# MATH 200:921 Multivariable calculus.

Summer term 1 2017/18

### **Instructor:** Roberto Pirisi

**Email:** rpirisi math.ubc.ca

**Classes:** Tuesday, Thursday and Friday 10 am to noon and Wednesday 10 am to 11,
room LSK 200

**Office hours:** Tuesday and Thursday 2:00 to 4:00 pm, in my office (MATHX 1220).

### Exams and Marking

Course mark will be based on the Homework

Webwork (15%),
five in-class quizzes (35%), and the final exam (50%).
The final exam will cover the entire course.
No calculators, electronic communication devices, books, notes or aids of any kind will be allowed for exams. Students are required to bring ID to all exams.

### Policies:

All exams are closed book. Calculators will not be permitted. Each student is allowed a single one-sided formula sheet.
The worst of your quizzes will be dropped from the average. If you miss a quiz that will be the one that is dropped. In case of a justified absence (with a doctor's note or prior consent from me) at most one more quiz can be dropped from the average.
Webwork assignments generally close at 11:59 pm on Tuesday and Friday night
(please look at the dates carefully in case there are some deviations).
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 the instructors or the
Mathematics Department.

### Homework

Homework assignments should be submitted online through Webwork
(Link to the course). To enroll in the WebWork course you must access it through Canvas.
Please use Piazza
as the main resource for help with webwork-related and other questions.
It is a forum, which will be monitored by our TA, where you can post questions and answers about webwork.
Please use the "e-mail instructor" button in webwork *only* if the question is not answered on Piazza, and you posted it and did not receive an answer.
Sign-up link for our class on Piazza.
### Getting help

In addition to the office hours, please take advantage of the
Math Learning Centre drop-in tutoring.
Do not wait till the exams -- if you feel uncomfortable with any of the material, talk to your classmates, talk to the instructor, and come ask questions at the Math Learning Centre.
For technical problems with webwork, Piazza registration, or exam conflicts, please e-mail me.

### Resources

Lecture notes
You can use Wolfram Alpha -- it is a wonderful tool for plotting graphs of functions of two variables, for example. If you want to visualize, for example, the surface x^2+xy-y^2+3z=0, just type in "plot (x^2+xy-y^2+3z=0)".
A note about Webwork and Wolfram Alpha: there will be many problems in Webwork which require thinking and which Wolfram Alpha cannot do; for the more mechanical ones that it can do, if you just use the software and copy the answers, it detracts from your learning. You might get a few extra points for the webwork problem, but you'll certainly lose much more on the exam for not having that skill. So use this great software to your advantage (to help you visualize the objects we study, and to learn), not to your disadvantage (to cheat on Webwork).
See review materials for the exams below the
"Announcements" section on this website.
Math
Learning Centre drop-in tutoring.

### Announcements:

Final will be on June 26, at noon in Buch A101.
Quiz 1 on Tuesday 5/21 Quiz Solutions.
Quiz 2 on Tuesday 5/28 Quiz Solutions.
Quiz 3 on Tuesday 6/05 Quiz Solutions.
Quiz 4 on Tuesday 6/12 Quiz Solutions.

### Review materials for the Final exam

Here are some handouts to help you review (please not that the "detailed
list of topics" handout reflects my personal view of which topics are
important; other instructors might have emphasized different topics).

The detailed overview of topics.
a table of
integrals and useful integration techniques .
You can access old final exams without solutions at:
The Math
department website .
The Math Club sells solution packages in MATX 1119. Please see their
Facebook page for the schedule.
Notes from the document
camera, from a review session from 2013.

There are three giant Webwork sets:
Part 1 : a collection of problems
from the
beginning of
the course, on vectors and geometry of space;
Part II : a large
collection of
problems about functions, partial derivatives, level curves, gradients,
and critical points and optimization probelms, including Lagrange
multipliers.
Part III: A collection of
integrals in 2 or 3
dimensions, in all kinds of coordinates.
These are pdf printouts generated by webwork for one user (your problems
will be slightly different). Use these files to identify problems of
interest, and then you can try your answers in webwork.
These Webwork sets ARE NOT FOR MARKS.
Final from 2003, with solutions .
Ignore Problem 8.

Some old midterms (still good for reviewing many topics):
Midterm 1 for Math 263, 2005.
(Ignore
Problem 2).
Midterm 1
from 2007. (Ignore
Problem 2).
Midterm 1 from 2012 (this one
was too easy, though -- you can expect a slightly harder exam this year
and it will cover more).
Midterm 1 from 2013 with solutions
Midterm 2 from 2013 with solution
(only look at problems 1(a)(b), (c) and 3).
Midterm from 2015 (with solution)

In the exams below, from Math 263, ignore all the problems about: vector
functions, surface area, arc length, or vector fields (this
course had more material).
Midterm 2 from 2004 but for Math 263
Math 263 final from 2007.
Ignore Problems 2,5,6.
Another old Math 263 final
Ignore problems 5,6,7,8.

### (Approximate) week-by-week course outline

This is only an approximate outline; it may be updated as the course progresses.

## Week 1:

10.1 (only up to "Cylinders") : Three-dimensional coordinate systems. Suggested problems 10.1: 1-3, 7, 9, 12, 16.
10.2: Vectors; basic operations with vectors; length of a vector, equation of a sphere in space, unit vector in a specified direction. Suggested problems: 10.2 1-5, 8, 11, 15, 20, 23, 27, 31.
10.3: Dot product; Using dot product to find an angle between lines. Application to finding forces. Suggested problems 10.3: 1-3, 11, 15, 19, 31, 39.
10.4: Cross product. Using cross product to find a vector orthogonal to two given ones; cross product and area. Suggested problems 10.4: 1-5, 9, 15, 27, 30, 31, 35, 39, 41.
## Week 2:

10.5 Equations of lines and plane in space. Symmetric and parametric equations of a line in space. Suggested problems
10.5: 7, 11, 21, 27, 31.
10.6 Equations for planes in space. Equations for a line of intersection of two planes, etc.
Finding distances in space: distance from a point to a plane, etc. Suggested problems 10.6: 1, 2, 9, 11, 14, 15, 17, 19, 25, 29, 32.
10.1: Cylinders and quadric surfaces (more in detail). Suggested problems 10.1: 15, 17, 23-26, 27, 32.
12.1: Functions of several variables. Domain and range. Level curves and level surfaces. Suggested problems 12.1: 1-6, 7, 11, 17, 19, 21, 23, 26, 27, 29, 31.
## Week 3:

Brief discussion of limits and continuity for functions of two variables.
Reference: section 12.2 (we will not cover everything in this section; refer to lecture notes).
12.3, Partial derivatives; higher-order partical derivatives. Suggested problems 12.3: 1-4, 5, 13, 19, 29, 33.
12.4 Differentials, tangent planes, and linear approximations.
Suggested problems 10.4: 7, 10, (find equation of tangent plane to z=f(x, y) at given point for 11, 12),
13, 15, (find linear approximation for 17, 18 at the given point).
12.5 Chain rule and implicit differentiation. Suggested problems 12.5: 1-5, 9, 17, 21, 29.
start 12.6 -- directional derivatives.
One additional topic to recall here: parametric equation of a segment connecting two points A and B.
## Week 4:

12.6 Directional derivatives and gradients, continued. Suggested problems 12.6: 1-6, 13, 15, 21, 23, 25, 27.
12.7 Geometric meaning of the gradient.
Tangent planes to level surfaces.
Tangent planes to graphs of functions of two variables, revisited. Suggested problems 12.7: 17, 19, 21, 23.
12.8 Critical points: the second derivative test, absolute maximum and minimum values. Suggested problems: 12.8 1-4, 5, 7, 11, 13, 15, 17 (also 11, 13, 15, 19 from 14.7 in Whitman ).
Secondary Textbook no. 1 ,
Section 14.8 Lagrange multipliers. 14.8 (from Whitman )
5, 10, 11, 12, 13, 15, 17.
## Week 5:

14.8 (From Whitman) Lagrange multipliers, continued. (two constraints not included). Suggested problems: see above.
13.1 Iterated integrals (over a rectangle). Double integrals over general regions. Suggested problems
13.1: 7, 9, 19, 21 (also see #3, 5, 10, 13, 15 from section 15.1 of Whitman) .
Interchanging the order of integration. Fubini's theorem (without proof).
Suggested problems: 13.2 1-4, 7, 9, 13, 17, 21, 25 (also see #17, 21, 23 from section 15.1 of Whitman)
13.3 Double integrals in polar coordinates. Suggested problems: 13.3 3, 4, 8, 13.
13.4 Center of mass. Suggested problems 13.4 1, 5, 6, 13, 24.
## Week 6:

13.6 Triple integrals. Six different ways of writing a triple integral as an iterated integral. Suggested problems: 13.6 5, 7, 9, 11, 13, 15, 19, 23
14.4 Secondary Textbook no. 2.
Triple integrals in cyindrical and spherical coordinates. Suggested problems: 14.4 (from Strang) 11, 13, 15, 19, 22, 23