Winter Term 2 2017/18

- Sections 201 and 202 (Prof. Julia Gordon).
- Section 203 (Prof. Nathaniel Bade)
- Section 204, Prof. Liangming Shen

- Homework assignments should be submitted online through Webwork . (Scroll down to the course named MATH200-ALL_2017W2); or you should be able to access it through Connect.
- The "Getting started with webwork" handout
- 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.

- In addition to your instructor's 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 all technical problems with webwork, Piazza registration, or exam conflicts, please e-mail math200dictator@gmail.com

- Final exam is on April 23, at noon.
- The UBC Math Club is selling packages of old exams with solutions. Please find UBC Math Club on Facebook for up-to-date information.
- Math Learning Centre will organize two review sessions, on April 17th, 2-4pm and and 19th, 4-6pm. See the MLC page for locations (currently, IBLC 261).
- Julia Gordon will have review sessions, see sections 201/202 website for times, locations, and doccam notes from these sessions.
- UBC teaching evaluations: You should have received an official e-mail asking you to complete formal teaching evaluation for this course. It can also be accessed here . Please do not forget to fill these out!

- 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.

Some old midterms (still good for reviewing many topics):

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).

- January 3-5:
10.1 (only up to "Cylinders") : Three-dimensional coordinate systems;
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: 10.1: 1-3, 7, 9, 12, 16

10.2: 1-5, 8, 11, 15, 20, 23, 27, 31 - January 8-12:
10.3 Dot product;
Using dot product to find an
angle between lines. Application to finding forces.
10.4 Cross product. Using cross product to find a vector orthogonal to two
given ones; cross product and area.

Quiz 1 on vectors.

Homework 1 due.

Suggested problems: 10.3: 1-3, 11, 15, 19, 31, 39.

10.4: 1-5, 9, 15, 27, 30, 31, 35, 39, 41. - January 15-19:
10.5 and 10.6 Equations of lines and
planes.
Symmetric and parametric equations of a line in space.
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.

Homework 2 due.

Suggested problems: 10.5: 7, 11, 21, 27, 31.

10.6: 1, 2, 9, 11, 14, 15, 17, 19, 25, 29, 32; - January 22-26:
10.1: Cylinders and quadric surfaces. Reading assignment: 9.1 (Conic Sections).

12.1 Functions of several variables. Domain and range. Level curves and level surfaces.

Quiz 2 on equations of lines and planes in space.

Homework 3 due.

Suggested problems: 10.1: 15, 17, 23-26, 27, 32.

12.1: 1-6, 7, 11, 17, 19, 21, 23, 26, 27, 29, 31 - January 29 - February 2
Brief dicsussion 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.
12.4 Differentials, tangent planes, and linear approximations.

Homework 4 due.

Suggested problems: Section 12.3: , problems 1-4, 5, 13, 19, 29, 33. Section 12.4: 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). - February 5-9.
12.5 Chain rule and implicit differentiation; start 12.6 -- directional derivatives.
One additional topic to recall here: parametric equation of a segment connecting two points A and B.

Homework 5 due.

Quiz 3 on partial derivatives and differentials.

Suggested problems: Section 12.5: 1-5, 9, 17, 21, 29. - February 12-16.
12.6 Directional derivatives and gradients, continued.
12.7 Geometric meaning of the gradient.
Tangent planes to level surfaces.
Tangent planes to graphs of functions of two variables, revisited.

Midterm

Midterm with solutions Homework 6 due.

Suggested problems: Section 12.6, problems 1-6, 13, 15, 21, 23, 25, 27 Section 12.7, problems 17, 19, 21, 23 - February 26- March 2.
Section 12.8 Critical points: the second derivative test, absolute maximum and minimum values.
Lagrange multipliers (Secondary text #1, Section 14.8).

Suggested problems: Section 12.8, problems 1-4, 5, 7, 11, 13, 15, 17 (also 11, 13, 15, 19 from 14.7 in secondary text #1) Section 14.8 (from secondary text #1) 5, 10, 11, 12, 13, 15, 17 - March 5-9.
14.8 Lagrange multipliers, continued. (two constraints not included). Starting integration: 13.1 (the definitions; area; integral of a function of two variables over a rectangle.
Iterated integrals (over a rectangle).
Fubini theorem (without proof).

Quiz 4 on critical points

Homework due.

Suggested problems: see above for 14.8, see below for 13.1 - March 12-16:
Double integrals over general regions.
Interchanging the order of integration. Sections 13.1, 13.2.
Polar coordinates (13.3 and read 9.4).

A summary of integration techniques from Math 101.

Homework 8 due.

Suggested problems: 13.1: 7, 9, 19, 21 (also see #3, 5, 10, 13, 15 from section 15.1 secondary text #1) 13.2: 1-4, 7, 9, 13, 17, 21, 25 (also see #17, 21, 23 from section 15.1 secondary text #1) 13.3: 3, 4, 8, 13;

- March 19-23:
13.4 Center of mass. 13.6 Triple integrals. Six different ways of writing a triple
integral as an iterated integral. Applications.

Quiz 5 on changing the order of integration in a double integral.

Homework 9 due.

Suggested problems: 13.4: 1, 5, 6, 13, 24;

13.6: 5, 7, 9, 11, 13, 15, 19, 23. - March 26-30:
Triple integrals in cyindrical coordinates, see
14.4 (from secondary text #2). Note: look at Section 14.4 only up to
the end of Example 7 on p. 544 (after that it is interesting reading, but
we are not covering it in class).

Homework 10 due.

- April 4-6:
Triple integrals in spherical
coordinates 14.4 (from secondary text #2 -- see the note above as to
where to stop); review.

Suggested problems: 14.4 (from secondary text #2): 11, 13, 15, 19, 22, 23

Homework 11 is due after the end of classes, on Wednesday April 11 night.