MAT B41 — Week 12
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!
Additional resources:
- Khan Academy on triple integrals (Pt. 1).
- Khan Academy on triple integrals (Pt. 2).
- Kristal King on triple integrals.
- PatrickJMT on triple integrals.
Suggested Exercises:
- 6.1 Geometry of Maps from
to
- 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.
Mock Final Exam!
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.
MAT B41 — Week 11
Homework 5 is due! Homework 6 (tex) is now available!
The Mock Midterm will be Friday July 27 in SY110 from 12–3pm.
Additional resources:
- Khan Academy on triple integrals (Pt. 1).
- Khan Academy on triple integrals (Pt. 2).
- Kristal King on triple integrals.
- PatrickJMT on triple integrals.
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:
MAT B41 — Week 10
There has been a minor change to the syllabus: Homework 6 will now be assigned in Week 11 and due in Week 12.
Additional resources:
- Khan Academy on constrained optimization.
- Eugene Khutoryansky on Double Integrals (after five minutes the video goes beyond our course).
- PatrickJMT on Changing Order of Integration (Pt.1)
- PatrickJMT on Changing Order of Integration (Pt.2)
Geogebra Demonstrations:
- Cavalieri’s Principle with Triangles by Irina Boyadzhiev
- Archimede’s Cone-Sphere Theorem by Brian Sterr
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
bound by the parabolic cylinder
and the planes
,
, and
.
- Final 2015: Evaluate
where
is the region bounded by
and
for
.
- Final 2016: Evaluate
where
,
, and
.
- Final 2016: Evaluate
.
Notes:
MAT B41 — Week 9
Homework 4 (tex) is now available.
Additional resources:
- Khan Academy on constrained optimization.
- Kristal King on Lagrange multipliers.
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
on the closed triangular region in
, and
.
- Final 2015: Find the maximum values of
on the solid ball
.
- Final 2015: Find the points on the intersection of the paraboloid
and the plane
that are closest and farthest from the origin.
Notes:
MAT B41 — Week 8
Additional resources:
- Khan Academy on multivariate maxima and minima.
- Kristal King on local extrema.
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
. Find and classify the critical points of
.
- Final 2016: Let
. Find and classify the critical points of
Notes:
MAT B41 — Week 7
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
MAT B41 — Week 6
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.
Parker scheduled to the midterm to avoid Ramadan, but he forgot about Eid Al-Fitr. If you want to celebrate Eid with your family, instead of writing the midterm at the usual time, please contact Parker immediately.
The Week after Reading Week!
Parker will be traveling to STLHE 2018 and the IBL Workshop.
Our Tuesday evening lecture will be delivered by Ivan Khatchatourian.
Our Thursday morning lecture will be delivered by Ray Grinnell.
MAT B41 — Week 5
Mock Midterm this Friday 12-2pm in IC 130. Midterm Test next week!
Several people asked about Question 7 off of Homework #3. The intent of the question was for 
Additional resources:
- Wikipedia on Clairaut’s theorem
- Khan Academy on Second Partial Derivatives
- Krista King on Second Partial Derivatives
- PatrickJMT on Second Partial Derivatives
- ThreeBlueOneBrown on Single Variable Taylor Series
- Mark Ancliff on Multivariate Taylor Series
Suggested Exercises:
- 3.1 Iterated Partial Derivatives: 1, 2, 3, 4, 5, 6, 7, 12, 14, 15, 16
- 3.2 Taylor’s Theorem: 1, 2, 5, 9
Past Term Tests:
2016 Term Test:
Give the 4th degree Taylor polynomial about the origin of 
2015 Term Test:
- Compute the 4th degree Taylor polynomial about the origin of
.
- Find the linear approximation to the function
at the point
.
Notes:
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