MTH 211-F: Calculus III (Calculus of several variables)
University of Miami, Fall 2019
Instructor: Christopher Scaduto
Email: c.scaduto @ math.miami.edu
Office: Ungar 525
Office hours: 10:30-11:30 Monday and Wednesday, 9-10 Friday, or by appointment
Each office hour session is on Zoom now; see your email for invitation links.
Time and Location: 1:25-2:15 MWF. We use to meet @ Stanford Commons 105. Now lectures are on Zoom; the Zoom invitation links are sent by email.
The *updated* course syllabus can be found here. (Old one is here.)
Notes: Before the class moved online (after Spring Break), I maintained summaries of each lecture in a pdf file, found here. Notes for each online lecture (starting on 3/23/20) can be found below.
Course Schedule
| Date |
Lecture Content |
Reading |
| 1/13/20 |
Syllabus overview, Coordinate systems, distance, describing surfaces |
10.1 |
| 1/15/20 |
Vectors and their operations |
10.2 |
| 1/17/20 |
The dot product |
10.3 |
| 1/20/20 |
MLK Holiday |
|
| 1/22/20 |
Cross product |
10.4 |
| 1/24/20 |
Cross product (cont.), Lines in space |
10.4, 10.5 |
| 1/27/20 |
Planes in space |
10.5 |
| 1/29/20 |
Planes (cont.), Parametric curves |
10.5, 10.7 |
| 1/31/20 |
More parametric curves, derivatives |
10.7 |
| 2/3/20 |
More derivatives |
10.7, 10.9 |
| 2/5/20 |
Arc length, functions of several variables |
10.8, 11.1 |
| 2/7/20 |
Level curves, Partial derivatives |
11.1, 11.3 |
| 2/10/20 |
More partial derivatives |
11.3 |
| 2/12/20 |
Level surfaces; Tangent planes and approximation |
11.1, 11.4 |
| 2/14/20 |
More approximations; Differentials |
11.4 |
| 2/17/20 |
The Chain Rule |
11.5 |
| 2/19/20 |
More Chain Rule; Gradients |
11.5, 11.6 |
| 2/21/20 |
More gradients; directional derivatives |
11.6 |
| 2/24/20 |
Review. Practice problems here. |
|
| 2/26/20 |
Midterm 1 (covers up to and including 11.4) |
|
| 2/28/20 |
Steepest ascent problems |
11.6 |
| 3/2/20 |
Local min/max: second derivative test |
11.7 |
| 3/4/20 |
Absolute maxima and minima |
11.7 |
| 3/6/20 |
Lagrange multipliers |
11.8 |
|
Spring Break |
|
| 3/20/20 |
Warm up class -- First online session! Riemann sums and integrals over rectangles |
12.1 |
| 3/23/20 |
Iterated integrals and integrals over general regions Notes |
12.1, 12.2 |
| 3/25/20 |
More integrals over general regions Notes |
12.2 |
| 3/27/20 |
Integration in polar coordinates Notes |
12.3 |
| 3/30/20 |
Integration in polar coordinates (cont.), Triple integrals Notes |
12.5 |
| 4/1/20 |
More triple integrals; center of mass Notes |
12.4, 12.5 |
| 4/3/20 |
Cylindrical and Spherical coordinates Notes |
12.6, 12.7 |
| 4/6/20 |
More Cylindrical and Spherical coordinates Notes |
12.6, 12.7 |
| 4/8/20 |
Vector fields, divergence, curl Notes |
13.1, 13.5 |
| 4/10/20 |
Review. Practice problems here. Notes (<- A bit messy, sorry. Email me for further questions.) |
|
| 4/13/20 |
Midterm 2 Solutions |
|
| 4/15/20 |
More Vector fields; Line integrals Notes |
13.2 |
| 4/17/20 |
More line integrals Notes |
13.2 |
| 4/20/20 |
Work; line integrals of vector fields Notes |
13.2 |
| 4/22/20 |
Line integrals and Flux Notes |
|
| 4/24/20 |
Fundamental Theorem for line integrals Notes |
13.3 |
| 4/27/20 |
Simply-connected regions; conservation of energy Notes |
|
| 4/29/20 |
Green's Theorem Notes |
|
| 5/1/20 |
No class. Office hours on this day at 1:30-3:30. |
|
| 5/4/20 |
Review. Practice problems here. Solutions |
|
| 5/6/20 |
Midterm 3 (previously known as "Final Exam") |
|
Homework Assignments
All homeworks are worth the same, even if graded out of different totals. Problems graded are in blue.
| Assignment |
Due Date |
Remarks |
| Homework 1: 10.1: # 3, 7, 10, 11, 14, 25, 26, 34; 10.2: # 2, 10, 14, 17, 21 |
1/24/20 |
Out of 10 |
| Homework 2: 10.3 # 1, 7, 9, 19, 21, 31, 45; 10.4 # 3, 13, 15, 19, 31, 33, 37 |
1/31/20 |
Out of 10 |
| Homework 3: 10.5 # 1, 3, 7, 9, 18, 23, 25, 34, 40, 49; 10.7 # 6, 8, 13, 27, 51, 57, 61 |
2/7/20 |
Out of 10 |
| Homework 4: 10.7 # 65, 67, 79; 10.8 # 1, 2, 4; 11.1 # 2, 3, 10, 27, 33, 41-46, 47, 48 |
2/14/20 |
Out of 10 |
| Homework 5: 11.3 # 9, 11, 17, 26, 31, 48, 57, 63; 11.4 # 5, 17, 19, 21, 24, 25, 27 |
2/21/20 |
Out of 10 |
| Homework 6: 11.5 # 3, 5, 9, 10, 13, 29, 37, 45; 11.6 # 3, 7, 13, 15, 26, 31, 49 |
3/6/20 |
Out of 10 |
| Homework 7: 11.7 # 2, 5, 7, 23, 33, 43; 11.8 # 3, 18, 27 |
3/27/20 |
Out of 10 |
| Homework 8: 12.1 # 11, 18, 23, 34; 12.2 # 6, 9, 15, 23, 29, 43, 49 |
4/3/20 |
Out of 10 |
| Homework 9: 12.3 # 7, 9, 11, 14, 21, 23, 26; 12.4 # 2, 5, 8, 11 |
4/10/20 |
Out of 10 |
| Homework 10: 12.5 # 4, 15; 12.6 # 17, 22; 12.7 # 21, 22; 13.1 # 11-14 |
4/24/20 |
Out of 10 |
No more homework!
|