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)
Notes:: Pickup syllabus if you weren't here on Monday.
No class Monday, Sept 3 (Labor Day).
Class website: http://dunfield.info/241.
Access to the online HW: https://www.webassign.net/uiuc/login.html

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)

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)
Notes:: If you have a laptop, please bring it to section on Tuesday.

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.
Notes:: The first midterm exam will be Tuesday, Sept 25 from 6:45–8:00pm.
See here for complete details.

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)
Notes:: Different tutoring and office hours this week.

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)

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)
Notes:: Having difficulty copying everything down in class? You can always fill stuff in from the lecture notes above.

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 (*)
Notes:: 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.

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)
Notes:: Different tutoring and office hours this week.
The final exam for this course will be Saturday, Dec 15.

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)

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.
Notes:: 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!

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.
Notes:: Different tutoring and office hours this week.

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)

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.
Notes:: No office hours Monday or Tuesday. Extra office hours and tutoring later in the week, see here for complete details.