## Class Summaries

I will try to post my lecture notes after class, but it is a really good idea to take notes yourself.

### WEEK 1

Lecture M 8/28: Course overview, Rn (12.1), vectors (12.2), and quadric surfaces (12.6). (NOTES). Here is an interactive quadric surfaces page.
Section Tu 8/29: Review worksheet. Solutions.
Lecture W 8/30: Linear algebra (12.2) and geometry: dot product (12.3), lines and planes (12.5). (NOTES).
Section Th 8/31: Projections, distances, and planes worksheet. Solutions.
Lecture F 9/1: Determinant and cross product (12.4), linear transformations (supplemental notes). (NOTES)
Make sure you are reading the sections in the book and looking at the notes online. There can be things there that we don't get to in class!

### WEEK 2

Lecture M 9/4: LABOR DAY. No class.
Section Tu 9/5: Linear transformations worksheet. Solutions.
Lecture W 9/6: Functions of several variables (14.1), limits (14.2). (NOTES).
Section Th 9/7: Limits worksheet. Solutions. Today's (9/7) office 4-5 cancelled and rescheduled 3-3:50 in 366 Altgeld Hall.
Lecture F 9/8: Continuity (14.2), partial derivatives. (14.3) (NOTES).

### WEEK 3

Lecture M 9/11: THE derivative, differentiability, tangent planes (14.4) (supplemental notes). (NOTES).
Section Tu 9/12: Partial derivatives and differentiability worksheet. Solutions.
Lecture W 9/13: Parameterized curves and derivatives (13.1, 13.2 first half). The chain rule (14.5) (supplemental notes and exercises). I suggest discussing the exercises on Piazza (but don't follow the discussion until you've tried to work the exercises!). (NOTES).
Section Th 9/14: Practice Midterm. (solutions). Friday's 8-9 office hours rescheduled for 6-7pm Thursday in 366 Altgeld Hall.
Lecture F 9/15: Gradient, directional derivatives, and level sets (14.6). Friday's 8-9 office hours cancelled. (NOTES).

### WEEK 4

No help room Wednesday or Thursday this week.
Lecture M 9/18: Optimization (14.7) + Review. (NOTES).
Section Tu 9/19: Quiz on 14.6.
Lecture W 9/20: Midterm 2, in class. (solutions).
For regrade requests: Bring all such requests, including arithmetic errors in score totalling, to your TA, in writing by Tuesday's discussion section. State your name, NetID, and clearly explain what problem you would like regraded, and why.
Section Th 9/21: Discussion CANCELLED (exam grading).
Lecture F 9/22: Return exams, Optimization (14.7), Lagrange multipliers (14.8). (NOTES).

### WEEK 5

Lecture M 9/25: Optimization (14.7), Lagrange multipliers (14.8). (NOTES).
Section Tu 9/26: Lagrange multipliers worksheet. Solutions.
Lecture W 9/27 Space curves, arc length and curvature (13.3) (NOTES).
Section Th 9/28: Curves and reparameterization worksheet. Solutions.
Lecture F 9/29: Velocity and acceleration (13.4). (NOTES).

### WEEK 6

Lecture M 10/2: Vector fields (16.1) and integration of vector fields over curves (16.2). Here is a real world picture of flow lines of a vector field. (NOTES).
Section Tu 10/3: Quiz on Lagrange multipliers. Discussion of line integral problems.
Lecture W 10/4: Fundamental Theorem of line integrals. (16.3) (NOTES).
Section Th 10/5: Integrating vector fields worksheet. Solutions.
Lecture F 10/6: Conservative vector fields (16.3) (NOTES).

### WEEK 7

Lecture M 10/9: Holomorphic functions and the Cauchy integral formula. (NOTES).
Section Tu 10/10: Quiz on curves and line integrals. Problems on conservative vector fields.
Lecture W 10/11: Double integrals. (15.1) (NOTES).
Section Th 10/12: Double integrals worksheet. Solutions.
Lecture F 10/13: Integrating over more complicated regions. (15.2) Double integrals in polar coordinates. (15.3) (NOTES).

### WEEK 8

Lecture M 10/16: Midterm 2 review. Applications of double integrals. (15.4) (NOTES).
Today's office hours extended 3:30-5:00 in 366 Altgeld.
Section Tu 10/17: Midterm 2 review.
Lecture W 10/18: Midterm 2. (solutions).

Office hours cancelled.
Section Th 10/19: Midterm 2 returned. Questions on applications of double integrals.
Office hours cancelled.
Lecture F 10/20: Surface area. (15.5) (NOTES).
Office hours cancelled.
LAST DAY TO DROP THE COURSE.

### WEEK 9

Lecture M 10/23: Gaussian curvature (part 1). Changing coordiantes for double integrals (15.9). (NOTES).
Section Tu 10/24: 2D changing coordinates worksheet. Solutions.
Lecture W 10/25: Changing coordinates (15.9). Triple integrals (15.6). (NOTES).
Section Th 10/26: More coordinate changes and triple integrals worksheet. Solutions.
Lecture F 10/27: Cylindrical and spherical coordinates. (15.7,15.8) (NOTES).

### WEEK 10

Lecture M 10/30: Green's Theorem. (16.4) (NOTES).
Section Tu 10/31: Quiz on multivariable integrals. Problems on Green's Theorem
Lecture W 11/1: Surfaces in R3 (16.6) (NOTES).
Section Th 11/2: Parmeterizing surfaces worksheet. Solutions.
Lecture F 11/3: Surface area and integrals. (16.7) (NOTES).

### WEEK 11

Lecture M 11/6: Examples of integrating functions on surfaces (16.7). (NOTES).
Section Tu 11/7: Integration on surfaces worksheet. Solutions.
Lecture W 11/8: Flux and oriented surfaces (16.7). (NOTES).
Section Th 11/9: Quiz: integrating functions on surfaces. Surface integral problems.
Lecture F 11/10: Integrating vector fields over surfaces (flux) 16.7, curl and divergence 16.5. (NOTES).

### WEEK 12

Lecture M 11/13: Divergence Theorem 16.9. (NOTES).
Section Tu 11/14: Midterm 3 review.
Lecture W 11/15: Midterm 3. (solutions).

Section Th 11/16: Return Midterm 3. Divergence problems.
Lecture F 11/17: Geometry of surfaces, Gaussian curvature, covariant derivatives, hyperbolic plane.

### WEEK 13

Lecture M 11/27: Stokes' Theorem. (16.8) (NOTES).
Section Tu 11/28: Divergence and Stokes' Theorems worksheet. Solutions.
Lecture W 11/29: More Stokes' Theorem: conservative vector fields and the meaning of curl. (16.8)
Section Th 11/30: Quiz on Divergence Theorem.
Lecture F 12/1: CLASS CANCELLED

### WEEK 14

Lecture M 12/4: General Stokes Theorem, part 1: differential forms. Supplemental notes.
Section Tu 12/5: Differential forms worksheet. Solutions.
Lecture M 12/6: General Stokes Theorem, part 2: pullback and integration. Supplemental notes.
Section Th 12/7: Differential forms worksheet 2. Solutions.
Lecture F 12/8: General Stokes Theorem, part 3: the theorem.

### WEEK 15

Lecture M 12/11: Gauss's Theorem. Evaluations.
Section Tu 12/12: Review for final.
Lecture W 12/13: Review for final. Here is a list of topic covered, taken more-or-less directly from the course diary. It might be useful in organizing the things we've covered.
Main course page.