8, 10, 11, 12, 13.
- Week 4 HW: Chapter 4 (pages 51-52): 1, 2, 3, 6, (pages 61-62): 1, 2, 3, 4, 5, 6 (pages 72-73) 1, 2, 3, 4, 5.
- Week 5 HW: Chapter 4 (pages 72-73): 6, 7, 9, 13, 14, (pages 75-78): 1, 3, 5, 14, (pages 81-82): 1, 3, 5, 7, 12, 13, 14
- Week 7 HW: Chapter 5 (page 91): 1, 2, 3, 4, 5, 7, (pages 99-100): 2, 3, 4, 5, 7, 8, 9.
- Week 8 HW: Chapter 5 (pages 104-105): 1, 2, 3, 5, 7, 9, 12, 13.
- Week 9 HW: Chapter 6 (pages 120-121): 1, 5, 6, 7, 9, 10.
- Week 10 HW: Chapter 6 (pages 133-135): 1, 2, 7, 8, 10, 13, 15, 17, 19, 21, 23.
- Week 12 HW: Chapter 7 (page 142): 1, 3, 4, (page 151): 1, 2, 3, 4.
- Week 13 HW: Chapter 7 (pages 159-160): 1, 2, 3, 4, 5.
- Week 15 HW: Chapter 7 (pages 171-173): 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Supplementary Problems, More Supplementary Problems.
Topics covered
The plan is to cover material from the following sections of the notes:

Chapter 1. Vector geometry in three-dimensional space
Chapter 2. Parametric curves and vector functions
Chapter 3. Functions of more than one variable
Chapter 4. Derivatives
Chapter 5. Maxima and minima
Chapter 6. Integrals
Chapter 7. Vector calculus

Note that this is every chapter in the notes, but depending upon time constraints, we may omit some material from some of the chapters. The following brief lecture outline will be more accurate, and will be updated very frequently.
Brief lecture outline
- Week 1: September 3, 5
  1. Wednesday, Chapter 1: Vector geometry in three-dimensional space. Basic vector algebra, Sections 1-5.
  2. Section 6-10: Dot product, cross product, determinants, and triple product..
  3. Section 11: Distance from a point to a 2-dimensional plane.
  4. Friday, begin Chapter 2 : Parametric curves and vector functions.
  5. Section 1-6: Examples of lines, circular motion, cycloid, helix.
  6. Section 7-9: Differentiation of a vector valued function, velocity, and acceleration, Newton's Law.
  7. Section 10: Rules for differentiation.
- Week 2: September 8, 10, 12
  1. Monday, Chapter 2, Section 11-12, Vector functions of constant length, and circular motion. Centripetal force, normal and tangential components of force for circular motion.
  2. Wednesday, Section 13, arc length, invariance under reparametrization, examples of helix, and quadratic helix.
  3. Friday, Section 14-16: arc length derivative, unit tangent and curvature, curvature and normal, and osculating plane.
- Week 3: September 15, 17, 19
  1. Monday, begin Chapter 3: Functions of more than one variable.
  2. Domain, graph, and level set of a function, linear functions and quadratic forms.
  3. Wednesday: Examples for classification of quadratic forms, polar coordinates.
  4. Friday, begin Chapter 4, Derivatives.
  5. Interior points and boundary points of a domain, continuity, partial derivatives, Taylor's theorem.
- Week 4: September 22, 24, 26
  1. Monday, Chapter 4, tangent plan to a graph, tangent plane to a sphere, Chain rule.
  2. Wednesday, Chapter 4, Gradients.
  3. Gradient is normal to level sets, equation for tangent plane in terms of gradients.
  4. Friday, Example of linear approximation, Implicit Function Theorem in 2 and 3 variables.
- Week 5: September 29, October 1, 3
  1. Monday, Chapter 4, Section 11: Chain rule with more independent variables.
  2. Implicit function theorem in 3 variables, rotation of coordinates, and polar coordinates.
  3. Wednesday, Chapter 4, Section 13, Higher partials and Clairaut's Theorem.
  4. Section 14, Finding a function from its derivatives.
  5. Friday, begin Chapter 5, review of maxima, minima, and second derivative test from Calc I.
- Week 6: October 6, 8, 10
  1. Exam Review.
  2. Exam I: Wednesday, October 8, during class (see email for exam location, which depends on your Discussion Section).
  3. Friday, continue with Chapter 5, global extrema, local maxima and minima, closed and bounded domains.
  4. Theorem: if f continuous on a closed and bounded domain D, then f has both a global maximum and a global minimum in D.
- Week 7: October 13, 15, 17
  1. Monday, critical points. Theorem: a local maximum or minimum is necessarily a critical point.
  2. Wednesday, Chapter 5, Section 9, the second derivative test.
  3. Friday, Section 9, the two variable second derivative test.
- Week 8: October 20, 22, 24
  1. Monday, Chapter 5, Section 12, Lagrange multipliers.
  2. Wednesday, continue with Lagrange multipliers.
  3. Friday, several examples of Lagrange multiplier problems in 3 variables.
- Week 9: October 27, 29, 31
  1. Monday, begin Chapter 6, Integrals. Definition of double integral in terms of Riemann sums.
  2. Equality of iterated integrals for rectangular regions.
  3. Wednesday, double integrals when the domain is not a rectangle.
  4. Friday, Double integrals in polar coordinates.
- Week 10: November 3, 5, 7
  1. Monday, begin triple integrals. Triple inegrals on 3-dimensional rectangles. Triple integral when the boundary of the domain is written as 2 graphs over the projection of the domain to a coordinate plane.
  2. Wednesday, averages, density, mass.
  3. Friday, center of mass, cylindrical and spherical coordinates.
- Week 11: November 10, 12, 14
  1. Monday, moments of inertia, exam review.
  2. Exam II: Wednesday, November 12, during class (see email for exam location, which depends on your Discussion Section).
  3. Friday, moments of intertia, how to diagonalize a symmetric matrix using Lagrange multipliers.
- Week 12: November 17, 19, 21
  1. Monday, begin Chapter 7, Vector Calculus. Vector fields, integration of a function along a curve.
  2. Wednesday, Integration of a vector field along a curve.
  3. Friday, fundamental theorem of calculus for line integrals, conservative vector fields.
- Week 13: November 24, 26
  1. Monday, flux integrals, Green's Theorem.
  2. Wednesday, physics video.
  3. November 28: Thanksgiving vacation
- Week 14: December 1, 3, 5
  1. Monday, Green's Theorem, conservative vector fields and Clairaut's Theorem.
  2. Wednesday, Using Green's Theorem to compute areas of domains, surfaces, areas of a surface patch, unit normal to a surface.
  3. Friday, integral of function on a surface, flux of a vector field across a surface.
- Week 15: December 8,10,12
  1. Monday, divergence theorem and Stokes' Theorem.
  2. Wednesday, properties of divergence and curl operators. Course evaluations.
  3. Friday, review for final.
- Tuesday, December 16
Contact Information

Math 234 (Fall 2014) Calculus III: Functions of Several Variables

Lectures

Textbook

Student Resources

Discussion Sections and TAs

Examinations and Homework

Topics covered

Brief lecture outline

Contact Information