# MAT 203 — Calculus with Analytic Geometry III — Fall 2018 Syllabus

## This Section

### Instructor

 Name Alexander Kasiukov Office Health, Science and Education Center, Room A-109 Email (preferred mode of communication) kasiuka@sunysuffolk.edu Phone (631) 851-6484 Web Site http://kasiukov.com Office Hours monday, 11:20 a.m.–1:20 p.m. (Health, Science and Education Center, Room A-109) tuesday, 1:20 p.m.–1:50 p.m. (Health, Science and Education Center, Room A-109) wednesday, 11:20 a.m.–1:20 p.m. (Health, Science and Education Center, Room A-109) thursday, 1:20 p.m.–1:50 p.m. (Health, Science and Education Center, Room A-109)

### Schedule

 Regular Meetings tuesday, 11:30 a.m.–1:10 p.m. (Workforce Development and Technology Center, Room 103) thursday, 11:30 a.m.–1:10 p.m. (Workforce Development and Technology Center, Room 103) Final Exam Date December 18, 2018 This date may be changed due to class cancellations. Last Meeting of Class December 20, 2018 This date may be changed due to class cancellations.

## Course Information

### Course Stats

 Title Calculus with Analytic Geometry III Catalog Code MAT 203 Credit Hours 4 Contact Hours 4 Prerequisites C or better in MAT 142 (Calculus with Analytic Geometry II), or equivalent Grades A, B+, B, C+, C, D+, D, F (failed), W (withdrawal) Students who stop attending the class will receive the grade F by default. The W grade must be discussed with the instructor before the date of the final exam.

### Catalog Description

Study of vectors and solid analytical geometry, vector calculus, partial derivatives, calculus of several variables, and multiple integration. Special topics may include Green's Theorem, Stokes' Theorem and other topics which may be of special interest to the class.

### Learning Objectives

Upon successful completion of this course, students should be able to:

• understand the basic concepts of three-dimensional Euclidian space, including rectangular, spherical and cylindrical coordinate systems;
• understand geometrical concepts in three dimensions, such as: level curves, level surfaces, equations and graphs of lines, curves, planes, cylindrical surfaces, surfaces of revolution and quadric surfaces;
• understand the basic concepts of vectors in $2$-space and $3$-space, including: vector projections, dot product, cross product, triple scalar product and direction cosines;
• understand the properties of a real vector space;
• understand vector-valued functions, including: limits, continuity and calculus of vector-valued functions;
• understand functions of several variables, including: limits, continuity, partial derivatives, total differential, directional derivatives and multiple integrals;
• demonstrate the ability to create and solve mathematical models using the tools of this course, chosen from work problems, arc length, volume, curvature, linear motion, motion along a curve and optimization problems;
• demonstrate a level of mathematical maturity that includes the ability to analyze and produce proofs of some of the basic facts presented in this course.

### Topics

1. The Cartesian Coordinate System
1. Definition of $1$-space, $2$-space, $3$-space, right-handed coordinate system
2. Distance and midpoint formulas in $3$-space; equation of a sphere
3. Cylindrical surfaces in $3$-space: their equations and graphs
2. Vectors (in $2$-space and $3$-space)
1. Definition of a vector: its magnitude (norm), its direction
2. Definition of zero vector and unit vector
3. Expressing a vector as a scalar times a unit vector in the same direction
4. Definition of dot product
5. Definition of a real vector space
6. Definition of orthogonal vectors
7. Vector projections, scalar projections
8. Proofs of elementary statements about vectors
3. Three-dimensional Space
1. Parametric equations
2. Equations of a line in $3$-space (parametric and symmetric forms)
3. Direction angles and direction cosines
4. Cross product $\overrightarrow{a} \times \overrightarrow{b}$, triple scalar product $\left( \overrightarrow{a} \times \overrightarrow{b} \right) \cdot \overrightarrow{c}$and their uses
5. Normal to a plane, equation of a plane
6. Surfaces of revolution: equations and graphs
7. Quadric surfaces: equations and graphs
8. Spherical and cylindrical coordinates
9. Graphs
10. Convert from one system to another
4. Vector-Valued Functions
1. Definition
2. Eliminate the parameter $t$ to obtain a Cartesian equation
3. Domain and range
4. Limits
5. Continuity
6. Definition of the derivative
7. Proof that the derivative can be done componentwise
8. Proofs of some of the rules for derivatives
9. Finding derivatives of all orders of parametric equations without eliminating the parameter
10. Integrals
11. Arc length
12. Velocity, acceleration and plane motion problems
13. Unit tangent and unit normal vectors
14. Curvature and radius of curvature
15. Arc length as a parameter (optional)
16. Tangential and normal components of acceleration (optional)
5. Functions of Several Variables
1. Definition
2. Range, domain and graphs
3. Limits and continuity
4. Partial derivatives and higher-order partials
5. Definition of a differentiable function
6. Total differential
7. Chain rule
8. Directional derivatives and gradients
9. Tangent planes and normals to a surface
10. Extreme values of functions of 2 variables; second partials test
11. Lagrange multipliers
12. Line integrals
6. Multiple Integrals
1. Definition
2. Double integrals in Cartesian and polar coordinates
3. Triple integrals in Cartesian, spherical and cylindrical coordinates
4. Stokes and Green's Theorems (optional)

## Policies and Procedures

### Requirements for Completion

To complete this course, students must:

• attend classes,
• actively participate in class work,
• prepare assigned homework and reading,
• pass all the quizzes and the final exam.

### Grading

There will be several quizzes, given randomly in class. They will last no more than 20 minutes each and will cover current material. The quizzes will determine 75% of the final score.

There will be a final exam at the end of the course. It will cover all topics of the course. The grade received on the final exam will determine 25% of the final score.

If a test (i.e. a quiz or the final exam) is missed, then the grade 0 is assigned for that test.

The letter grade will be determined as follows:

Letter Grade Necessary and Sufficient Conditions
A Final Score 90 and above
B+ Final Score 85–89
B Final Score 80–84
C+ Final Score 75–79
C Final Score 70–74
D+ Final Score 65–69
D Final Score 60–64
F Final Score below 60 or stopped attending the class without communicating with the instructor
W Withdrew officially
• by returning a withdrawal slip to the Registrar's Office — before mid-semester, or
• by getting permission to withdraw from the instructor — after mid-semester.

### Attendance

All students are expected to attend every session of each course for which they are registered. Students are responsible for all that transpires in class whether or not they are in attendance. The College defines excessive absence or lateness as more than the equivalent of one week of class meetings during the semester. Excess absence or lateness may lead to failure in a course or removal from the class roster.

### Make-ups

Make-up tests will be given only for documented emergencies, and then only at the instructor's discretion and convenience. However, if you have a good reason, please do ask for consideration.

### Extra Help

• Don't hesitate to ask a question right away — this class will encourage and facilitate immediate feedback.
• Come to the instructor's office hours.
• Use free tutoring and supplementary materials available at the Centers for Academic Excellence. (You must sign in with your student ID each time you use the Centers.) The Grant Campus Center is located in LRC, Room 149.
• Get counseling and advising at the Counseling Centers.

### Disruptions

Disruptive behaviors, as defined by the Student Handbook, will not be tolerated. In case of violations, the College policy allows the instructor "to remove a student from a class for one class meeting, and, in those cases where the continued presence of the student poses a substantial threat or would be disruptive to the class, request that the Associate Dean of Student Services impose an interim suspension pending a disciplinary hearing."

### Academic Integrity

The College's Student Code of Conduct expressly prohibits engaging in any form of academic dishonesty. In case of violations, the College policy allows the instructor "to initiate student conduct action through the Campus Associate Dean of Student Services. The faculty member may impose any of the following penalties: require that the student repeat the assignment or the exam; give the student a failing grade for the assignment or exam; or give the student a failing grade for the course. Should the student believe that s/he has been wrongly or unfairly accused of academic dishonesty, the student shall have the right to pursue the matter though the Grade Grievance Process."

### Use of Technology

 Non-Graphing Calculator as a standalone device (not an app on a phone, tablet or a computer) Calculator as an app on a phone, tablet or a computer Phone, Tablet, Computer, ... used as a distraction (making or receiving calls, answering SMS, browsing Internet, ...) Phone, Tablet, Computer, ... used for class activities (taking notes, looking up information related to class, using computer modeling, ...) Regular Class Permitted but not recommended Permitted but not recommended Prohibited Repeated use is a sufficient reason for your removal from the class for the remainder of the class session. If someone needs to contact you urgently when you are in class, you should discreetly leave the room before answering. Keep your phone on vibrate or turn it off when in class. Recommended We may occasionally use computers during lectures. Having your own computer could be helpful on those occasions. Test (i.e. a quiz or final exam) Strictly prohibited, even if not used Having such devices in the open when taking a test is a sufficient reason for an immediate failing grade for that test. If you use computers for taking notes, please make arrangements for an alternative way to access those notes during a test, if you need them.

### Disability Services

Suffolk County Community College provides reasonable accommodations to registered students with disabilities who have self-identified and been approved by the Office of Disability Services. Once approved for reasonable accommodations, such students will be provided with a laminated letter, describing the specific accommodations. Students must present this laminated letter to each of their professors before accommodations can be provided.

Students who have, or think they may have, a disability are invited to contact Disability Services for a confidential consultation. Call the Disability Services Office at (631) 851-6355, email the office at disabilityserv-west@sunysuffolk.edu or stop by to make an appointment in Caumsett Hall, Lower Level, Room 20.

### Religious Observance

As provided for in New York State Education Law §224-a, student absences from class necessitated by religious observance will be deemed an excused absence, with no academic consequences. Students must notify their professor in advance of their religious observance, via their College email accounts or otherwise in writing, of their intention to be absent from a particular class due to a religious observance; notification should occur at least one week prior to the religious observance. Observing students shall be granted reasonable arrangements and/or be permitted a reasonable amount of time to make up missed quizzes, tests, assignments, and activities covered in their absence. Please refer to the Religious Observance Policy for additional information.

Fall 2018