Week 1

UL XM521 Mutivariable Differential Calculus

Instructor: Margarita Kanarsky

XM521: 1

Week 1XM521: 2

Welcome to the course!

Meetings and communication:

AC meetings

AC Class meetings Wednesday, 5:00-6:15 pm PT AC Office hours Monday, 5:40-6:40 pm PT

Email

kanarsky@stanford.edu Any time

Week 1Week 1: 3

Introduction (mine):

• MS Applied Math (Moscow State University, Russia) 1993

• PhD Mathematics, MS Computer Science (Emory University, Atlanta) 2000

• Taught Mathematics and Statistics in local community colleges

• Tutored various EPGY courses since 2011

• Last four years: teaching university-level math courses at SPCS

Week 1Week 1: 4

Introduction (yours):

• Name

• Your grade level at school

• Where do you live? (on the map)

• Answer a question: if you happen to have few hours of free time, what would you do?

Week 1XM521: 5

Assessments:Two exams (midterm and final). No other assignments are to be submitted/graded.

Proctoring: Letter Grade independent proctoring ( a teacher/counselor at school etc.)Non-letter Grade parent or independent proctoring

* You may switch a “letter grade” to a “non-letter grade” any time throughout the course, even after the final exam.* You can receive a letter grade only when both exams were proctored by an independent proctor.* No grade is assigned for non-passing grades (no record on the transcript).

Grading:

The course grade is the average of scores obtained on two exams.

The Pass/Fail scale:

CR: 60-100

NP: <60

The grading scale is:

A:86-100

A-:83-85

B+: 80-82

B:76-79

B-:73-75

C+: 70-72

C:65-69

C-:60-64

NP: <60

Week 1XM521: 6

Withdrawals/refunds:

Week 1 through end of Week 2 (Sunday): Full refund of tuition is possible. Please state the reason for withdrawing. Week 3 through end of Week 4 (Sunday): Refund of 80% of tuition.Week 5 and later: No refund available.

* Registration fees are non-refundable, the above only refers to tuition.* There is always a possibility to transfer to a future term instead of withdrawing.

Transfer:

You may be able to rollover to the next term (for a $150 fee). This can be done only once.

Week 1XM521: 7

Time management:Expect a lot of independent work from the start. Allocate several hours a week.

Communication: (Learn to) feel comfortable to ask questions during the class meeting and/or in email.In your email, be specific! - Indicate your course and your name.- If a question is about a problem from your textbook include the image of the

problem or retype it – I need to have it, as we most likely have different editions!

You can expect my prompt response to your messages on any issues.

Week 1XM521: 8

Weekly work:

• Read corresponding sections of the textbook“Calculus” (Anton, Bivens, Davis; Edition 6, 7, 8 or 9)See Course Schedule for reading assignments

• Watch pre-recorded lectureslagunita.stanford.edu

• Do online exercises course lectures and pdf file from Downloads

• Do offline exercises (including textbook exercises)download the assignments from Downloads

Week 1XM521: 9

Week 1XM521: 10

Rectangular coordinate system in 3-space:

Coordinate planes; octants; coordinates

Week 1XM521: 11

The distance formula. Equation of the sphere.

The distance formula in 3-space:

The standard equation of the sphere:

k > 0

k = 0

k < 0

Week 1XM521: 12

Week 1XM521: 13

Cylindrical surfaces; graphing equations in 2 variables in 3-space

extrusion

Week 1XM521: 14

Week 1XM521: 15

Week 1XM521: 16

Week 1XM521: 17

Operations on vectors: addition

Vectors viewed geometrically

Week 1XM521: 18

Operations on vectors: scalar multiplication

Week 1XM521: 19

Operations on vectors: Subtraction

Week 1XM521: 20

Coordinate representation of vectors with initial point at the origin:

Arithmetic operations on vectors:

Week 1XM521: 21

Coordinate representation of vectors with initial point not at the origin:

Week 1XM521: 22

Rules of vector arithmetic:

Week 1XM521: 23

Norm of a vector:

2-space

3-space

Week 1XM521: 24

Unit Vectors:

Example: Example:

Week 1XM521: 25

Normalizing a vector:

Week 1XM521: 26

Exercises:

Week 1XM521: 27

COLLABORATE:

Week 1XM521: 28

Exercises:

Week 1XM521: 29

Week 1XM521: 30