# Math 253 - 2019S Summer Term 1, May–June 2019

 Instructor: Colin Macdonald Email: cbm (at) math ubc ca Office: LSK 303c Office Hours: TBA Lectures: TBA

Information about the textbook, the topics, the marking scheme, and policies can be found in the Course Outline.

## General information

This course is using UBC's Canvas system: more detailed information will be available there.

### Textbook

We are the using the UBC textbook CLPâ€“III Multivariable Calculus by Joel Feldman and Andrew Rechnitzer. It is freely downloadable from the link above.

For additional practice problems or for alternate coverage of the material, we suggest APEX Calculus Volume 3 (Version 3.0) by Gregory Hartman (freely available) and/or "Multivariable Calculus, Stewart, 7th Edition" (traditional textbook).

### Homework

TBA!

Optional problems: There will be suggested practice problems from the book and other sources which will not be collected or marked for credit.
You are encouraged to do lots of problems, this is the best way to learn the subject.
There will also be optional WeBWorK, which will not count towards your mark for the course. Initially its due date will be the same as the required WeBWorK assignment. Answers will become available at the due date. Optional WeBWorK is can also be accessed until the Final Exam.

Grade change requests: Any requests to reconsider grades (homework, midterm, etc) should include the regrade request form.

Email sent without "253" in the subject is very likely to be ignored.

## Material covered

Most of this information will be on Canvas, but provided here for reference before you have access to Canvas.

Introduction, three dimensional coordinate systems, vectors, dot product (textbook sections 1.1, 1.2).

Practice problems from the alternate text "APEX Calculus 3:
Apex10.1: 7, 9, 11;
Apex10.2: 2, 3, 7, 11, 21, 23;
Apex10.3: 5, 7, 15, 17, 21, 27.

Practice problems from the alternate text "Multivariable Calculus, Stewart, 7th Ed":
Ste12.1: 1-15 (odd), 19a, 23, 27, 29, 33, 35, 37, 41, 43;
Ste12.2: 1, 3, 5, 9, 11, 13, 19-31 (odd), 35, 37, 39, 41;
Ste12.3: 1, 3, 5, 7, 11, 13, 15, 19, 23, 25, 27, 35, 37, 47, 57.

Cross product, equations of lines and planes, equations of curves and their tangent vectors (1.2, 1.3, 1.4, 1.5, 1.6).

Practice problems from "APEX Calculus":
Apex10.4: 7, 13, 15, 17, 21, 31, 33, 35;
Apex10.5: 5, 9, 15, 19, 25, 27, 29, 31;
Apex10.6: 3, 7, 9, 13, 19, 25, 27, 29;

Practice problems from "Stewart":
Ste12.4: 1, 3, 7, 9, 11, 15, 23, 25, 41;
Ste12.5: 1, 3, 5, 13, 19, 25, 27, 31, 33, 43, 45, 49, 57, 61;

Cylinders and quadric surfaces, functions of several variables (1.7, 1.8, 1.9, Appendix G, 2.1).

Note: The epsilon-delta arguments of continuity in 2.1 are not examinable.

Practice problems from "APEX Calculus":
Apex10.1: 15, 17, 21, 23, 25, 27, 29, 31.
Apex12.1: 7, 10, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31.

Ste12.6: 1-9 (odd), 11, 13, 15, 21-28, 29, 33, 35, 41, 50.
Ste14.1: 1, 3, 5, 11-19 (odd), 23, 30, 35, 37, 39-45 (odd), 55, 57, 59, 61, 63.

Partial derivatives, tangent planes, the differential and linear approximation (2.2, 2.3, 2.5 early, 2.6).

Partial differential equations, linear approximation, tangent plane (2.8, 2.5, 2.6)

The chain rule, directional derivatives and gradient (2.4, 2.7)

Directional derivatives and gradient continued, Tangent planes via the normal, Maximum and minimum values, Lagrange multipliers (2.7, 2.5 again, 2.9, 2.10)

Lagrange multipliers, double integrals over rectangles, iterated integrals (2.10, 3.1)

Iterated integrals continued, double integrals (3.1)

Double integrals in polar coordinates, applications (3.2, 3.3)

Applications of double integrals continued (3.3).

Surface area, triple integrals (3.4, 3.5)

Triple integrals in cylindrical and spherical coordinates (3.6, 3.7).