Instructor in Charge: | Dr. Colin Macdonald (also Section 101 instructor) |

Email: | cbm (at) math ubc ca |

Office: | LSK 303c |

Section 101 Office Hours: |
10 mins after lectures; LSK303c: M 1pm-2pm, W 12:15-1pm, Th 3:45-4:30pm |

Section 101 Lectures: | MWF 11:00-11:50 - location: Math 100 |

Section-specific websites: |
Section 101 Section 102 Can Selçuk Section 103 Sebastián Barbieri Section 104 Mark Mac Lean Section 105 Juncheng Wei |

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

A detailed weekly syllabus is given below. The material below generally applies to all sections, unless other information has been provided by your instructor.

This course is using UBC's new Canvas system which is gradually replacing the legacy Connect.

There is help available at the
** MATHEMATICS LEARNING CENTRE (MLC)**,
a drop-in tutorial centre for undergraduate
Math courses
located in the Leonard S. Klinck (LSK)
Building. It is usually open Monday through Friday, check website above for details.

We are using "APEX Calculus, Version 3.0, Volume 3 (Chapters 9 - 13)". Hardcopies may not be available from the bookstore, but you can buy them from the author's website or from online retailers in $CAD. An electronic copy of this book is also available online at no cost from http://www.apexcalculus.com.

There will be two kinds of graded homework: weekly WeBWorK and fortnightly written assignments from the textbook. Both types of assignment will usually be due on Fridays at 11:00 a.m., with the first due on Friday September 15.

WeBWorK assignments can be
found
here. You will need to log on with your Campus Wide Login. For
most problems, you will have an unlimited number of attempts
and will not be penalized for incorrect attempts, so you can
continue to work until you have it
correct. Use the ** email instructor ** button for any questions
(mathematical or otherwise) regarding WeBWorK. The "instructor" is
not your section instructor; it is
Nicholas Lai,
a teaching assistant helping with WeBWorK.

There will be written homework assignments, due roughly every two weeks at beginning of class at 11:00 on Fridays, which will be graded. The assignments will be listed in the weekly schedule below. Late assignments will not be accepted.

Written homework can be picked up in the MLC.

**Optional recommended 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, and then the optional WeBWorK will reopen until the Final Exam.

**Grade change requests:** At least for Section 101, 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.

Reload this page regularly for updates.

Introduction, three dimensional coordinate systems, vectors, dot product (10.1 [first 3 pages], 10.2, 10.3)

Due **Wednesday** Sept 13, 5:00pm:
WeBWorK Assignment 0
(does not count directly for a grade, intended to get you used
to WeBWorK). No written assignment this week.

Practice problems from our text, "APEX Calculus":

**10.1:** 7, 9, 11;

**10.2:** 2, 3, 7, 11, 21, 23;

**10.3:** 5, 7, 15, 17, 21, 27.

Additional practice problems from "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 (10.4, 10.5, 10.6, 11.1, 11.2)

Due Friday Sept 15 11:00am:
WeBWorK Assignment 1.

Written Assignment 1: **math253_hw1.pdf** Solutions.

Practice problems: WeBWorK Assignment 1 Optional.

Practice problems from "APEX Calculus":

**10.4:** 7, 13, 15, 17, 21, 31, 33, 35;

**10.5:** 5, 9, 15, 19, 25, 27, 29, 31;

**10.6:** 3, 7, 9, 13, 19, 25, 27, 29;

Additional 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 (10.1, 12.1, 12.2)

Note: In 12.2, epsilon-delta arguments of continuity are not examinable.

Due Friday Sept 22 11:00am: WeBWorK Assignment 2. No written assignment this week.

Practice problems:

WeBWorK Assignment 2 Optional.

Practice problems from "APEX Calculus":

**10.1:** 15, 17, 21, 23, 25, 27, 29, 31.

**12.1:** 7, 10, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31.

Additional practice problems from "Stewart":

**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 (12.3, 12.4).

Note the APEX Calculus doesn't do tangent planes until 12.7; we'll
see them again in that style but I think its useful to see them now
because of the close connection linear approximation).

Supplemental notes on Partial Differential Equations (also available as a Jupyter notebook). Includes a few relevant practice problems.

Due Friday Sept 29 11:00am:
WeBWorK Assignment 3.

Written Assignment 2:
**hw2** Solutions

Practice problems:

WeBWorK Assignment 3 Optional.

Practice problems from "APEX Calculus":

**12.3:** 7, 9, 11, 13, 19, 25, 27, 29, 31, 33;

**12.4:** 5, 7, 9 (in these first three problems, also give an expression for the tangent plane), 13, 15, 17, 21.

Additional practice problems from "Stewart":

**Ste14.3:** 1, 3, 5, 7, 9, 11, 15-37 (odd), 39, 41, 43, 45, 47, 49, 51-67 (odd), 71, 72, 73, 81, 87;

**Ste14.4:** 1-5 (odd), 11, 13, 15, 17, 19, 25, 27, 29, 31, 33, 37, 41.

Linear approximation, tangent plane (continued), chain rule (12.5).

Due Friday Oct 6 11:00am: WeBWorK Assignment 4. No written assignment this week.

Practice problems:

WeBWorK Assignment 4 Optional.

Practice problems from "APEX Calculus":

**12.5: **7, 11, 13, 17, 19, 21, 23, 25, 27.

Additional practice problems from "Stewart":

**Ste14.5:** 1-11 (odd), 13, 17, 19, 21, 23, 25, 27-33 (odd), 35, 39, 45, 51, 53.

Chain rule (12.5), directional derivatives and gradient (12.6)

No assignments due this week.

**Midterm 1**, October 11, held in class.
Solutions to Midterm 1.

**
You must write the test in the section in which
you are registered, and bring your UBC ID card.
No aids of any kind are permitted during the test (no calculators, papers, etc.)**

Midterm will cover up to and including Section 12.4, as documented in the weekly schedules above. Midterm problems will be of the sort you have seen
in: WeBWorK 1-4, Written Assignments 1-2, Practice Problems
up to and including Section 12.4.

**Additional practice material for Midterm 1:**

Here are some old homework assignments with solutions. Not all their problems are relevant, the relevant
problems are as follows:

# 3, 5, 7, 8 of Set 1,

# 1, 2, 3, 4, 5, 6, 7 of Set 2,

# 2, 3, 4, 5, 6, 7 of Set 3,

# 1, 2, 8, 11 of Set 4.

[Update: fixed broken links]

Here are some midterms from previous years:

Midterm 1 2012,
Solutions to Midterm 1 2012,
Midterm 1 2013,
Solutions to Midterm 1 2013,
Midterm 1 2014,
Solutions to Midterm 1 2014,
Midterm 1 2015,
Solutions to Midterm 1 2015,
Midterm 1 2016,
Solutions to Midterm 1 2016.
[Update: fixed broken links]

Directional derivatives and gradient continued, Tangent planes via the normal, Maximum and minimum values, Lagrange multipliers (12.6, 12.7, 12.8).

Due Friday Oct 20 11:00am:
WeBWorK Assignment 5.

Written Assignment 3:
~~math253_hw3.pdf~~,
math253_hw3rev1.pdf,
solutions.

Practice problems:

WeBWorK Assignment 5 Optional.

Practice problems from "APEX Calculus":

**12.7:** 1, 9, 11, 13, 15, 17, 19 21, 23;

**12.8:** 1, 2, 7, 11, 13, 15, 17.

Additional practice problems from "Stewart":

**Ste14.7:** 1, 3, 5-17 (odd) [find critical values only], 19, 29-35 (odd), 39, 41, 43, 45, 47, 49, 51;

**Ste14.8:** 1, 3-17 (odd), 19, 25, 27-39 (odd), 41.

Lagrange multipliers, double integrals over rectangles, iterated integrals (13.2, 13.1).

**Note:** Lagrange multipliers not covered in the APEX text;
see pages
378--383 of this textbook by David Guichard.

Due Friday Oct 27 11:00am: WeBWorK Assignment 6. No written assignment this week.

Practice problems:

WeBWorK Assignment 6 Optional.

Practice problems for *Lagrange Multipliers*:

**From Guichard text above, Sec 14.8, pg 382/383:** 5, 10, 11, 12, 13, 15.

Practice problems from "APEX Calculus":

**13.1:** 5, 6, 11;

**13.2:** 1-4, 5.

Additional practice problems from "Stewart":

**Ste15.1:** 3a, 11, 13, 17;

**Ste15.2:** 1-21 (odd), 25, 27, 29, 35.

Iterated integrals continued, double integrals (13.1, 13.2).

~~
Due Friday Nov 3 11:00am:
WeBWorK Assignment 7.
~~

Please start WeBWorK Assignment 7, but the due date is extended until next Monday.

No written assignment this week.

Practice problems: WeBWorK Assignment 7 Optional.

Practice problems from "APEX Calculus":

**13.1:** 7, 9, 19, 21;

**13.2:** 1-4, 7, 9, 13, 17, 21, 25.

Additional practice problems from "Stewart":

**Ste15.3:** 1, 3, 5, 7-27 (odd), 31, 39-49 (odd), 51, 55.

Double integrals in polar coordinates, applications (13.3, 13.4).

Due Monday Nov 6 11:00am: WeBWorK Assignment 7.

Due Friday Nov 10 11:00am: Written Assignment 4: math253_hw4.pdf, solutions.

~~Due Friday Nov 10 11:00am:~~

Due Sunday Nov 12 11:00am:
WeBWorK Assignment 8.

Practice problems: WeBWorK Assignment 8 Optional.

Practice problems from "APEX Calculus":

**13.3:** 3, 5, 9, 13, 15.

Additional practice problems from "Stewart":

**Ste10.3:** 1, 3, 5, 7, 9, 11, 15, 19, 25, 29, 31;

**Ste15.4:** 1, 3, 5, 7-13 (odd), 15, 17, 19-27 (odd), 29, 31, 33, 35, 37;

**Ste15.5:** 1, 3-9 (odd), 11, 13, 15, 17, 21, 23.

Applications of double integrals continued (13.4);

Moments of inertia are mentioned briefly on pg 790
and in these
supplimental notes
(also as a Jupyter notebook).

No assignment due this week.

**Midterm 2, November 15, held in class.**
Solutions to Midterm 2.

You must write the test in the section in which you are registered, and bring your UBC ID card. No aids of any kind are permitted during the test (no calculators, papers, etc.)

Midterm will cover Sections 12.5 (chain rule) to 13.2 (double integration) (inclusive) but of course
relies also on earlier topics. Section 13.3 (double integration in polar coordinates) is *not* on the midterm.
Relevant problems: WeBWorK 5-8, Written Assignments 3 & 4, and the various practice problems.

**Additional practice material for Midterm 2:**

Here are some old homework assignments with solutions. Not all their problems are relevant, the relevant
problems are as follows:

# 3-7, 9, 10, 12-14, 16, 17 of Set 4,

# 1-4, 5a of Set 5,

# 1-8 of Set 6,

# 1, 2 of Set 7.

Here are some midterms from previous years:

MT2 2012,
Solutions to MT2 2012,
MT2 2013,
Solutions to MT2 2013,
MT2 2014,
Solutions to MT2 2014,
MT2 2015,
Solutions to MT2 2015,
MT2 2016,
Solutions to MT2 2016.

Practice problems from "APEX Calculus":

**13.4:** 5, 6, 13, 14, 15, 22, 23.

Additional practice problems from "Stewart":

**Ste15.6:** 1-23 (odd).

Surface area, triple integrals (13.5, 13.6)

Due Friday Nov 24 11:00am: WeBWorK Assignment 9.

Practice problems:

WeBWorK Assignment 9 Optional.

Practice problems from "APEX Calculus":

**13.5:** 2, 5, 6, 7, 9, 13, 17, 19.

**13.6:** 5, 7, 9, 11, 13, 15, 19, 23.

Additional practice problems from "Stewart":

**Ste15.7:** 1-29 (odd), 33, 35.

Triple integrals in cylindrical and spherical coordinates.

**Note:** These topics are not covered in our APEX text; see Section 14.4 of this textbook by Gil Strang.

Due Monday Nov 27 11:00am: Written Assignment 5: math253_hw5.pdf, solutions.

Due Friday Dec 1 11:00am:
WeBWorK Assignment 10.

Practice problems:

WeBWorK Assignment 10 Optional

Note: spherical coordinates are *not* covered in WeBWorK Assignment 10,
but is a possible topic for the Final Exam.
I suggest regarding the Practice Problems for spherical coordinates (and
WeBWork Assignment 10 Optional) as is they were required.

Practice problems:

**Strang14.4** Problems 11, 13, 15, 19, 22, 23 (from the alternative text by Strang, linked above).

Additional practice problems from "Stewart":

**Ste15.8:** 1-31 (odd);

**Ste15.9:** 1-35 (odd), 39, 44 (answer=2464).

**Course Evaluation**: Please take a few minutes now and
complete the evaluation for MATH 253. Your evaluations really can make a difference.
We use your feedback to assess and improve our teaching;
Heads and Deans look at evaluation results as an important
component of decisions about reappointment, tenure, promotion and
merit for faculty members; and evaluations are used to shape
Departmental curriculum. Please help us make the course effective by telling us what works well and
what can be improved.

**Final Exam:** The final exam will be based on all topics of the course, with around 50%
of the marks devoted to integration.

Here are some old final exams to assist with your studying:
2007,
2009,
2010,
2011,
2012, 2012 Solutions,
2013,
2014, 2014 Solutions,
2015, 2015 Solutions,
2016, 2016 Solutions.

(other solutions are not available). Some solutions need a login; this is the same as the homework solutions.

Copyright © 2016-2017 Colin Macdonald.

Verbatim copying and distribution of this webpage is permitted
in any medium, provided this notice is preserved.

However, reproducing some content may require additional permission
from their respective authors.