UC Davis Math 21D
Vector Analysis

Basic information

CRN code: 49577 (section B01), 49578 (section B02), 49579 (section B03)
Room/Time: 1:10-2:00p.m. MWF in Wellman 202
Instructor: Alexander Soshnikov
Office: 584 Kerr Hall
Office Hours: Wed,Th 4:10-5:00p.m
E-mail: soshniko@math.ucdavis.edu
 
TA for B01: Johannes Eberharter
Discussion: 7:10-8:00p.m.Wellmn 129
Office: 152 Kerr Hall
Office Hours: Wed 11-11:50 a.m., F 11:00-11:50 a.m.
E-mail: hannes@math.ucdavis.edu
 
TA for B02 and B03: Max McCoskey
Discussion: 5:10-6:00p.m.Wellmn 235 (B02) and 6:10-7:00p.m. Wellmn 235 (B03)
Office: 468 Kerr Hall
Office Hours: MW 4:10-5p.m.
E-mail: mccoskey@math.ucdavis.edu
 
Midterm : Friday, November 5, 1:10-2:00 pm
Final: Monday, December 13, 8:00-10:00 am (STORER 1322)
Grading: Problem sets 20%, Midterm 30%, Final 50%
Webpage: www.math.ucdavis.edu/~soshniko/21D
 

Syllabus and text

Textbook: Calculus and Analytic Geometry, fifth edition, by Stein and Barcellos.

1. Vectors (section 12.1, one lecture)

2. Projections (section 12.2, one lecture)

3. Dot products (section 12.3, one lecture)

4. Lines and planes. Determinants. (sections 12.4 and 12.5, one lecture)

5. Cross product (section 12.6, one lecture)

6. Derivative of a vector function (section 13.1, one lecture)

7. Properties, derivative of a vector function (section 13.2, one lecture)

8. Directional derivative, gradient (section 14.7, one lecture)

9-10. Normals, tangent plane, differential (section 14.8, two lectures)

11. Lagrange multipliers (section 14.10, one lecture)

12. Acceleration vector. Acceleration components (sections 13.3-13.4, one lecture)

13. Vector and scalar fields (section 16.1, one lecture)

14-16. Line integrals. Applications of the line integral (sections 16.2-16.3, three lectures)

17-18. Green's Theorem (section 16.4, one lecture)

19. Applications of Green's Theorem (section 16.5, one lecture)

20. Conservative vector fields (section 16.6, one lecture)

21-24. Surface integrals. Divergence Theorem. Stokes' Theorem. (sections 17.1-17.3, four lectures)

25. Applications of Stokes' Theorem (section 17.4, one lecture)

Homework

Homework will be assigned (in class, and posted online), each Friday, due next Friday. Homework is due at the end of Friday lecture (2 p.m.). You are expected to justify your answers in complete sentences except for questions that are clearly pure computations.

PROBLEM SET 1:

Section 12.1: 1,3,7,11(a), 13, 15(a), 19, 25, 27

Section 12.2: 3,5,9,11

Section 12.3: 1,5,9(c), 13, 16, 19, 35, 37, 41

PROBLEM SET 2:

Section 12.4: 11, 13, 15, 17, 21, 27, 28, 30, 31, 33, 41

Section 12.5: 7, 10, 13, 20

PROBLEM SET 3:

Section 12.6: 3,5,9,15,27,28

Section 13.1: 9, 13, 18, 23, 25

Section 13.2: 1, 5, 15

PROBLEM SET 4:

Section 14.7: 5,7,17, 19,23,25,35,37

Section 14.8: 5,7,11,13,15,23,33,35

PROBLEM SET 5:

Section 14.8: 9,17, 19, 21

Section 14.9: 1,3,9,13,15,19,21,25,28,31,34,35,39.

PROBLEM SET 6:

Section 14.9: 38, 40, 42, 44, 46, 48, 50

Section 14.10: 4, 8, 12, 14, 20, 22, 24, 26, 28, 30, 32, 34

PROBLEM SET 7 (DUE ON November 29, Monday)

Section 16.1: 6,7,8,12,17,18,20,23,28

Section 16.2: 6,12,13,22,28,29,30,

Section 16.3: 8,9,11,12

PROBLEM SET 8 (DUE ON December 3, Friday)

Section 16.4: 3,4,7,8,10,13,22,27

Section 16.5: 2,3,4,7,10,11

PROBLEM SET 9 (DUE ON December 10, Friday)

Section 17.1: 13, 16, 19, 24, 34

Section 17.2: 5, 8, 10, 15, 19, 20

Section 17.3: 3, 4, 5, 6, 8, 12, 16

Section 17.4: 1, 4, 13, 14