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**Grade change requests:** At least for Section 102, any requests to reconsider grades (homework, midterm, etc) should include the regrade request form.

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Fall 2017 Term 1: MATH 253 Multivariable Calculus: section 102

- When and where: Monday-Wednesday-Friday 11:00am to 12:00am Buchanan building room A201 (link here)
- My office: Pulp and paper building PPC 323 (here).
- e-mail: cselcuk@math.ubc.ca
- Office hours: Monday 1pm to 2pm (LSK300B). Or at my office by if you can’t make these hours.
- Final exam: 50%
- 2 midterms: 20% + 20% = 40%
- WebWork assignements: 5%
- Weekly homeworks: 5%

The common web page can be found here. The Course outline can also be found here.

**Week 1, Sept 6–8**: Lecture 1 – Lecture 2 – numerical simulation of flow generated by a drone

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.

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**Week 2, Sept 11–15: **Lecture 3 – Lecture 4 – Lecture 5

gnuplot script of the example we saw in class: visualize the intersection of planes giving a line. Download the script file planes_line_gnuplot.txt. Open gnuplot in a terminal. Then type: load “planes_line_gnuplot.txt” . You will be able to visualize the planes, rotate them and see where they intersect.

Cross product, equations of lines and planes, cylinders, and quadric surfaces (10.4, 10.5, 10.6, 10.1)

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;

**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.

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**Week 3, Sept 18–22: Lecture 6 – Lecture 7 – Lecture 8
**

Cylinders and quadric surfaces, functions of several variables (10.1, 12.1, 12.2)

The matlab/octave routine to visualize the (saddle shape) 3D surface along with the trace curves is available here

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.

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**Week 4, Sept 25–29 Lecture 9 – Lecture 10 –Lecture 11
**

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).

Due Friday Sept 29 11:00am: WeBWorK Assignment 3. Written Assignment 2: **hw2** Solutions

Link to the solutions of the partial differential equations that we had a look : here

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.

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**Week 5, Oct 2–6: Lecture 12 – Lecture 14
**

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

Lecture 13 was a review on how to visualize surfaces, how to relate contour plots and surfaces and how to exploit the trace curves to explore how a surface looks like.

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.

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**Week 6, Oct 11–13: Lecture 15
**

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

No assignments due this week.

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

** 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]

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**Week 7, Oct 16–20 Lecture 16 – Lecture 17 – Lecture 18
**

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.

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**Week 8, Oct 23–27: Lecture 19 – Lecture 20 – Lecture 21
**

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.

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**Week 9, Oct 30–Nov 3: Lecture 22 — Lecture 23 – Lecture 24
**

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.

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**Week 10, Nov 6–10: Lecture 25 — Lecture 26 — Lecture 27
**

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 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.

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**Week 11, Nov 15–17: Lecture 28
**

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).

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**Week 12, Nov 20–24: Lecture 29 — Lecture 30 — Lecture 31
**

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.

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**Week 13, Nov 27–Dec 1 Lecture 32 — Lecture 33 — Lecture 34
**

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).