MTH 211-O: Calculus III (Calculus of several variables)
University of Miami, Fall 2023
Instructor: Christopher Scaduto
Email: c.scaduto @ math.miami.edu
Office: Ungar 525
Office hours: 8:15-9:15 Tuesday, 11-12 Thursday, or by appointment
Time and Location: TuTh 9:30AM - 10:45AM, Dooly Memorial 202
Course syllabus can be found here.
Course Schedule
| Date |
Lecture Content |
Reading |
| 8/22/23 |
Syllabus overview, Coordinate systems, distance, describing surfaces, vectors |
10.1, 10.2 |
| 8/24/23 |
More vectors, dot product |
10.2, 10.3 |
| 8/29/31 |
Cross product |
10.4 |
| 8/31/23 |
Lines and planes in 3-dimensional space |
10.5 |
| 9/5/23 |
Parametric curves and their derivatives |
10.7, 10.9 |
| 9/7/23 |
More derivatives. Arc Length |
10.8 |
| 9/12/23 |
3D graphs of functions. Level curves. Partial derivatives. |
11.1, 11.3 |
| 9/14/23 |
Tangent planes. Linear approximations. |
11.4 |
| 9/19/23 |
More approximations. Differentials. Chain rule. |
11.4, 11.5 |
| 9/21/23 |
More chain rule. Gradients of functions. |
11.5, 11.6 |
| 9/26/23 |
We will go over: practice problems - solutions |
|
| 9/28/23 |
Midterm 1 - solutions |
|
| 10/3/23 |
Directional derivatives. Steepest ascent problems. |
11.6 |
| 10/5/23 |
Local min/max. Second derivative test. |
11.7 |
| 10/10/23 |
Absolute min/max. |
11.7 |
| 10/12/23 |
Lagrange multiplier method. |
11.8 |
| 10/17/23 |
Fall Recess |
|
| 10/19/23 |
Double integrals over rectangles. |
12.1 |
| 10/24/23 |
Double integrals over type I and II regions, and in polar coordinates. |
12.2, 12.3 |
| 10/26/23 |
More double integrals in polar coordinates. Triple integrals. |
12.3, 12.5 |
| 10/31/23 |
Meanings of integrals. |
12.4 |
| 11/2/23 |
We will go over: practice problems - solutions |
|
| 11/7/23 |
Midterm 2 - solutions |
|
| 11/9/23 |
Spherical and cylindrical integration. |
12.6, 12.7 |
| 11/14/23 |
Vector fields. |
13.1 |
| 11/16/23 |
Line integrals. Work. |
13.2 |
| 11/21/23 |
Thanksgiving Recess |
|
| 11/23/23 |
Thanksgiving Recess |
|
| 11/28/23 |
More work. Fundamental Theorem for Line Integrals. |
13.3 |
| 11/30/23 |
Green's Theorem. |
13.4 |
| 12/5/23 |
We will go over: practice problems - solutions |
|
| 12/7/23 |
Final Exam 11:00am-1:30pm in our usual classroom |
|
Homework Assignments
All homeworks are worth the same, even if graded out of different totals.
| Assignment |
Due Date |
Remarks |
| Homework 1: 10.1: # 3, 7, 10, 14, 25, 26, 34; 10.2: # 2, 10, 14, 17; 10.3: # 1, 7, 9 |
8/31/23 |
|
| Homework 2: 10.3 # 19, 21, 31, 45; 10.4 # 3, 13, 15, 19, 31, 33, 37 |
9/7/23 |
|
| Homework 3: 10.5 # 1, 3, 7, 9, 18, 23, 25, 34, 40, 49; 10.7 # 6, 8, 13, 27, 51, 57, 61 |
9/14/23 |
|
| Homework 4: 10.7 # 65, 67, 79; 10.8 # 1, 2, 4; 11.1 # 2, 3, 10, 27, 33, 41-46, 47, 48 |
9/21/23 |
|
| Homework 5: 11.3 # 26, 63; 11.4 # 19; 11.5 # 9, 10, 13, 29, 37, 45; 11.6 # 3, 7, 13, 15, 26 |
10/5/23 |
|
| Homework 6: 11.6 # 31, 49; 11.7 # 1, 2, 3, 5, 6, 7, 23, 33, 43 |
10/12/23 |
|
| Homework 7: 11.8 # 3, 18, 27; 12.1 # 1, 11, 18, 23, 34; 12.2 # 6, 9, 15 |
10/26/23 |
|
| Homework 8: 12.2 # 23, 29, 43, 49, 12.3 # 7, 9, 11, 14, 23; 12.5 # 4, 15 |
11/2/23 |
|
| Homework 9: 12.6 # 17, 22; 12.7 # 21, 22; 13.1 # 5, 6, 11-14, 21, 22, 26 |
11/16/23 |
|
| Homework 10: 13.2 # 3, 8, 18, 19, 31; 13.3 # 3, 13, 20; 13.4 # 1, 5, 11 |
12/5/23 |
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