MATH 263: Multivariable calculus.

Text: James Stewart, Calculus (edition 6e).

Section 101, Instructor: Julia Gordon.

Where and when:

• Monday and Wednesday, 10-11am, and Friday 9-11am, at Hennings , Room 201.

Instructor's office: Math 217.
e-mail: gor at math dot ubc dot ca
Office Hours: Monday 4:30-5:30pm, Wednesday 4-5pm. TA: Mark Thom. TA's office hours: Tuesdays, 2-4pm, in LSK, Room 310 .

Section 102 of this course.

Announcements:

The final exam will be at 8:30am on Tuesday December 14, in Hennings 200.

The final exam will be comprised of roughly 50% material on vector calculus (chapter 17) and 50% prior material. While the focus will be on vector calculus, don't forget about the prior material either.

More office hours for Julia: Monday December 13, 3-5pm.

Review session for the final exam: Monday December 13, 10-12am in Hennings 201.

Please check the review materials for the final exam -- scroll down this page.

Julia's office hours after the end of classes: Thursday December 9, 4-6pm; and Friday December 10, 11am-1pm.

Review sessions for Midterm II: Monday November 1 and Tuesday November 2, 5-7pm, in GEOG 200.

October 27: Julia's office hours this week are: Thursday 4:30pm -6pm. Next week office hours will be Monday and Wednesday as usual.

October 27: Midterm II review materials posted: please scroll down (they are below "Homework").

October 27: Click here for an analysis of the feedback you gave (Section 101 only).

October 26: October 26: Assignment 7 in webwork consists of two parts. Please make sure you complete both Homework7_part1 and Homework7_part2 by November 2.

Midterm I solutions are now posted.

October 14: I'll have an extra office hour today, October 14, 4-5pm, in Math 217.

September 25: Review sessions Thursday, September 30 and Friday October 1, 5-7 pm, in CHEM C124 .

September 21: our TA, Mark, has scheduled regular office hours on Tuesdays, 2-4pm, in LSK, Room 310 .

September 21: Julia's office hour on Wednesday, September 22, has to be cancelled. Sorry about the inconvenience.

September 20: Homework 2 due date postponed till Thursday, September 23, 11:59pm.

Change of midterm dates: Midterm I -- Monday October 4; Midterm II -- Wednesday November 3.

NOTE: For those students who registered after the Setp. 6th and have a problem logging in to the system, please send an email with the following information to webwork.support@ubc.ca to activate your account.

• Your full name
• Your email
• Your student ID
• Your CWL username
• Course and section you registered

Exams and Marking

Course mark will be based on the Webwork (10%), two midterms (20% each) and the final exam (50%).

1st midterm (click here to see the exam with solutions) was on Oct. 4, Monday, 10 - 10:50 am

2nd midterm: Nov.3, Wednesday, 10 - 10:50 am

The two midterms will not overlap in the material covered. The final exam will cover the entire course. All exams will be common between all sections, and marked jointly.

Policies:

All exams are closed book, but you can bring 1 formula sheet written on both sides. Calculators will not be permitted.

Missing a midterm results in a score of 0, except with prior consent of the instructor or with a doctor's note. In these latter cases, you will receive no score from the missed exam, and your final exam will count for 70% of the grade. Please note that self-excusing without a doctor's note due to flu symptoms is no longer recognized by the University (this was the policy last year, but it is no longer in effect - note that it is a University-wide policy, not ours). So if you are sick, you will need a doctor's note to confirm it.

Each Webwork assignment closes at 11:59pm on Tuesday or Thursday night (please look at the dates carefully). No extensions are possible.

If for any reason you have to miss the final exam, it is the university-wide policy that you need to apply for "standing deferred" status through your faculty. Missed finals are not handled by me or the Mathematics Department.

Homework

• All homework assignments should be submitted online through Webwork .
Here is the list of functions that webwork understands, to help you input your answers.
• The first-day handout about about Webwork.

Review materials for the final Exam

• Detailed list of topics to review.
• handout about surfaces, surface integrals, and also vector fields and their integrals (was handed out in class in Section 101).
• You can do some of the problems in the set Practice_problems1 in Webwork, and compare your answers to the answers available online.
• handout about some standard parametric curves and surfaces .
• Final exam from 2007 , with solutions.
• Final exam from 2004 , with solutions.
• Final exam from 2006 , without solutions.
• Final exam from a similar course, Math 200, in 2003 -- all but Chapter 17, with solutions.
• Sample exam questions on Chapter 17 , with solutions.

Review materials for midterm II:

Please note that some of the old midterms cover more and some less than ours. This midterm will cover Sections 15.6-15.7, and 16.1-16.8 (from the non-ET edition). Here is the detailed list of topics for the midterm. Copies of this list will not be allowed in the exam. Here are some old midterms and other practice problems: (for best results, try the problems yourself first before looking at the solutions).

• 2004 Midterm II (with solutions).
• One more old midterm (with solutions)
• More practice problems from 2006 . (Ignore the Chapter 17 problems for now). Solutions to these problems .

Review materials for midterm I:

Please note that some of these old midterms cover more material than we plan to (due to the variation in the dates of the exam); for example, ignore all the questions about "the direction of the fastest increase (decrease, change)" of a function of two variables, and questions about maximal or minimal values of a function of two variables. We will cover these topics after the midterm.

• List of topics covered.
• Midterm I, 2004 . Solutions
• Midterm I, 2005 . Solutions .
• Midterm I, 2006 .
• Midterm I, 2007 .
• Midterm I, 2008 . Solutions .
• Some harder practice problems .

(Approximate) Course outline

• Wed, Sep. 8: 13.1, 13.2: Vectors; length of a vector, equation of a sphere in space, unit vector in a specified direction.
• Workshops on webwork on Thursday September 9, Friday September 10, and Monday September 13, 4-5 pm.
  Students from Section 101 should go to room LSK, Room 121 . Students from Section 102 should go to room LSK, Room 310 .
• Fri, Sep. 10: 13.3, 13.4, 13.5: Dot product, cross product. Using dot product to find an angle between lines. Using cross product to find a vector orthogonal to two given ones; cross product and area. Equations of lines and planes in space (symmetric, vector, and parametric equations of a line). Distance from a point to a given plane.


• Mon, Sep. 13: 13.5, continued. More about equations of lines and planes; tricks for finding the line of intersection of two planes, etc.
• [Homework 1 covering 13.1 -- 13.4 due on Sep. 14]
• Wed, Sep. 15:
• Note: Section 101 is a bit behind; finished 13.5 on Wednesday September 15; will start 14.1 on Friday. 14.1, 14.2: Notion of a vector function; parametric curves in space. Derivatives (and integrals) of vector functions.
  Additional assigned reading: Sections 11.1 and 11.2 in addition to 14.1, 14.2.
• Fri, Sep. 17: 14.1, 14.2, 14.3. The tangent vector to a curve; arc length. Unit tangent vector; unit normal vector.


• Mon, Sep. 20: 14.3: Reparametrization with respect to arc length.
• Wed, Sep. 22: 14.4: Normal and binormal vector, osculating plane, curvature of a curve. Velocity and acceleration. Tangential and normal components of acceleration. The notion of centripetal force.
• [Homework 2 covering 13.5-14.4 due on Sep. 23]
• Fri, Sep. 24: 15.1 Functions of several variables; level curves (for a function of two variables). 15.2, Limits and continuity (not completely rigorously).


• Mon, Sep. 27: 15.3 Partial derivatives, Clairaut's theorem (without rigorous proof).
• Wed, Sep. 29: 15.4 Linearizations; tangent plane to a graph of a function of two variables. Using differentials to estimate a change in the function corresponding to a small change in all variables.
• Fri, Oct. 1: Catch up an review.


• [Homework 3 covering 14.4, 15.1-15.4, due on October 2]
• Mon, Oct. 4: Midterm I. [test covers: chapters 13, 14, 15 up to (including) 15.4]
• Wed, Oct. 6: 15.5 The chain rule and implicit differentiation.
• Fri, Oct. 8: 15.6, start 15.7 Directional derivatives and the gradient vector. Equation of a tangent plane (and a normal line) to a surface at a given point.


• Mon, Oct. 11: NO CLASS.
• [Homework 4 covering 15.5 - 15.6 due on Oct.12]
• Wed, Oct. 13: 15.7. Critical points for a function of two variables.
• Fri, Oct. 15: 15.7, continued: global max/min of a function of two or three variables. 16.1, 16.2. Integral of a function of two variables over a rectangle: the definition. Iterated integrals (over a rectangle). Fubini theorem (without proof).


• Mon, Oct. 18: 16.3 Double integrals over general regions. Changing the order of integration.
• [Homework 5 covering 15.7, 16.1 -16.2 due on Oct. 19].
• Wed, Oct. 20: 16.4 Double integrals in polar coordinates.
  Additional assigned reading: 11.3 and 11.4 in addition to 16.4.
• Fri, Oct. 22: 16.5, 16.6 Applications of double integrals: moments, centre of mass, moment of inertia; Triple integrals. Six different ways of writing a triple integral as an iterated integral. Applications.


• Mon, Oct. 25: 16.6, continued.
• [Homework 6 covering 16.3 -- 16.5, due on Oct. 26]
• Wed, Oct. 27: 16.7 Using cylindrical coordinates to evaluate triple integrals.
• Fri, Oct. 29: 16.8 Triple integrals in spherical coordinates.


• Mon, Nov. 1: Review.
• Review sessions: Monday November 1 and Tuesday November 2, in GEOG 200, 5-7pm.
• [Homework 7 covering 16.6-16.8 due on Nov.2]
• Wed, Nov. 3: Midterm test II, covering 15.5--15.7 and chapter 16.
• Fri, Nov. 5: 17.1 Vector fields. Examples. Gradient vector field of a function. 17.2 Line integrals.


• Mon, Nov. 8: 17.3 the notion of a conservative vector field, and the fundamental theorem for line integrals.
• Wed, Nov. 10: 17.3, continued.
• Fri, Nov. 12: 17.4 Green's theorem (with explanation for why it works, for a simple region). The regions for which Green's theorem holds.


• Mon, Nov. 15: 17.5 Curl and divergence.
• [Homework 8 covering 17.1-17.3 due on Nov.15]
• Wed, Nov. 17: 17.5 Vector forms of Green's theorem.
• Fri, Nov. 19: 17.6 Parametric surfaces and their areas.


• Mon, Nov. 22: 17.7 Surface integrals of functions.
• [Homework 9 covering 17.4-17.5 due on Nov. 23]
• Wed, Nov. 24: 17.7 Surface integrals (flux) of vector fields.
• Fri, Nov. 26: 17.8 Stokes' theorem. Applications.


• Mon, Nov. 29: 17.9 Divergence theorem. Applications.
• [Homework 10 covering 17.6 -17.7 due on Nov.30]
• Wed, Dec. 1: catch up
• Fri, Dec. 3: Review.
• [Homework 11 covering 17.8 -17.9 due on Dec.12]

  THE END