MATH 200: Multivariable calculus, Section 203. Term 2,
2019/20
 Instructor: Julia Gordon.

Where and when:
 Tue Th 12:302pm in LSK 201.
 Instructor's office: Math 217.
 email: gor at math dot ubc dot ca

New Office Hours: Tuesday 56pm and Thursday 4:155:45pm.
All the information about the course is at
the common course website.
Announcements:
Test 3 is coming up on Tuesday March 10! See review materials on
the common website. The test will be at the beginning of the class.
Extra office hours this week: Monday March 9, 121pm and 23pm.
 The term test dates:
Test 1  Tuesday January 28
Test 2  Tuesday February 25
Test 3  Tuesday March 10
Test 4  Thursday March 26.
Sectionspecific notes
These notes are mostly unedited doccam scans. All reading is from
CLPIII unless
otherwise specified.

Week 1: January 79:
Topics covered: coordinate system in 3d; vectors  definition, addition,
multiplication by scalars. Dot product.
Notes for January 7 .
Notes for January 9
Read: 1.1, 1.2.1  1.2.3.
 Tue Jan 14:
The unit vector in a given direction,
projections.
Using vectors to find forces. Started cross product.
Read for this week: 1.2.11.2.5
Worksheet 1 .
Notes for January 14 .
(these notes contain the worksheet solutions).
 Thursday Jan 16:
Cross product.
Properties; mixed (scalar) triple product and an
explanation for the two definitions of cross product: relationship with
volume of a box in space.
Started equations of planes in space (section 3.1)
Notes for Thursday Jan 16
 Tuesday Jan 21:
Equations of
lines and planes in 3space.
Reading: Sections 1.3, 1.4, 1.5
Notes
 Thursday Jan 23:
Symmetric equations of a line in space; skew lines; more examples dealing
with lines
and planes; distances.
Notes .
 Tuesday Jan 28:
Test 1 (in the first half of the class).
Then the discussion of cylinders and quadric surfaces.
(Section 1.7, 1.8 and 1.9)
Please read it all by this class!
Lecture notes
Supplement: how to remember
quadric surfaces .
 Thursday Jan 30:
Start functions of two variables. Domain and range. Apex calculus section
12.1. (Read for next class: CLP, sections 2.1,
2.2).
Notes for Thursday Jan 30 .
 Tuesday Feb 4:
Limits. The notion of continuity for functions of two varaibles.
(Section 2.1). Please read all of CLP 2.1 and start 2.2.
Start partial derivatives (Section 2.2).
Notes .
 Thursday Feb 6:
Partial derivatives; higherorder partial derivatives (Sections 2.2, 2.3);
Clairaut's theorem.
Linearization of a function of two or three variables.
Notes
(these notes include soltuions to Worksheet 5).
Supplementary notes
(these notes include an
explanation (at the end)
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 note is just to make sure all the
things in the course agree with each other and make sense).
 Tuesday Feb 11:
Finish section 2.6: differentials and error estimates; started
Chain rule in several variables.
Implicit differentiation.
(Section 2.4)
Notes .
 Thursday Feb 13:
Chain rule in several variables, continued.
(Section 2.4)
Directional derivatives and gradients.
Notes .
Complete solution to worksheet 7 .
 Tuesday Feb 25:
Test 2! After the test we will finish the discussion of
directional derivateives and gradients. Geometric meaning of the gradient:
normal vector to level curves (for a function of 2 variables) or level
surfaces (for a function of 3 variables).
Special note on how this
agrees
with the earlier method of finding the tangent plane to a graph of a
function of 2 variables.
Notes from the class .
 Thursday Feb 27:
Geometric meaning of the gradient, continued.
Here are a lot of notes and reading points about this.
 Notes from the class .
 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).

Complete solution to
worksheet 8
.
 Read Section 12.7!
 We also defined critical points and discussed the
classification of critical points for a function of two variables  the
second derivative test.
 Start reading Section 2.9 (skip Example 2.9.10). The second
derivative test is discussed on pp.175186; read up to Example 2.9.20.
 Tuesday March 3:
Finish classification of critical points; absolute max/min problems.
 finding max/min of a function on a
closed bounded domain. Continue reading 12.9.
 Thursday Mar 5:
Constrained optimization. Lagrange multipliers.
Read: all of Section 2.9 section 2.10 (not including the optional section
about 2 constraints).
(and optionally,
Section 14.8 from the
Secondary text No. 1
Notes .
 Tuesday Mar 9:
Test 3. Then:
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 (once the class happens).
 Thursday March 11:
Integration, continued.
Notes
from the class
 March 13: the pandemic hits and from
here onwards everything is on Canvas. Please keep checking both
"Math200_ALL" and our section's Math200_203 Canvas sites. This site will
not be updated :(