Detailed schedule for Math 241.

Math 241: Week 1

Aug 22: Introduction (§12.1). Notes.
HW 1 (due Fri Aug 26); Other HW: Section 12.1: #5, 25, 31.
Aug 23: Review of parts of Calc I and II. Worksheet.
Aug 24: Vectors (§12.2) and the dot product (§12.3). Notes.
HW 2 (due Mon Aug 29); Other HW: Section 12.2: #4, 5.
Aug 25: Parametric curves via vector arithmetic. Worksheet.
Aug 26: Dot product applications (§12.3) and equations for planes (§12.5). Notes.
HW 3 (due Wed Aug 31); Other HW: Section 12.3: #1, 11, 53. Section 12.4: #43.
Notes:: Pickup syllabus if you weren't here on Monday. Class website: http://dunfield.info/241.
Class key for the WebAssign online HW system: uiuc 0810 7360
Important: Use NetID@illinois.edu as your email address when signing up!

Math 241: Week 2

Aug 29

Cross product (§12.4). Notes.
HW 4 (Due Fri, Sept 2); Other HW: Section 12.4: #43, 49.

Aug 30

Projections, distances, and planes. Worksheet.

Aug 31

Functions of several variables (§14.1). Notes. Hopf fibration video.
HW 5 (Due Tues, Sept 6); Other HW: Section 14.1: #23, 25, 27, 34.

Sept 1

HW problem discussion and quiz.

Sept 2

Level sets in 3d (§14.1); quadric surfaces (§12.6); intro to limits (§14.2). Notes.
Interactive guide to quadric surfaces.
HW 6 (Due Wed, Sept 7); Other HW: Section 14.1: #61, 64.

Notes:

Monday office hour changed to 1:30–2:30 for the rest of semester.

Full tutoring room schedule:

Mon, Tues, Wed, and Thur: 3:30–6:30pm in 1 Illini Hall and 6:00–9:00pm in 345 Altgeld (New!).
Tues and Thursday 11:30am–12:50pm in 142 Henry Admin Building.

If you have a laptop, please bring it to section on Tues, Sept 6.

Week 3

Sept 5: Labor day, no class.
Sept 6: Visualizing quadric surfaces.
Sept 7: Limits in several variables (§14.2). Notes.
Extras: Limit pictures; The sinking of the Sleipner A.
HW 7 (Due Mon, Sept 12); Other HW: None
Sept 8: Functions of several variables; Limits. Worksheet.
Sept 9: Continuity in several variables (§14.2); partial derivatives (§14.3). Notes.
HW 8 (Due Wed, Sept 14); Other HW: None
Notes:: If you have a laptop, please bring it to section on Tuesday.

Week 4

Sept 12: Applications of partial derivatives (§14.3 and §14.4). Notes.
Visualization: Heat equation.
HW 9 (Due Fri, Sept 16); Other HW: Section 14.3: #59, 94; Section 14.4: #13.
Sept 13: Partial derivatives and differentiability. Worksheet.
Sept 14: Chain rule (§14.5). Notes.
HW 10 (Due Mon, Sept 19); Other HW: Section 14.5: #55. Section 14.6: #1, 36, 38.
Sept 15: Practice exam for Midterm 1. Solutions.
Sept 16: More on the chain rule (§14.5) and directional derivatives (§14.6). Notes.
HW: Included in previous assignment.
Notes:: The first midterm exam will be Tuesday, Sept 20 from 7:00–8:30pm.
See here for complete details.

Week 5

Sept 19: The gradient (§14.6) and overview of optimization (§14.7-14.8). Notes.
HW: None.
Sept 20: Section: Review for midterm.
Midterm the First: 7:00 - 8:30pm. SOLUTIONS.
Sept 21: No class.
Sept 22: Midterm returned and discussed.
Sept 23: Local min and max (§14.7). Notes.
HW 11 (Due Wed, Sept 28); Other HW: Section 14.6: #54. Section 14.7: #2, 3, 4.
Notes:: Different tutoring and office hours this week.

Week 6

Sept 26: More on min/max (§14.7). Notes.
Visualization: Min/max example.
HW 12 (Due Fri, Sept 30); Other HW: Section 14.7: #20, 38, 52.
Sept 27: Taylor series, the second derivative test, and changing coordinates. Worksheet.
Sept 28: Constrained min/max (§14.8). Notes.
HW 13 (Due Mon, Oct 3); Other HW: Section 14.8: #1, 21.
Sept 29: Constrained min/max via Lagrange multipliers. Worksheet.
Sept 30: Introduction to space curves (§13.1, first half of §13.2, §13.3). Draft notes.
HW 14 (Due Wed, Oct 5); Other HW: Section 13.1: #14, Section 13.2: #1, 4.

Week 7

Oct 3: More on arc length (§13.3) and integrating functions on curves (§16.2, pages 1034–1037). Notes.
HW 15 (Due Fri, Oct 7); Other HW: None.
Oct 4: Lagrange multipliers problem discussion. Quiz.
Oct 5: Vector fields (§16.1) and integrating them along curves (§16.2). Notes.
HW 16 (Due Mon, Oct 10); Other HW: Section 16.1: #35, Section 16.2: #17, 37, 48.
Oct 6: Curves and integration. Worksheet.
Oct 7: More on integrating vector fields along curves (§16.2 and §16.3). Notes.
HW 17 (Due Wed, Oct 12); Other HW: None.
Notes:: No office hours Monday or Tuesday. Please visit the tutoring room instead.

Week 8

Oct 10

Conservative vector fields I (§16.3). Notes.
HW 18 (Due Fri, Oct 14); Other HW: Section 16.3: #11, 20, 23, 24, 26, 33.

Oct 11

Integrating vector fields. Worksheet.

Oct 12

Conservative vector fields II (§16.3). Notes.
HW: Included in previous assignment.

Oct 13

Discussion of line integral problems. Quiz.

Oct 14

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, Sept 20 from 7:00–8:30pm.
See here for complete details.

Monday and Tuesday office hours cancelled, but expanded on Thursday to 9:30–10:30 and 2:00–4:00. (This week only.)

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

(*) 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 17: Integrating over more complicated regions (§15.3 and §15.4). Notes.
HW 19 (Due Friday, Oct 21); Other HW: Section 15.4: #1–4.
Oct 18: Section: Review for midterm.
Midterm the Second: 7:00 - 8:30pm.
Oct 19: No class.
Oct 20: Midterm returned. Discussion topic: Multivariable integrals. Worksheet.
Oct 21: Polar coordinates (§15.4) and applications (§15.5). Notes.
HW 20 (Due Wed, Oct 26); Other HW: Section 15.4: #36.
Notes:: Different tutoring and office hours this week.

Week 10

Oct 24: Triple integrals (§15.6). Notes.
HW 21 (Due Fri, Oct 28); Other HW: Section 15.6: #27.
Oct 25: Transformations of the plane. Worksheet.
Oct 26: Integrating in cylindrical and spherical coordinates (§15.7 and §15.8). Notes.
HW 22 (Due Mon, Oct 31). Other HW: Section 15.7: #29; Section 15.8: #7, 11, 28.
Oct 27: Discussion of multivariable integral problems. Quiz.
Oct 28: Changing coordinates I (§15.9). Notes.
HW 23 (Due Wed, Nov 2); Other HW: Section 15.9: #7, 9, 10.

Week 11

Oct 31: Changing coordinates II (§15.9). Notes.
HW 24 (Due Fri, Nov 4); Other HW: Section 15.9: #17, 18, 24. Chapter 15 Review: 49.
Nov 1: Integrating by changing coordinates. Worksheet.
Nov 2: Green's Theorem (§16.4). Notes.
HW 25 (Due Mon, Nov 7); Other HW: Section 16.4: #22, 27.
Nov 3: Discussion of change of coordinate problems. Quiz.
Nov 4: Surfaces in R³ (§16.6). Notes.
HW 26 (Due Wed, Nov 9);
Other HW: None.

Week 12

Nov 7: Area and integration on surfaces (§16.6 and §16.7). Notes.
HW 27 (Due Fri, Nov 11); Other HW: Section 16.6: #60.
Nov 8: Surface Parameterpolooza. Worksheet.
Nov 9: Integrating vector fields: the flux. (§16.7). Notes.
Visualization: Flux and flow.
HW: included in previous assignment.
Nov 10: Parametrizations and integrals. Worksheet.
Nov 11: Divergence and applications (§16.5). Notes.
HW: None.
Notes:: The third midterm exam will be Tuesday, Nov 15 from 7:00–8:30pm.
See here for complete details.
No office hours on Thursday.
Friday's lecture given by Prof. Nevins.

Week 13

Nov 14: Surface integrals of vector fields (§16.7). Notes.
HW 28 (Due Fri, Nov 18); Other HW: None
Nov 15: Section: Review for midterm.
Midterm the Third: 7:00 - 8:30pm. SOLUTIONS.
Nov 16: No class.
Nov 17: Midterm returned and discussed.
Nov 18: Parameterizing the real world: surfaces in computer-aided design. Notes.
Visualization: Bezier curves and surfaces.
Current reseach: CARGO project, additional paper
HW: None.
Notes:: Different tutoring and office hours this week.
Next week is Thanksgiving break. Enjoy!

Week 14

Nov 28: Stokes Theorem (§16.8). Notes.
HW 29 (Due Fri, Dec 2).
Other HW: Section 16.8: #1, 13.
Nov 29: Surface integrals of vector fields and related theorems. Worksheet. Section ICES.
Nov 30: More on Stokes Theorem (§16.8). Notes.
HW 30 (Due Mon, Dec 5); Other HW: Section 16.5: #22. Section 16.8: #16, 19.
Dec 1: Discussion of surface integral problems. Quiz.
Dec 2: Conservative vector fields in R³ (§16.8). Notes.
HW 31 (Due Wed, Dec 7).
Other HW: Section 16.7: #47. Section 16.8: #15. Section 16.9: #23, 24.
Notes:: The final exam will be Tuesday, Dec 13 from 1:30–4:30pm.
See here for complete details.

Week 15

Dec 5: Electrostatics and Gauss's Law. Notes.
Dec 6: Review for final.
Dec 7: Maxwell’s equations. Notes.
Dec 8: Reading day. Tutoring and office hours as usual, but no section meetings.
Dec 9: Finals begin. Tutoring from 10-2 in 159 Altgeld.
Notes:: No office hours on Monday, Dec 5.
Final exam: Tuesday, Dec 13 from 1:30–4:30pm.
Extra tutoring and office hours on Dec 11 and 12, see final info for details.

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