**
LECTURE:
** M-W-F
8:00 -- 8:50 DBH 1600

Tu-Th 5:00 -- 5:50 ICF 103

INSTRUCTOR: Martin Zeman, RH 410E

OFFICE HOURS: Wednesday 10:00am - 12:00noon
and by appointment

TA: Raymond Watkin, RH 410R

OFFICE HOURS: Tuesday 2:00pm - 3:00pm and Thursday 2:00pm - 4:50pm

**
COURSE INFORMATION AND POLICIES
APPROXIMATE SYLLABUS
UCI Academic Honesty Policy
UCI Student
Resources Page
**

**MIDTERM 1 INFORMATION**
**MIDTERM 2 INFORMATION**
**FINAL EXAM INFORMATION**

**HOMEWORK ASSIGNMENTS****HW1**
**HW2**
**HW3**
**HW4**
**HW5**

**COURSE PROGRESS****PREVIOUS WEEKS**

**WEEK 10****M:** Orientation of a surface. Surface integral of a vector field. Flux
of a vector field across a surface. Heat flow. Positive orientation of a
boundary of an oriented surface. Stokes theorem. curl(**F**)=0 implies
**F** is conservative.
**Recommended practice problems: **
Section 16.7 Exercise 21-32, 47, 48 and Section 16.8 Exercise 7-10, 11(a),
12(a), 17

**W:**

**F:**

**WEEK 9**

**M:** Curl and divergence. Operator ``nabla". Gradient as the multiple of
``nabla" with scalar a field, curl as the cross product of ``nable" with a
vector field, and divergence as the scalar product of ``nabla" with a vector
field. Criterion: curl(**F**)=**0** iff **F** is conservative.
Theorem: div(curl(**F**))=0.
**Recommended practice problems: **
Section 16.5 Exercise 1-8, 9-11, 12, 19, 20, 21, 22

**W:** Parametric surfaces. Examples: Cylinder, sphere. Partial derivatives
of **r**(u,v) and tangent planes. Normal vector to the tangent plane as
the cross product **r_u**(u,v) x **r_v**(u,v). Parametric and
non-parametric equations of the tangent plane.
**Recommended practice problems: **
Section 16.6 Exercise 1-2, 3-6, 13-18, 19-26, 33-36

**F:** Smooth/piecewise smooth surfaces. Surface integral of a function over
a surface. Example: Sphere with radius a, f(x,y,z)=y^2. Orientation of a
surface.
**Recommended practice problems: **
Section 16.7 Exercise 5-20, 39, 40

**WEEK 8**

**M:** Applications of Green's theorem: Area surrounded by a
closed curve. Discussion of the two assumptions in Green's theorem: Simplicity
of C, positive orientation. Extended version of Green's theorem: The vector
field can be defined on any open simply connected region. Applications of
Green's theorem to vector fields defined on open connected regions with holes.
**Recommended practice problems: **
Section 16.4 Exercise 11-14, 19, 27, 28, 29

**W:** Green's theorem and regions which are not simply conncted.
Explanation, why Green's theorem holds. Turbulence. Midterm review.
**Sample writing for midterm**

**F:** Midterm 2

**WEEK 7**

**M:** Holiday.

**W:** Geometry of plane and space: closed curve, simple curve, open region,
simply connected region. Criteria on conservativity of a vector field:
Euivalences of the following:

(A) Path independence of the integral of **F**dr versus the integral of
**F**d**r** along a closed curve is 0.

(B) Path independence of the integral of **F**d**r** versus **F**
being conservative.

(C) Equality of partial derivatives Q_y=P_x versus P(x,y)i+Q(x,y)j being
conservartive.

**Recommended practice problems: **
Section 16.3 Exercise 3-10, 12-18, 19-20, 25-26, 31-34, 35, 36

**F:** Orientation of a closed curve. Green's theorem. Applications of
Green's theorem: Evaluating line integral, calculating the area of a region
surrounded by a close curve.
**Recommended practice problems: **
Section 16.4 Exercise 1-4, 5-10, 17, 18

Last Modified: March 12, 2018