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

Email: | cbm (at) math (dot) ubc (dot) ca |

Office: | LSK 303c |

Section 101 Office Hours: | M 1pm–2pm, W 12:15pm–1:15pm, Th 11am–noon (subject to change) |

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

Other sections: |
Section 102 Dr Nate Bade Section 103 Dr Mathav Murugan Section 105 Dr Richard Balka |

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 applies to all sections.

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 open long hours Monday through Friday. Check
the MLC website for details.

We are using "APEX Calculus, Version 3.0, Volume 3 (Chapters 9 - 13)".
Sorry, hardcopies *cannot* be purchased from the bookstore,
however, 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: WeBWorK and written assignments from the textbook. Both types of assignment will be due on Fridays at 11:00 a.m., with the first due on Friday September 16.

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 instructor giving lectures, but is
Rob Fraser,
a
teaching assistant helping with WeBWorK.

There will be nine written homework assignments, due at the 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.

**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.

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 14, 5:00pm:
WeBWorK Assignment 0
(does not count 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, cylinders, and quadric surfaces (10.4, 10.5, 10.6, 10.1)

Due Friday Sept 16 11:00am:
WeBWorK Assignment 1.
Written Assignment 1: **10.1:** 10, **10.2:** 20, **10.3:** 26, 32.
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;

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

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;

**Ste12.6:** 1-9 (odd), 11, 13, 15, 21-28, 29, 33, 35, 41, 50.

Functions of several variables (12.1, 12.2)

Note: 12.2 is not directly examinable.

Due Friday Sept 23 11:00am:
WeBWorK Assignment 2.
Written Assignment 2: **10.4:** 30, **10.5:** 12, **10.6:** 10, **10.1:** 28.
Solutions.

Practice problems:

WeBWorK Assignment 2 Optional

Practice problems from "APEX Calculus":

**10.1:** see last week;

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

Additional practice problems from "Stewart":

**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 30 11:00am:
WeBWorK Assignment 3.
Written Assignment 3:
**10.1:** 24 (also making 3 separate carefully labelled plots showing the traces y = 2, z = 1 and x = 0),
26 (also making 3 separate carefully labelled plots showing the traces y = 2, z = 1 and x = 0);
**12.1:** 10, 18.
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 7 11:00am:
WeBWorK Assignment 4.
Written Assignment 4:
**12.3:** 8, 20;
**12.4:** 14, 22.
Solutions.

**Update:** Some have noted #14 is a bit ambiguous. Replace with
"Is the *distance traveled by the projectile* more sensitive to errors
in initial speed or angle of elevation?"

Regarding #14 (not for the homework, just FYI): repeat this question with length
unit of kilometers, e.g., 250 ft/s = 0.0762 km/s: does your sensitivity analysis
change? Solve the problem once more, assuming the errors in speed and angle are at most 10% of the given values.

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.

Directional derivatives and gradient (12.6)

No assignment due this week.

**Midterm 1**, October 12, 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
(omit Section 12.2). Midterm problems will be of the sort you have seen
in: WeBWorK 1-4, Written Assignments 1-4, 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.

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.

Practice problems from "APEX Calculus":

**12.6:** (9, 15, 21), (11, 17, 23), 25, 27.

Additional practice problems from "Stewart":

**Ste14.6:** 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 47, 53, 55, 61.

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 21 11:00am:
WeBWorK Assignment 5.
Written Assignment 5: **12.5**: 8, 14, 24; **12.6**: 8, 14, 20 (in (c) they mean "maximal decrease").
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 our APEX text;
see pages
378--383 of this textbook by David Guichard.

Due Friday Oct 28 11:00am: WeBWorK Assignment 6.

Due Friday Oct 28 11:00am:
Written Assignment 6: **12.7:** 22; **12.8:** 12;
**#3:** Consider
*f(x, y) = 3(y+1) ^{2} - 2x^{2}*.
Find and classify the critical points.
Find the absolute maximum and absolute minimum of

Solutions.

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 4 11:00am: WeBWorK Assignment 7.

Due Friday Nov 4 11:00am:
Written Assignment 7:

**13.2:** 6, 24;

**#3** The material for the *rectangular* bottom of an aquarium costs half as
much as the high strength glass for the four sides. Find the shape
of the cheapest aquarium that holds a given
volume *V*. (source: Guichard text);

**#4** In the augmented-reality game Ingress, "portals" exist at
fixed real-world positions. Players try to add "resonators" to a
portal by standing near the portal's position while fidgetting with
their smartphones. For tactical reasons, a player seeks to place a
resonator while standing exactly 40 meters away from a portal, which
is located at the point (0, 0) in the *x-y* plane. She also
wants to maximize her wireless signal strength which Fido tells her
is given by
*f(x, y) = x ^{3}y*. Here

Solutions.

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 **Friday** Nov 11 11:00am:
WeBWorK Assignment 8.

Due **WEDNESDAY** Nov 9 11:00am:
Written Assignment 8: **13.1:** 14, 22; **13.2:** 10.
Solutions.

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 16, 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.
Midterm problems will be of the sort you have seen in:
WeBWorK 5-8, Written Assignments 5-8, and Practice Problems
from the relevant weeks.

**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.

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 25 11:00am:
WeBWorK Assignment 9.
Written Assignment 9: **13.3**: 6, 10; **13.4**: 16, 24, 28.
Solutions.

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 Friday Dec 2:
WeBWorK Assignment 10.

No written assignment.

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 as required, not optional as usual. The topic is also treated in WeBWorK Assignment 10 Optional, which despite its name should be regarded as required even though it does not count toward your grade.

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 do 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 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.

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

Copyright © 2016 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.