MATH 200: Multivariable calculus, Sections 201 and 202
 Instructor: Julia Gordon.

Where and when:
 Section 201: MWF 910am in LSK 201.
 Section 202: MWF 1112 in MATH 100.
 Instructor's office: Math 217.
 email: gor at math dot ubc dot ca, but for all conflicts with exams, troubles with login, etc. please email math200dictator at gmail.com

Office Hours: Mondays, 45pm; Wednesdays 23pm, Fridays 12:151:30pm.
All the information about the course is at
the common course website.
Announcements:
 Webwork 11 extended by another week, till April 18!
 My review sessions: April 18th, 24pm, and April 19th, 10amnoon in
MATX 1100.
The first review session covered triple integrals and Lagrange
multipliers.
Notes from review session 1.
The second review session started with gradients, level curves/surfaces,
etc., and then had a triple integral, and then more problems on chain
rule and gradients.
Notes from review session 2.
 Office hours after the end of term (NOT at regular times, but on
these times only; plus the review sessions above):
 Monday April 16th, 12pm.
 Wednesday April 18th, 45pm (after the review session)
 Thursday April 19th, 12pm.
 Friday April 20th, 10amnoon.
Sectionspecific notes
These files are doccam scans for Section 201. Lectures in Section 202
might be slightly different (the differences might be briefly described
next to the notes).

Wed January 3:
Section 10.1 (up to "cylinders", not inclusive)  3dimensional coordinate systems,
righthand rule, a formula for the distance between points in 3space.
(No notes).
 Fri Jan 5:
Notes for January 5 .
Topics covered: vectors  definition, addition, multiplication by scalars. Dot product (starts on p.6)
For Section 202 (11am12): Please note: only the first 6 pages correspond
to our class, plus we did an example with an airplane (which I will try to write up and post soon).
 Mon Jan 8:
Notes for January 8 .
Topics covered: dot product, the unit vector in a given direction, started components and porjections. Will continue with
components, projections, and forces (and do examples) next class.
For Section 202: please start by reading pp. 69 of the notes from January 5.
 Wed Jan 10:
Forces, more on vectors, projections, and dot product. examples.
Notes for January 10 (improved),
including worksheet
solutions .
 Fri Jan 12:
Work. Cross product (two definitions).
Notes for Friday January 12
Quiz 1 for Section 201 (with
solutions)
Quiz 1 for Section 202 (with solutions).
 Mon Jan 15:
Cross product, continued. Properties; mixed (scalar) triple product and an
explanation for the two definitions of cros product: relationship with
volume of a box in space.
Started equations of planes.
Notes for Monday January 15
(In Section 202, stopped short of the last page).
 Wed Jan 17: Equations of
lines and planes in 3space.
Reading: Sections 10.6, 10.5
Notes for Wednesday (including the
solutions to
the first two worksheet problems; for the last one, see next class).
 Fri Jan 19:
Examples on lines
and planes; distances, skew lines in space.
Reading: Sections 10.6, 10.5.
Notes. (these are centered on the worksheet
problem from the last class and a new worksheet problem).
Complete solution to the worksheet
.
Reading for next class: please read all of Section 10.1 !
 Mon Jan 22:
Quadric surfaces and cylinders. (Section 10.1)
Notes . (Note: there is a small error in Example 4
on p.3: the last picture on the page does not match the equation  the
surface pictured is given by the equation z+x^2=0).
Supplement: how to remember
quadric surfaces . (has a typo at the end in the equation of a cone 
see Piazza for correction).
 Wed Jan 24:
Section 12.1  functions of two variables; domain and range; graphs;
level curves.
Notes .
 Fri Jan 26:
The notion of continuity for functions of two varaibles. More on level
curves. Quiz.
Notes (the notes refer to this plot ).
Quiz 2 Section 201 (corrected);
Quiz 2 Section 202 Quiz 2 Section 202
 Mon Jan 29:
Partial derivatives (Section 12.3).
Notes .
 Wed Jan 31:
More on partial derivatives; the wave equation; linear approximations;
tangent planes. (Section 12.4).
Notes for Section 201
Notes for section 202 (this version is
the same material but more detailed; in particular, see pp. 34 for
detailed discussion of the Question 2 from the worksheet; there is a
supplement (in red on p.3) to what I said in lecture which hopefully
clarifies the matter of the function c(y) that appeared in the solution.
 Fri Feb 2:
Linearization of a function of two or three variables. The differential.
Notes (the notes have a lengthy explanation
of how two ways of finding the tangent plane to the graph z=f(x,y) agree.
You do not need to know all this for exams, just use linearization
 no need for
any cross products here. This was explained just to make sure all the
things in the course agree with each other and make sense).
 Mon Feb 5:
Chain rule in several variables. Implicit differentiation.
(Section 12.5)
Notes .
 Wed Feb 7:
Chain rule in several variables, continued.
(Section 12.5)
Notes .
 Fri Feb 9:
Directional derivatives and gradients (Section 12.6).
Quiz on 12.3 and 12.4.
Lecture notes . Supplement
on implicit differentiation . Please also read the subsection on
implicit differentiation at the end of Section 12.5 in the book (it does
the same but for just 2 variables).
Quiz for Section 201 with solutions .
Quiz 3 for Section 202 without solutions .
Quiz 3 for Section 202 with solutions
 Tuesday Feb 13:
MIDTERM! (see the common website).
Midterm with solutions
 Wed Feb 14:
Directional derivateives and gradients. Geometric meaning of the gradient.
Notes
 Fri Feb 16:
Geometric meaning of the gradient, continued.
Read Section 12.7!
Notes . Complete
solution to the problem about the hiker (refers to the map, which is
inside the lecture notes).
 Feb 1923 the break!
 Mon Feb 25:
Critical points. Notes
(Start reading Section 12.8)
 Wed Feb 28:
Classifying critical points for a function of two variables  the second
derivative test.
Started absolue max/min problems.
Notes ; Map with
critical points marked.  the illustration on how to recognize
critical points by looking at level curves.
Continue reading 12.8.
 Fri Mar 2:
Absolute max/min on a closed bounded domain. Constrained
optimizarion. Started Lagrange multipliers (Read: all of Section 12.8 and
Section 14.8 from the
Secondary text No. 1
Notes .
 Mon Mar 5:
Lagrange Multipliers (only one constraint covered).
Section 14.8 from the
Secondary text No. 1
Notes .
 Wed Mar 7:
Starting integration for functions of 2 variables  Section 13.2
(note: 13.2, NOT 13.1  we are doing it in slightly different order from
the textbook).
Notes
 Fri Mar 9:
Integration, continued. Read 13.2 and 13.1 (in this order). Notes will be
posted after the lectures.
Quiz 4 on critical points, Lagrange multipliers, absolute max/min.
Section 201 quiz ;
Section 202 quiz .
Solutions will be posted later.
Notes (only pp. 12 were covered in class, but
the whole notes are useful).
 Mon Mar 12:
Iterated integrals for general 2dimensional regions. Changing the order
of integration. Read 13.1 (and 13.2).
Notes
 Wed Mar 14:
Changing the order of integration in double integrals.
Started polar coordinates.
Read: 13.1 and Chapter 9.4 in the textbook (9.4 introduces polar
coordinates), and start reading 13.3.
Notes
 Fri Mar 16:
Integration in polar coordinates, continued. Area of a domain.
Notes (Notes are expanded compared to the
lecture, including an explanaion of some common confusion that became
apparent in office hours: about area under the graph from calculus 1 and
our new way of computing the area. The last line of the last page is cut
off. It should be: "but you cannot solve for y!").
 Mon Mar 19:
Mass and centre of mass.
Notes (with complete solution to the worksheet
problem).
 Wed Mar 21:
Triple integrals.
Notes
 Fri Mar 23:
Triple integrals; sketching, changing the order of integration.
Quiz.
Quiz 5 for section 201 (with solutions);
Quiz 5 for section 202 (with solutions).
Notes
 Mon Mar 26:
Triple integrals: changing the order; example from last class, continued.
Notes
 Wed Mar 28:
Cylindrical and spherical coordinates.
Notes
 Friday March 30 and Mon April 1 
no class (UBC holiday).
 Wed April 4:
Spherical coordinates.
Notes
 Friday April 6:
Last class! Will review triple integrals (especially in spherical and
cylindrical coordinates). Expect a worksheet.
Notes ; Sketch  a better sketch for the last problem with some
notes on sketching spheres (completely optional).