# MATH 200: Multivariable calculus, Section 203. Term 2, 2019/20

• Instructor: Julia Gordon.
• Where and when:
• Tue Th 12:30-2pm in LSK 201.
• Instructor's office: Math 217.
• e-mail: gor at math dot ubc dot ca
• New Office Hours: Tuesday 5-6pm and Thursday 4:15-5:45pm.
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, 12-1pm and 2-3pm.
• The term test dates:
Test 1 -- Tuesday January 28
Test 2 -- Tuesday February 25
Test 3 -- Tuesday March 10
Test 4 -- Thursday March 26.

## Section-specific notes

These notes are mostly unedited doccam scans. All reading is from CLP-III unless otherwise specified.
• Week 1: January 7-9:
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: 1.2.1--1.2.5
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 3-space. 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; higher-order 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 .