Detailed schedule for Math 241.

Math 241: Week 1

Aug 27
Introduction (§12.1). Notes.
HW 1 (due Fri Aug 31)
Aug 28
Review of parts of Calc I and II. Worksheet. Solutions.
Aug 29
Vectors (§12.2) and the dot product (§12.3). Notes.
HW 2 (due Tue Sept 4 because of Labor Day)
Aug 30
Parametric curves via vector arithmetic. Worksheet. Solutions.
Aug 31
Dot product applications (§12.3) and equations for planes (§12.5). Notes.
HW 3 (due Wed Sept 5)
Pickup syllabus if you weren't here on Monday.
No class Monday, Sept 3 (Labor Day).
Class website:
Access to the online HW:

Math 241: Week 2

Sept 3
Labor Day, no class and HW 2 is due tomorrow not today.
Sept 4
Projections, distances, and planes. Worksheet. Solutions.
Sept 5
Cross product (§12.4). Notes.
HW 4 (Due Mon, Sept 10)
Sept 6
HW problem discussion and quiz.
Sept 7
Functions of several variables (§14.1). Notes. Hopf fibration video.
HW 5 (Due Wed, Sept 12)

Week 3

Sept 10
Level sets in 3d (§14.1); quadric surfaces (§12.6); intro to limits (§14.2). Notes.
Interactive guide to quadric surfaces.
HW 6 (Due Fri, Sept 14)
Sept 11
Visualizing quadric surfaces and quiz. Solutions.
If you have a laptop, please bring it to section today.
For more visualizations like those in this section, try this web-based 3D plotting tool.
Sept 12
Limits in several variables (§14.2). Notes.
Extras: Limit pictures; The sinking of the Sleipner A.
HW 7 (Due Mon, Sept 17)
Sept 13
Functions of several variables; Limits. Worksheet. Solutions.
Sept 14
Continuity in several variables (§14.2); partial derivatives (§14.3). Notes.
HW 8 (Due Wed, Sept 19)
If you have a laptop, please bring it to section on Tuesday.

Week 4

Sept 17
Applications of partial derivatives (§14.3 and §14.4). Notes.
Visualization: Heat equation.
HW 9 (Due Fri, Sept 21)
Sept 18
Partial derivatives and differentiability. Worksheet. Solutions.
Sept 19
Chain rule (§14.5). Notes.
HW 10 (Due Mon, Sept 24)
Sept 20
Practice exam for Midterm 1. Solutions.
Sept 21
More on the chain rule (§14.5) and directional derivatives (§14.6). Notes.
Visualization: Gradient and level sets.
HW: Included in previous assignment.
The first midterm exam will be Tuesday, Sept 25 from 6:45–8:00pm.
See here for complete details.

Week 5

Sept 24
The gradient (§14.6) and overview of optimization (§14.7-14.8). Notes.
HW: None.
Sept 25
Section: Review for midterm.
Midterm the First: 6:45 - 8:00pm. Solutions.
Sept 26
No class.
Sept 27
Midterm returned and discussed.
Sept 28
Local min and max (§14.7). Notes.
HW 11 (Due Wed, Oct 3)
Different tutoring and office hours this week.

Week 6

Oct 1
More on min/max (§14.7). Notes.
Visualization: Min/max example.
HW 12 (Due Fri, Oct 5)
Oct 2
Taylor series, the second derivative test, and changing coordinates. Worksheet. Solutions.
Oct 3
Constrained min/max (§14.8). Notes.
HW 13 (Due Mon, Oct 8)
Oct 4
Constrained min/max via Lagrange multipliers. Worksheet. Solutions.
Oct 5
Introduction to space curves (§13.1, first half of §13.2, §13.3). Notes.
Visualization: Cycloid.
HW 14 (Due Wed, Oct 10)

Week 7

Oct 8
More on arc length (§13.3) and integrating functions on curves (§16.2, pages 1034–1037). Notes.
HW 15 (Due Fri, Oct 12)
Oct 9
Lagrange multipliers problem discussion. Quiz.
Oct 10
Vector fields (§16.1) and integrating them along curves (§16.2). Notes.
HW 16 (Due Mon, Oct 15)
Oct 11
Curves and integration. Worksheet. Solutions.
Oct 12
More on integrating vector fields along curves (§16.2 and §16.3). Notes.
HW 17 (Due Wed, Oct 17)
Having difficulty copying everything down in class? You can always fill stuff in from the lecture notes above.

Week 8

Oct 15
Conservative vector fields I (§16.3). Notes.
HW 18 (Due Fri, Oct 19)
Oct 16
Integrating vector fields. Worksheet. Solutions.
Oct 17
Conservative vector fields II (§16.3). Notes.
HW: Included in previous assignment.
Oct 18
Discussion of line integral problems. Quiz.
Oct 19
Intro to multiple integrals (§15.1 and §15.2). Notes.
HW: None.
Last day to drop the course (*)
The second midterm exam will be Tuesday, Oct 23 from 6:45–8:00pm.
See here for complete details.

(*) Unsure whether to drop Math 241? Try taking the practice test for the next midterm under timed conditions to see how you're doing.

Week 9

Oct 22
Integrating over more complicated regions (§15.3 and §15.4). Notes.
HW 19 (Due Friday, Oct 26)
Oct 23
Section: Review for midterm.
Midterm the Second: 6:45 - 8:00pm. Solutions.
Oct 24
No class.
Oct 25
Midterm returned. Discussion topic: Multivariable integrals. Worksheet. Solutions.
Oct 26
Polar coordinates (§15.4) and applications (§15.5). Notes.
HW 20 (Due Wed, Oct 31)
Different tutoring and office hours this week.
The final exam for this course will be Saturday, Dec 15.

Week 10

Oct 29
Triple integrals (§15.7). Notes.
HW 21 (Due Fri, Nov 2)
Oct 30
Transformations of the plane. Worksheet. Solutions.
Oct 31
Integrating in cylindrical and spherical coordinates (§15.8 and §15.9). Notes.
HW 22 (Due Mon, Nov 5)
Nov 1
Discussion of multivariable integral problems. Quiz.
Nov 2
Changing coordinates I (§15.10). Notes.
HW 23 (Due Wed, Nov 7)

Week 11

Nov 5
Changing coordinates II (§15.10). Notes.
HW 24 (Due Fri, Nov 9)
Nov 6
Integrating by changing coordinates. Worksheet. Solutions.
Nov 7
Green's Theorem (§16.4). Notes.
HW 25 (Due Mon, Nov 12)
Nov 8
Discussion of change of coordinate problems. Quiz.
Nov 9
Surfaces in R3 (§16.6). Notes.
HW 26 (Due Wed, Nov 14)

Week 12

Nov 12
Area and integration on surfaces (§16.6 and §16.7). Notes.
HW 27 (Due Fri, Nov 16)
Nov 13
Surface Parameterpolooza. Worksheet. Solutions.
Nov 14
Integrating vector fields: the flux. (§16.7). Notes.
Visualization: Cones.
Visualization: Flux and flow.
HW 28 (Due Wed, Nov 28)
Nov 15
Parametrizations and integrals. Worksheet. Solutions.
Nov 16
Divergence and applications (§16.5). Notes.
HW: included in previous assignment.
The third midterm exam will be Thurday, Nov 29 from 6:45–8:00pm.
See here for complete details.
Next week is Thanksgiving break. Enjoy!

Week 13

Nov 26
Surface integrals of vector fields (§16.7). Notes.
Nov 27
Section: Surface integrals of vector fields. Worksheet. Solutions. Section ICES.
Nov 28
Parameterizing the real world: surfaces in computer-aided design. Notes.
Visualization: Bezier curves and surfaces.
Current research: CARGO project, additional paper
HW 29 (Due Mon Dec 3)
Nov 29
Section: Review for midterm.
Midterm the Third: 6:45 - 8:00pm.
Nov 30
No class.
Different tutoring and office hours this week.

Week 14

Dec 3
Stokes Theorem (§16.8). Notes.
HW 30 (Due Fri, Dec 7).
Dec 4
Midterm returned and discussed.
Dec 5
More on Stokes Theorem (§16.8). Notes.
HW 31 (Due Mon, Dec 10)
Dec 6
Discussion of surface integral problems. Quiz.
Dec 7
Conservative vector fields in R3 (§16.8). Draft notes.
HW 32 (Due Wed, Dec 12)

Week 15

Dec 10
Electrostatics and Gauss's Law. Draft notes.
Dec 11
Review for final.
Dec 12
Maxwell’s equations. Draft notes.
Dec 13
Reading day.
Dec 14
Finals begin.
Dec 15
Final the Ultimate.
No office hours Monday or Tuesday. Extra office hours and tutoring later in the week, see here for complete details.

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