**MAT 211 Calculus III, Section 81, CN
45112 Fall 2021**

**Class meets MWF 1:00 PM - 2:25
PM, in SAC 3136**

**Instructor:** Serban Raianu, office: NSM E-108,
office phone: (310) 243-3139, cell phone (657) 204-5612

e-mail address: sraianu@csudh.edu,
URL: http://math.csudh.edu/~sraianu;

office hours**: (via zoom**, **the zoom meeting information will be announced on Blackboard)**

Monday, Wednesday: 8:20 AM
– 9:50 AM, Friday: 11:30 AM – 12:30 PM, or by appointment.

**Course
Description: **MAT 211, Calculus III, covers from the
textbooks:

Multivariable
calculus: analytic geometry, scalar and vector products, partial
differentiation, multiple integration, change of coordinates, gradient,
optimization, line integrals, Green's theorem, elements of vector calculus.

** **

**Text:
CLP-3 Multivariable Calculus and CLP-4 Vector Calculus, by Joel Feldman,
Andrew Rechnitzer, Elyse Yeager, available
online at http://www.math.ubc.ca/~CLP/**

** **

**Objectives: **After
completing MAT 211 the student should be able to:

- Gain an intuitive
understanding of functions of several variables via level curves and
surfaces, and related concepts of limit, continuity and differentiability.
- Perform partial
differentiation and multiple integration of functions of several
variables.
- Change from Cartesian
co-ordinates to polar, cylindrical or spherical co-ordinates and vice
versa, perform differential (partial or ordinary) and integration
(multiple or single) in curvilinear co-ordinate systems and effect
transformation via the Jacobian.
- Utilize vectors to deal
with spatial curves and surfaces, and calculus of several variables
- Understand and use the
concepts of vector calculus: gradient, curl, divergence, line and surface
integrals, Green's, Stokes' and the divergence theorem.

**Prerequisites: **MAT
193 or equivalent with a grade of "C" or better.

**Grades: **Grades will be based on **two zoom video meetings 15-minutes
examinations** (50% total), a comprehensive **final examination** (20%), and **quizzes**,
**homework**, **video** and other assignments (30%) for the remainder.

The exact grading system for your section is the following:

An oral examination will consist in giving a definition or a
statement for a notion or result studied in class, and explaining two homework
problems from the homework assignments. A list of the possible definitions and
statements is posted on Blackboard. A definition or a statement will be chosen
by selecting a random number from 1 to the number of definitions and statements
on the list. The homework problems will be selected by choosing randomly the
lecture number, then a problem number from 1 to the total number of problems in
the assignment corresponding to that lecture. For example, the
definition/statement number 5 will refer to the fifth item on the list of
possible definitions or statements on the list. The homework problem (1,13)
will refer to problem 9 in Section 1.3 in CLP-1: this is the 13^{th}
problem in the homework assignment for Lecture 1.1. Each of the **two oral exams** will be graded on a 100
scale, then the sum of the scores is divided by 4 and denoted by E.

**Homework** will be due every week, the day
before quiz days, and each homework is worth 10 points. Each week one of the
problems from the homework due for that week will be selected and graded on a
scale from 0 to 4. The remaining 6 points will be awarded for completeness of
the homework assignment. Submitting solutions copied from the back of the book
is not forbidden but strongly discouraged, since copying solutions will not
prepare you for answering questions during the oral examinations. The average
of all homework scores is denoted by H. Homework will be submitted as a pdf
with your paper work on Gradescope. There is no need
to match the pages with the problems when submitting the homework, see

https://www.youtube.com/watch?v=u-pK4GzpId0

Gradescope can be accessed from the link
in Content in your Blackboard course, and you can practice submitting your work
on Gradescope using the assignment called Submission
practice, which will remain open throughout the semester. You might be asked to
explain your work on a submitted problem. Failure to provide an explanation
might result in a score of zero for the entire homework assignment.

**15 minutes quizzes** will be given in principle
every week, and will be graded on a scale from 1 to
10. The average of the quizzes scores is denoted by Q. Each quiz will consist
of one problem, similar but not necessarily identical to one of the homework
problems assigned for that week.

There are also 10 points awarded for **explaining one homework problem on video**. This portion of the grade
is denoted by V. Videos will be due the day before quiz days and will have to
be uploaded on Flipgrid

https://flipgrid.com/raianu9049

The homework problems from which to choose one problem to
explain on video will be announced in class.

The **final exam, which
will consist of fifteen problems similar to problems
assigned as homework throughout the semester,** will be graded out of a
maximum possible 200, then the score is divided by 10 and denoted by F.

To determine your **final
grade**, compute E+H+Q+V+F. The maximum is 100, and the grade will be given
by the rule:

A: 93‑100; A‑: 90‑92;
B+: 87‑89; B: 83‑86; B‑: 80‑82

C+: 77‑79; C: 73‑76; C‑: 70‑72; D+:
67‑69; D: 60‑66; F: Less than 60. You will be able to follow your
progress in the class in Blackboard under Grade Center throughout the semester.

**Accommodations
for Students with Disabilities: **California State University, Dominguez Hills adheres to all
applicable federal, state, and local laws, regulations, and guidelines with
respect to providing reasonable accommodations for students with temporary and
permanent disabilities. If you have a disability that may adversely affect your
work in this class, I encourage you to register with Student disAbility Resource Center (SdRC)
and to talk with me about how I can best help you. All disclosures of
disabilities will be kept strictly confidential. Please note: no accommodation
may be made until you register with the SdRC in WH
D-180. For information call (310) 243-3660 or to use telecommunications Device
for the Deaf, call (310) 243-2028.

**Academic Integrity: **The mathematics department does not
tolerate cheating. Students who have questions or concerns about academic
integrity should ask their professors or the counselors in the Student
Development Office, or refer to the University Catalog for more information.
(Look in the index under "academic integrity".)

**Technology: **Symbolic calculators, such as
TI-89, TI-92 or TI-nspire CAS are not acceptable for
this course.

**Tentative schedule and homework assignments**

**M 8/23: Lecture 1.1: **From CLP-3: 1.1 Points: 1,2,3; 1.2.1 Vectors,
add, multiply by scalar: 1,2,16

(6
problems)

**W 8/25: Lecture 1.2: **1.2.2 Dot product: 3,6,7,21,22,23 (6 problems)

**F 8/27: Lecture 1.3: **1.2.5 Cross product: 8,9,10,26,27,28,29 (7 problems)

**M 8/30: Lecture 1.4: **1.3 Lines in 2d: 5,6,7; 1.4 Planes in 3d:
4,5,6,7,8; 1.5 Lines in 3d: 3,4,5,6,7

(13
problems)

**W 9/1:** **Lecture 1.5:** 1.6
Curves and their tangent vectors: 10,11,12,13,14,15,16,17 (8 problems)

**F 9/3: Lecture 1.6: **1.7,1.8,1.9 Surfaces: 7,8,9,10,11 (5 problems)

**M 9/6: Labor Day**

**W 9/8:** **Lecture 1.7:** 2.1
Limits: 6,7,8,9,10,11 (6 problems)

**F 9/10: Lecture 1.8: **2.2 Partial derivatives: 3,4,5,6; 2.3 Higher
order derivatives: 3,4,5
(7 problems)

**M 9/13: Lecture 1.9: **2.4 Chain rule: 1,4,5,6,7,8,9 (7 problems)

**W 9/15: Lecture 1.10:** 2.5 Tangent planes and normal
lines: 5,6,7,8,9,10,11,12,13 (9 problems)

**F 9/17: Lecture 1.11: **2.6 Linear approximation and error: 3,4,5,6,7 (5 problems)

**M 9/20: Lecture 1.12: **2.7 Directional derivatives and the
gradient: 1,2,3,4,5,6,7 ** **(7 problems)** **

**W 9/22: Lecture 1.13: **2.9 Maximum and minimum values: 4,5,6,15,16,17**
**(6 problems)

**F 9/24:** **Lecture 1.14: **2.10
Lagrange multipliers: 3,4,5,6,7,8**
**(6 problems)

**M 9/27: Lecture 1.15: ** 3.1 Double integrals: 1,2,3,4,5,6,7 (7 problems)

**W 9/29: Lecture 1.16: **3.2 Double integrals in polar coordinates:
1,2,3,4,5,6,7,8,9,10** **(10 problems)

**F 10/1: Lecture 1.17:** 3.3 Applications of double
integrals: 2,3,4,5,6 (5 problems)

**M 10/4:** **Lecture 1.18: **3.4
Surface area: 4,5,6,7,8,9,10** **(7
problems)

**W 10/6: Lecture 1.19:** 3.5 Triple Integrals: 1,2,3,5,6
(5 problems)

**F 10/8: Review **

**M 10/11:** **Oral Exam Week 1**

**W 10/13: Oral
Exam Week 1**

**F 10/15:** **Oral
Exam Week 1**

**M 10/18: Lecture 2.1: **3.6 Triple integrals in cylindrical coordinates:
1,2,3,4,5,6,7,8** **(8 problems)

**W 10/20:** **Lecture 2.2: **3.7
Triple integrals in spherical coordinates: 1,2,3,4,5,6,7,8,9,10 (10
problems)

**F 10/22: Lecture 2.3: **From CLP-4: 1.1 Curves, derivatives, velocity,
etc.: 1,2,3,4,14,15,16,17

** **(8 problems)

**M 10/25:** **Lecture 2.4:** 1.2 Reparametrization: 1,2,3,4,5 (5 problems)

**W 10/27: Lecture 2.5: **1.6 Integrating along a curve: 1,2,4,5,6,7,8**
**(7 problems)

**F 10/29: Lecture 2.6: **2.1 Vector fields, definitions and first
examples: 1,2,3,4,5,6,7,8
(8 problems)** **

**M 11/1: Lecture 2.7: **2.3 Conservative vector fields: 1,2,3,4,5,6,7,8**
**(8 problems)

**W 11/3:** **Lecture 2.8:** 2.4
Line integrals: 3,4,5,6,8,9,10,11,12 (9 problems)

**F 11/5: Lecture 2.9: **3.1 Parametrized surfaces: 1,2,3,4,5,6**
**(6 problems) ** **

**M 11/8:** **Lecture 2.10: **3.2
Tangent planes: 6,7,8,9,10,11,12 (7 problems)

**W 11/10: Lecture 2.11: **3.3 Surface integrals: 4,5,6,7,8,9,10** **(7 problems)

**F 11/12: Lecture 2.12: **3.4 Interpretation of flux integrals: (from 3.3)
24,25,28,29,30,35,36
(7 problems)

**M 11/15: Lecture 2.13: **4.1 Gradient, divergence and curl: 1,2,3,4,5**
**(5 problems)

**W 11/17:** **Lecture 2.14: **4.2 The
divergence theorem: 1,2,3,4,5** **(5
problems)

**F 11/19: Lecture 2.15: **4.3 Green’s theorem: 1,2,3,4,5,6,7,8**
**(8 problems)

**M 11/22: Lecture
2.16: **4.4 Stokes’ theorem: 1,2,3,4,5,6,7 (7 problems)

**W 11/24:** **Review**

**F 11/26: Thanksgiving Day Break **

**M 11/29: Oral Exam Week 2**

**W 12/1: Oral
Exam Week 2**

**F 12/3: Oral
Exam Week 2**

**Final examination: Monday,
December 6, 1:00 PM - 3:00 PM.**

**Important Dates:**