- Instructor
- Ilia Smirnov
- Class Times (all in Jeffery Hall 126)
- Mon. 12:30 - 1:30
- Wed. 11:30 - 12:30
- Thurs. 1:30 - 2:30
- Office Hours (in Jeffery Hall 201)
- Mon. 1:30 - 2:30
- OnQ Page
- OnQ Login
- Grading Scheme
- Homework: 30% (best 10 of 12)
- Midterm Exam: 20%
- Final Exam: 50%
- Textbook
- Calculus: Early Transcendentals by James Stewart, 8th edition (ISBN 978-1-285-74155-0).
Older editions will also do.
- Collaboration
- You are encouraged to collaborate with classmates on the homework, but please write up the solutions on your own. The University's Academic Integrity Policy.
|
| Date |
Topic |
For Practice |
Problem Sets |
| Sept. |
12 |
Introduction to the Course |
Review §12.2-12.4 |
|
| |
14 |
Parametrized Paths I |
§13.1: 7-14, 21-26 |
|
| |
15 |
Parametrized Paths II: Tangent Lines, Slopes, and Arclength |
§13.2: 3, 5, 7
§13.3: 3, 5, 11 |
|
| |
19 |
Path Integrals of Real-Valued Functions; Integral Estimates |
§16.2: 1, 7, 11, 37
|
|
| |
21 |
Two Families of Examples: Cycloids and Catenaries
Supplemental Note on Catenaries
|
§3.11: 1, 3, 7, 8, 51
§10.1: 40
|
Problem Set 1 |
| |
22 |
Vector Fields and Flow Lines |
§16.1: 5, 7, 9, 11-14 |
Solutions 1 |
| |
26 |
Gradient Fields |
§16.1: 23, 25, 29-32 |
|
| |
28 |
Work |
§16.2: 17, 19, 39 |
Problem Set 2 |
| |
29 |
Path-Dependence of Work |
§16.2: 41, 45, 46, 47 |
Solutions 2 |
| Oct. |
03 |
Gradient Fields are Path-Independent;
Finding Potentials for Path-Independent Fields I |
§16.3: 13, 15, 17, 19 |
|
| |
05 |
Finding Potentials for Path-Independent Fields II;
Piecewise Paths
|
|
Problem Set 3 |
| |
06 |
Flux Across a Path
Solution to Exercise From Class |
|
Solutions 3 |
| |
10 |
Thanksgiving - No Class |
|
|
| |
12 |
Double Integrals;
Fubini's Theorem I: Rectangles |
§15.1: 11, 15, 17, 21 |
|
| |
13 |
Polar Coordinates I: Definition, Arclength, Double Integrals |
§10.3: 10, 45
§10.4: 17, 19, 45, 47 |
Problem Set 4 |
| |
17 |
Fubini's Theorem II: More General Regions |
§15.2: 7, 9, 13, 17, 25 |
Solutions 4 |
| |
19 |
Polar Coordinates II: Unit Direction Vector Fields,
Velocity and Acceleration, Path Integrals, Gradient |
§15.3: 39 |
|
| |
20 |
Cross Product in the Plane;
Change of Variables for Double Integrals I |
§15.9: 1, 3, 5, 11 |
Problem Set 5 |
| |
24 |
Change of Variables for Double Integrals II |
§15.9: 15, 17, 19 |
Solutions 5 |
| |
26 |
Green's Theorem I: Planar Curl and Work |
§16.4: 11, 13, 17 |
|
| |
27 |
Green's Theorem II: Simply-Connected Spaces;
Curl Test for Path-Independence of Work |
§16.3: 3, 5, 7 |
Problem Set 6
Worked-Out Example |
| |
31 |
Halloween - Counterexamples Day!
''I turn with terror and horror from this lamentable scourge of
continuous functions with no derivatives.'' - C. Hermite |
|
Solutions 6 |
| Nov. |
02 |
Green's Theorem III: Planar Divergence and Flux |
§16.4: 21, 28, 29 |
|
| |
03 |
Parametrized Surfaces |
§16.6: 13, 15, 17,
19, 21, 23 |
Problem Set 7 |
| |
07 |
Smoothness and Tangent Planes; Cross Product in 3-Space |
§12.4: 53 |
Solutions 7 |
| |
09 |
Surface Area; Surface Integrals of Real-Valued Functions |
§16.7: 9, 13, 17 |
|
| |
10 |
Flux Through a Surface |
§16.7: 25, 27, 29 |
Problem Set 8 |
| |
14 |
Orientability; Triple Integrals
|
§15.6: 3, 5, 13 |
Solutions 8 |
| |
16 |
Cylindrical Coordinates |
§15.7: 15, 21, 27 |
|
| |
17 |
Spherical Coordinates
Change of Variables for Triple Integrals |
§15.8: 27, 35, 43
§15.9: 22 |
Problem Set 9 |
| |
21 |
The Divergence Theorem in 3-Space |
§16.5: 30
§16.9: 1, 9, 24 |
Solutions 9 |
| |
23 |
Curl and Stokes' Theorem in 3-Space |
§16.5: 1, 5, 7, 12, 13
§16.8: 13, 15 |
|
| |
24 |
Relationships between Div, Grad and Curl; Vector Potential |
§16.5: 19, 20, 21, 22 |
Problem Set 10 |
| |
28 |
Finding Vector Potentials |
|
Solutions 10 |
| |
30 |
Extended Versions of Green, Gauss and Stokes |
§16.8: 17
§16.9: 17 |
|
| Dec. |
01 |
The Laplacian; Harmonic Functions; Green's Identities |
§16.5: 34 |
Problem Set 11 |
| |
05 |
|
|
Solutions 11 |
| |
07 |
|
|
|
| |
08 |
|
|
Problem Set 12 |
|