## 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, **R**^{n} (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 **R**^{3} (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.