Calculus 3: syllabus
MAC2313
Program and syllabus for Summer 2021
Instructor name: Eric TAIEB.
E-mail: Write through the Inbox (canvas).
Office: Eric Taieb
Class hours: Monday- Wednesday- Friday: 4:30PM- 6:30PM.
The objective of this course is to give some notions about the multivariable calculus.
Text: a textbook will be uploaded in the Canvas.
Other recommended books
- Calculus, James Steward. Brooks/Cole. 7th edition.
- Calculus, Early Transcendentals, by W. Briggs and L. Cochran
- Calculus and analytic geometry, Louis Leithold.
- Advanced Calculus: Differential Calculus and Stokes' Theorem, Buono, Pietro-
Luciano. Series: De Gruyter Textbook. Berlin : De Gruyter. 2016
- Multivariable and vector calculus: an introduction. Santos David, Musa Sarhan,
Mercury learning and information.
Evaluation
9 partial examinations: The average will be 70% of your grade.
You will have a partial examination each Friday, except the 1st and the last Friday of the
term.
Partial 1: May 21st
Partial 2: May 28th
Partial 3: June 4th
Partial 4: June 11th
Partial 5: June 18th
Partial 6: June 25th
Partial 7: July 2nd
Partial 8: July 9th
Partial 9: July 16th
Final exam: Monday July 26th at 3:30 PM.
Examinations:
You will have 9 partial examinations and the final examination. The final will count
30% of your final grade. The average of the partials will count for 70% of your final
grade.
In case you miss one partial examination, unless a medical excuse is provided, you
will have a 0 grade. Be aware that you must have a medical certification.
In case you provide a medical excuse, usually you will not have a make-up test, but
your average will be done with one grade less. You may have a make-up test at the
instructor convenience.
If you are present the day of a partial examination you must take this partial, even
though you were absent before this test.
A global extra credit assignment can be considered to improve your final grade, with
a maximum of 5 extra points on your final grade, in order to increase your GPA.
The homework will not be recollected or graded. The professor may check whether your
homework is done, in case it is not, he may exclude you from the classroom. The
homework is an essential part of your apprenticeship... It is very important for you to
note that you must do your homework carefully.
You are expected to arrive on time at each class.
In addition to the homework, you are expected to solve some exercises, the most as
possible to practice. To have a good chance to pass this material you must work hard.
You are expected to arrive on time at each class.
I will not take the attendance. Your presence is mandatory just for the examinations. Be
aware, even if you are absent, you must be aware about what we discussed in class
exactly as you were present. That is valid even you missed the classes before an
examination.
Zoom meeting
The classes will be done by zoom meeting. For participating please turn on your
camera, so I can see you. In general, disable your microphone, you can unable it
anytime if you have a question. While you follow the class, have a paper and a pencil
with you, so you can solve the problems I will give you during the class.
Examination procedure
The examinations will be done through the Honorlock. For that you must use a
computer and the Google Chrome browser.
It is important that the camera not only shows your face but also your both hands.
If the criteria are not met, I may not grade your exam (0 grade).
In a general principle, an examination will consist on a set of questions you must
answer writing down on a paper. Then you must upload it in the Canvas. The time
allowed, it is to solve your exam and scan or photograph it and to upload it. If the time
is out before you can send your job, you will have the option to use the Inbox of the
Canvas, but I will take off points for that: 5 points less if you upload less than 5 minutes
late, and 1 additional point less for each extra minute if I have the test 5 minutes or
more late. The reference for that will be the hour I will have received your mail.
Your entire exam must be uploaded on a unique PDF file in the Canvas.
To practice that it is particularly important to complete the Honorlock practice. This one
will not be graded, but I may let comments so you can change if something is wrong.
Calculators
A graphic programmable calculator is strongly recommended for this course. You will
be allowed to use it during examination except if stated otherwise. You can just use
devices designed to be a calculator. You cannot use something like an iPhone or a
Samsung Galaxy in the examinations.
Grades:
0-59: F
60- 65: D
66-69: D+
70-73: C
74-77 C+
78-81 B-
82-85 B
86- 89 B+
90-93 A-
94-100 A
Florida State Honor code
Students are expected to uphold the Academic Honor Code published in The Florida
State University Bulletin and the Student Handbook. The Academic Honor System of
The Florida State University is based on the premise that each student has the
responsibility (1) to uphold the highest standards of academic integrity in the student's
own work, (2) to refuse to tolerate violations of academic integrity in the university
community, and (3) to foster a high sense of integrity and social responsibility on the
part of the university community.
ADA policy
Students with disabilities needing academic accommodation should; (1) register with
and provide documentation to the Student Disability Resource Center; (2) bring a letter
to the instructor indicating the need for accommodation and what type. This should be
done during the first week of class.
A note on sexual misconduct
Our school is committed to fostering a safe, productive learning environment. Title IX
and our school policy prohibits discrimination based on sex. Sexual misconduct —
including harassment, domestic and dating violence, sexual assault, and stalking — is
also prohibited at our school.
Our school encourages anyone experiencing sexual misconduct to talk to someone
about what happened, so they can get the support they need, and our school can
respond appropriately.
If you wish to speak confidentially about an incident of sexual misconduct, want more
information about filing a report, or have questions about school policies and
procedures, please contact our Title IX Coordinator, which can be found on our
school's website.
Our school is legally obligated to investigate reports of sexual misconduct, and
therefore it cannot guarantee the confidentiality of a report, but it will consider a
request for confidentiality and respect it to the extent possible.
As a teacher, I am also required by our school to report incidents of sexual misconduct
and thus cannot guarantee confidentiality. I must provide our Title IX coordinator with
relevant details such as the names of those involved in the incident.
Program
9 and 10 Analytic geometry in the space
9.1- Vectors
9.2- Length or magnitude of a vector
9.3- Parametric equations for a straight line
9.4- Plane: definition and equation
9.5- Dot product
9.5.1- Definition- Analytic expression
9.5.2- Cartesian equations of a plane defined with a normal vector
9.6- Cross product
9.6.1- Definition
9.6.2- Geometric interpretation
9.6.3- Properties
9.6.4 -Analytic formula
9.6.5- Scalar triple product
10.6- Quadrics: definitions
10.7.1- The sphere
10.7.2- Definition of quadrics
10.7- List of quadrics
Note: You will be supposed to know about conics and their Cartesian equations. Review
if you need.
11- Vector functions
11.1- Generalities-definitions
11.2- Limits, continuity, differentiability and integration
11.2.1- Limits
11.2.2 Continuity
11.2.3 Differentiability
11.2.4 Rules of derivative
11.3- Cinematic interpretation of derivatives and antiderivatives
11.4- Length of a curve
11.6- Curves in the space
11.6.1- Unitary tangent and principal normal vectors
11.6.2- Binormal vector
11.6.3- Definition of the torsion
11.6.4- Formulas to calculate the curvature and the torsion
11.7- Study of curves with parametric equations (dimension 2)
11.8- Polar coordinates, study of curves defined by polar equations
11.8.1- Definition
11.8.2- Conversion between rectangular and polar coordinates
11.8.3- Extension to r<0
11.8.4- Conversion between polar coordinates and rectangular coordinates
11.8.5- Study of curves with polar equation
12- Multivariable functions: differential calculus
12.1- Generalities
12.1.1- The vector space n
12.1.2- Multivariable functions
12.1.3- Domain
12.1.4- Level curve, level surface and graphs
12.2- Limits and continuity
12.2.1- Limits: definition
12.2.2- Continuity
12.3- Partial derivatives
12.3.1- Definition
12.3.2- Superior order partial derivatives
12.3.3- Chain rule
12.3.4- Implicit functions theorem.
12.4- Tangent line- Tangent plane
12.5- Differential
12.6- Optimization without constraint
12.7- Optimization with constraint
13- Multiple integrals
13.1- Double integral
13.1.1- Definition
13.1.2- Double integral over a rectangle domain
13.1.3- Double integral over a regular domain
13.1.4- Double integral in polar coordinates
13.1.5- Calculus of area
13.2- Triple integral
13.2.1- Definition
13.2.2- Calculus of a triple integral on a box
13.2.3- Triple integral on a regular domain
13.2.4- Cylindrical coordinates
13.2.5- Spherical coordinates
13.3- Applications of the double and triple integrals
13.3.1- Mass
13.3.2- Center of mass and centroid
14- Vector fields
14.1- Vector fields
14.2- Line integrals
14.3- The fundamental theorem for line integral
14.4- Green’s theorem
14.5- Parametric surfaces and their areas
14.6- Surface integrals
14.6.1- Surface integral of a function
14.6.2- Orientation of a surface in the space
14.6.3- Surface integral of a vector field
14.7- Stokes’ theorem
14.8- The divergence theorem (Gauss-Ostrogradzky’s theorem)
