## Science Unlimited — Knot Theory and Cat’s Cradle: A Brief Introduction to Storer Calculus

Posted in Lecture Notes by pgadey on 2018/08/14

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The handout for the talk is available here:

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## MAT B41 — Final Exam Details

Posted in 2018 -- MAT B41 by pgadey on 2018/08/01

## MAT B41 — Week 12

Posted in 2018 -- MAT B41, Lecture Notes by pgadey on 2018/07/31

You made it to the last week! You’re done!

On Homework 5, you solved the Napkin Ring Problem. Check it out! That is super cool!

Suggested Exercises:

• 6.1 Geometry of Maps from $\mathbb{R}^2$ to $\mathbb{R}^2$: 1, 3, 6, 11
• 6.2 The Change of Variables Theorem: 3, 4, 7, 10, 11, 21, 23, 26, 28
• 6.3 Applications : 1, 3, 4, 5, 6, 11, 13, 16

Notes:

The notes are available here.

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## Mock Final Exam!

Posted in 2018 -- MAT B41 by pgadey on 2018/07/28
The Mock Final is now available!

Thanks everyone, who came out and wrote today! We had about thirty people in total. The last writer finished at approximated 14:50pm. It seems like the final will take approximately three hours. Please attempt the mock final, it is the best preparation for the real final.

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## MAT B41 — Week 11

Posted in 2018 -- MAT B41, Lecture Notes by pgadey on 2018/07/24

(Archimedes Thoughtful by Domenico Fetti 1620 from Wikimedia)
Homework 5 is due! Homework 6 (tex) is now available!

The Mock Midterm will be Friday July 27 in SY110 from 12–3pm.

Suggested Exercises:

• 5.4 Changing the Order of Integration: 2,3,7,9,14
• 5.5 The Triple Integral: 1,3,4,9,10,11,12,16,18,20,21

Notes:

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## MAT B41 — Week 10

Posted in 2018 -- MAT B41, Lecture Notes by pgadey on 2018/07/17

(Photo by Ian Alexander) Homework #5 (tex) is available. Drop deadline next Monday.

There has been a minor change to the syllabus: Homework 6 will now be assigned in Week 11 and due in Week 12.

Geogebra Demonstrations:

Suggested Exercises:

• 5.1 Introduction to Double and Triple Integrals: 1,2,3,8,9,13
• 5.2 The Double Integral over a Rectangle: 1,2,3,4,5,6
• 5.3 The Double Integral over a More General Regions: 1,2,3,7,13

Past Finals:

• Final 2015: Find the volume of the solid $B$ bound by the parabolic cylinder $x = (y-4)^2 + 3$ and the planes $z=x+2y-4$, $z=x+4y-7$, and $x+2y=11$.
• Final 2015: Evaluate $\int_D e^{x+y} dA$ where $D$ is the region bounded by $y=x-1$ and $y=12-x$ for $2 \leq y \leq 4$.
• Final 2016: Evaluate $\int_D (1-2x) dA$ where $D$ is triangle with vertices $(0,0)$, $(2,3)$, and $(5,3)$.
• Final 2016: Evaluate $\int_0^1 \int_x^{\sqrt[3]{x}} e^{x/y} dy dx$.

Notes:

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## MAT B41 — Week 9

Posted in 2018 -- MAT B41, Lecture Notes by pgadey on 2018/07/10

Homework 4 (tex) is now available.

Suggested Exercises:

• 3.4 Constrained Extrema and Lagrange Multipliers: 1a, 3, 4, 5, 13, 14, 15, 19, 20, 28

Past Finals:

• Final 2016: Find the minimum value of $f(x,y) = 4x^2y - x^3y - x^2y^2$ on the closed triangular region in $\mathbb{R}^2$ with vertices $(0,0)$, $(6,0)$, and $(0,6)$.
• Final 2015: Find the maximum values of $f(x,y,z) = x^2 - 4x + y^2 - 2y + z^2 - 4z - 1$ on the solid ball $x^2 + y^2 + z^2 \leq 9$.
• Final 2015: Find the points on the intersection of the paraboloid $z=x^2+y^2$ and the plane $x+y+z=1$ that are closest and farthest from the origin.

Notes:

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## MAT B41 — Week 8

Posted in 2018 -- MAT B41, Lecture Notes, Uncategorized by pgadey on 2018/07/03
Parker comes back! Public lecture on Friday in IC 200 at 11am.

Suggested Exercises:

• Course Notes: Quadratic forms and determinants
• 3.3 Extrema of Real-Valued Functions: 1,2,3,11,13,21,29,31,52

Past Finals:

• Final 2015: Let $f(x,y,z) = x^3 + x^2 + y^2 + z^2 - xy - zx$. Find and classify the critical points of $f$.
• Final 2016: Let $f(x,y,z) = z^3 - x^2 + y^2 - 6yz + 4x + 4y + 6z + 1$. Find and classify the critical points of $f$.

Notes:

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## MAT B41 — Week 7

Posted in 2018 -- MAT B41, Lecture Notes, Uncategorized by pgadey on 2018/06/26

Midterms are graded! New list of suggested exercises is available!

There is a new list of suggested exercises available here.

Suggested Exercises

• Chapter 1 Review (p. 71): 1, 4, 5, 7, 8, 16, 18, 20
• Chapter 2 Review (p. 145): 1, 2, 3, 5, 6, 10, 15, 25
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## MAT B41 — Week 6

Posted in 2018 -- MAT B41, Lecture Notes, Uncategorized by pgadey on 2018/06/12

Term Test is this Friday. Reading week is next week!

We have a modified class schedule this week.

• Tuesday: Taylor Series and Review.
• Thursday: Class Survey and Work Period, everyone is invited to bring problems to practice.
• Friday: Term Test, will be held Friday afternoon.

Term Test Policy

From the Course Syllabus, we have the following policy:

The Term Test will be written outside of regular lecture hours. If you cannot attend reasons of creed or religion, then you will must contact Parker as early as possible to arrange for an alternative sitting. If you miss the midterm test for medical reasons, you must contact Parker within 24 hours of the test.

You will need to send a UTSC Verification of Student Illness or Injury form:

Students who miss the midterm test will be asked to provide the Verification Form and a timetable for the next five days. You will be given only one opportunity to write the make-up test.