UofT MAT235 2022-2023 Term Test 4 Solutions Take-Up

In this video I go over the fourth term test from 2022-2023 MAT235 at the University of Toronto St. George Campus (UofT). I, like many others, performed much better on this term test due to the length being shorter and the difficulty of the questions being easier. As always, I've included PDFs of my written solutions as well as a blank copy of the term test in case you do want to attempt it before watching.
Blank Test: drive.google.com/file/d/1M28i...
Written solutions (my notes): drive.google.com/file/d/1SjbN...
Entire folder of MAT235 resources: drive.google.com/drive/folder...
Recommended channels for complete content:
/ @professorleonard -- • Calculus 3 Lecture 11....
/ @alexandraniedden5337 -- • Ch 12: Vectors and the... • Ch 13: Vector Functions • Ch 14: Partial Derivat... • Ch 15: Multiple Integrals • Ch 16: Vector Calculus
/ @drtrefor -- • Calculus III: Multivar... • Calculus IV: Vector Ca...
/ @khanacademy -- • Multivariable function...
0:00 About Term Test 4
0:37 Multiple Choice i) Potential Function
3:53 Multiple Choice ii) Triple Integral (Changing Order of Integration, Changing to Polar Coordinates, and Evaluating)
14:59 Multiple Choice iii) Surface Area
18:23 Long Answer Q2 a) Sketching a Vector Field
22:37 Long Answer Q2 b) Computing the Line Integral by Definition
34:52 Long Answer Q3 Spherical Part
42:20 Long Answer Q3 Cylindrical Part
52:22 Long Answer Q4 Change of Variables (Jacobian)
1:07:42 Long Answer Q5 Mass of a Wire
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MAT235 Course Description: Parametric equations and polar coordinates. Vectors, vector functions and space curves. Differential and integral calculus of functions of several variables. Line integrals and surface integrals and classic vector calculus theorems. Examples from life sciences and physical science applications.