Study of limits, continuity, theory and application of the derivative; related rate problems; maxima and minima; definite and indefinite integrals; areas under curves.

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

• use the definition of limits to calculate the value of limits; use technology to calculate the value of limits;
• apply the relationship between infinite limits and asymptotes to the sketching of graphs of functions; use technology to simulate asymptotic behavior numerically;
• apply the concept of continuity to polynomial, rational, composite, trigonometric, exponential, and logarithm functions;
• show and apply the relationship among the tangent to a graph of a function, the difference quotient, the two forms of the definition of the derivative, continuity, and differentiability;
• compute the derivative of polynomial, rational, trigonometric, exponential, and logarithmic functions; compute derivatives using the product rule, the quotient rule, and the chain rule;
• apply the concept of derivatives to related rates, optimization problems, curve sketching, higher order derivatives, implicit differentiation;
• calculate approximation of a function with the Taylor polynomial of degree $1$, $2$, and $3$;
• use summation formulae to evaluate Riemann sums; use Riemann sums to approximate the definite integral;
• find antiderivatives of polynomial functions and those functions whose derivatives are known;
• state and apply the results of the Mean Value Theorem, the Fundamental Theorem of the Calculus, and the average value of a function;
• use definite integrals to calculate the area between curves.

1. Limits (2 weeks)
   1. Definition, calculation and geometric meaning of:
      1. the basic notion of $\rule[-5px]{0px}{30px}\displaystyle \lim_{x \rightarrow x_0} f( x ) = L$
      2. one-sided limits $\rule[-5px]{0px}{30px}\displaystyle \lim_{x \rightarrow x_0+} f( x )$ and $\rule[-5px]{0px}{30px}\displaystyle \lim_{x \rightarrow x_0-} f( x )$
      3. infinite limits $\rule[-5px]{0px}{30px}\displaystyle \lim_{\quad} f( x ) = + \infty$, $\rule[-5px]{0px}{30px}\displaystyle \lim_{\quad} f( x ) = - \infty$ and $\rule[-5px]{0px}{30px}\displaystyle \lim_{\quad} f( x ) = \infty$
      4. limits at infinity $\rule[-5px]{0px}{30px}\displaystyle \lim_{x \rightarrow + \infty} f( x )$, $\rule[-5px]{0px}{30px}\displaystyle \lim_{x \rightarrow - \infty} f( x )$ and $\rule[-5px]{0px}{30px}\displaystyle \lim_{x \rightarrow \infty} f( x )$
   2. Limit theorems, their use in calculation of limits and proofs of some of them:
      1. $\rule[-5px]{0px}{30px}\displaystyle \lim$ of sum, product and quotient
      2. the squeeze theorem and the limits $\rule[-5px]{0px}{30px}\displaystyle \lim_{t \rightarrow 0} \frac{ \sin( t )}{t} = 1$ and $\rule[-5px]{0px}{30px}\displaystyle \lim_{t \rightarrow 0} \frac{ 1 - \cos( t )}{t} = 0$
2. Continuity (1 week)
   1. Continuity at a point:
      1. definitions
      2. essential (non-removable) and removable discontinuities
      3. theorems on continuity and their applications
   2. Continuity on an interval:
      1. arithmetic of continuous functions
      2. continuity of composite and inverse functions
      3. continuity of polynomial, rational, trigonometric, exponential, logarithmic functions; and radicals
3. The Derivative (4–5 weeks)
   1. The tangent line to a graph of a function $f(x)$ at a given point $x_0$
   2. The differential: definition of $\mathrm{d}|_{x_0}f(x)$, its geometric meaning, computation and use in approximating $f(x)$
   3. The derivative $f'(x)$: various forms of definition (instantaneous rate of change, slope, etc.) and its relation the differential
   4. Differentiability of a function on an interval; one-sided derivatives
   5. Relationship between differentiability and continuity
   6. Derivative of composite and inverse functions
   7. Differentiation of polynomial, rational, trigonometric, exponential, logarithmic functions; and radicals
   8. Implicit differentiation
   9. Higher order derivatives
4. Applications of the Derivative (4 weeks)
   1. Differentiation applied to related rates
   2. Mean Value Theorem
   3. Extrema and monotonicity of functions on open and closed intervals; characterization in terms of the derivative
      1. increasing and decreasing functions
      2. critical points and the first-derivative test for extrema
      3. second-derivative test for extrema
   4. Convexity, concavity and inflection points: definition and characterization in terms of second derivative $f''(x)$; curve sketching
   5. Taylor Polynomial Approximations
5. The Antidifferential (2 weeks)
   1. Antidifferentiation: definition and main rules
   2. Applications:
      1. differential equations
      2. antidifferentiation applied to rectilinear motion
6. The Definite Integral (1 weeks)
   1. Summation techniques
   2. Finding area under a curve by summation and limits, Riemann sum
   3. Definition and geometric meaning of definite integral
   4. Properties of definite integral
   5. Integrability of functions
   6. The average value of a function
   7. The Fundamental Theorem of the Calculus
7. Applications of the Definite Integral in Physics(1 weeks)
   1. Center of mass
   2. Computation of Energy
   3. Finding equations of motion

This class will be conducted in the traditional format of face-to-face lectures. When taking this class, students must:

• attend the class, as scheduled;
• actively participate in class work;
• prepare assigned reading;
• submit assigned homework;
• pass all in-class quizzes and the final exam.

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.

The class will be conducted in real time, face-to-face, in the format of a traditional lecture, as scheduled.

The College expects that each student will exercise personal responsibility with regard to class attendance. All students are expected to attend every class 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, even if absences are the result of late registration or add/drop activity at the beginning of a term as permitted by College policy. The College defines excessive absence or lateness as more than the equivalent of one week of class meetings during the semester. Excessive absence or lateness may lead to failure in, or removal from, the course.

Any student who enrolls in this course after the first meeting, regardless of reason, is accountable for all course requirements including assignments and attendance.

Arriving late, leaving early or taking unreasonably long breaks will be recorded as partial absence.

A student may be required to drop or withdraw from a course when, in the judgment of the instructor, absences have been excessive. A student may also be withdrawn from a course by the Associate Dean of Student Services or the Student Conduct Board following a disciplinary hearing for violating the Student Code of Conduct as described in the Student Handbook.

Students are advised to report COVID-positive test results to the Health Services Office via email healthserv-grant@sunysuffolk.edu or phone (631) 851-6709.

A PCR, or a rapid test taken at a facility, or a home test, will all be acceptable.  Students must provide a copy of the test result along with a copy of a photo ID.

Students who miss class for any illness should contact the instructor as soon as possible to discuss reasonable adjustments that might need to be made. When possible, students should contact the instructor before missing class.

As provided for in New York State Education Law §224-a, student's absence from a class necessitated by religious observance will be deemed an excused absence, with no academic consequences. Students must notify their professor at least one week prior to their absence due to a religious observance. The notification must be made via their College email, or otherwise in writing, 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.

• Don't hesitate to ask a question right away while in class — this class will encourage and facilitate immediate feedback.
• Come to the instructor's office hours.
• Use free online or in-person tutoring at the Academic Tutoring Centers. All tutoring sessions are offered by appointment only. Appoimtments are done online through WCOnline system.
  1. To create a WCOnline account: go to https://sunysuffolk.mywconline.net/register.php, and complete the registration form using your Suffolk email address and a 10-plus character password (other than the one you use for SUNY Suffolk).
  2. To make an appointment:
     1. Login to your WCOnline account at https://sunysuffolk.mywconline.net/index.php;
     2. Select Math Tutoring - Fall 2024 from the "AVAILABLE SCHEDULES"; The schedule is color-coded as follows: 
        • White blocks = Available;
        • Dark blue blocks = Not available;
        • Bright blue blocks = Other appointments;
        • Yellow blocks = Your in-person appointments;
        • Green blocks = Your Zoom appointments.
     3. Click on a white box of your choice. Each white box is a 30-minute or 45-minute session depending on the subject. Complete the appointment pop-up form by choosing whether you would like a Zoom or in-person session. You can also upload any documents you would like to share with the tutor.
     4. Click ‘CREATE APPOINTMENT’. If prompted, use the course MAT141 – Calculus with Analytic Geometry I and instructor Alexander Kasiukov.
     5. After scheduling an appointment, check your Suffolk email for confirmation. 
     6. Be on time. Please allow time for technical difficulties and contact us if they occur. If you scheduled a Zoom appointment, the tutor will email you the Zoom information before the session. In-person appointments will meet at your scheduled time at the Academic Tutoring Center located in the Learning Resource Center (LRC-149) on the Grant Campus. Vaccination is required for in-person tutoring.
  3. To join the waiting list: if a session you would like to attend is filled, you can join the waiting list. Click on the link link at the bottom right of each day on the schedule  and fill in the pop-up form. If an appointment opens up, a notification will be sent to you via text or email.
  4. To cancel an appointment
     1. Login to your WCOnline account at https://sunysuffolk.mywconline.net/index.php;
     2. Click on your appointment box and click on the 'CANCEL' button. As a courtesy to your tutor and other students, we ask that you cancel appointments at least 2 hours before the session. This will allow time for another student to schedule that session.  If you do not cancel within that time, it will be counted as a missed (no show) appointment. After 3 no shows, your account will be deactivated. 
  5. To contact the Center: email at tutoringcenterwest@sunysuffolk.edu or call (631) 851-6369.

  In-person tutoring takes place in Learning Resource Center, Room 149. Up to 8 people can be scheduled for the same in-person time slot.

  
  
• Use the college library online or, by appointment, in person. Limited in-person services will be provided. To request an appointment, follow the instructions at the Library Home Page. The following services will be provided in person by appointment:
  • reference desk (1 hour maximum);
  • internet/computer use (2 hour maximum);
  • study space – chair and desk (2 hour maximum);
  • print circulating material (request online, deliivered at door of the library).
• Get counseling and advising at the Counseling Centers. The Grant Campus Counseling Center is located in Caumsett Hall, Lower Level, Room 20 and can be reached at (631) 851-6250.
• If you need support related to your psychological, emotional or social well being, there are counselors available through Mental Health & Wellness Services to provide free and confidential counseling. You can contact the Services at mentalhealth@sunysuffolk.edu or call a counselor directly. Michael J. Grant Campus counselor is Hypatia Martinez and she can be contacted at (631) 851-6872, martinhy@sunysuffolk.edu

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."

Suffolk County Community College provides students with the opportunity to demonstrate their knowledge by submitting coursework that is uniquely theirs and giving proper attribution to the work of others. Participating honestly in the SCCC academic community ensures that students can take pride in their education and their contributions to scholarship. Without academic integrity, students gain unfair advantage over others and prevent their own intellectual progress. As a student in this class, you are expected to uphold the SCCC core value of integrity and understand the Special Procedures for Academic Dishonesty (section P. starting on page 23 of the Student Code of Conduct). Specifically, when academic integrity is violated, 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 Course Grade Grievance Procedure."

The Code prohibits academic misconduct, which includes any action that results in students giving or receiving unauthorized assistance in an academic exercise, or receiving credit for work that is not their own. Academic exercise includes all forms of work submitted for credit. Academic misconduct includes, but is not limited to, the following behaviors:

• cheating - unauthorized use of textbooks, notes, mobile devices, artificial intelligence tools or other sources during an academic exercise;
• plagiarizing - using another person's work or ideas without crediting them, including using material generated by artificial intelligence tools for an assignment without instructor authorization;
• complicity - helping a student, or being helped, to engage in academic misconduct;
• multiple submissions - submitting the same work for credit in more than one course without the instructor's permission;
• falsification and forgery - inventing information or falsifying the identity of a student.

Information about the Student Code of Conduct, plagiarism and the citation process can be found on the Academic Integrity Procedures webpage. To learn more about academic integrity, college policies and expectations in this area, and proper ways to avoid possible violations, see the Academic Integrity and Plagiarism Guide.

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 an Accommodation Letter, describing the specific accommodations. Students must present this 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 Office of Disability Services for a confidential consultation. You can call the Office at (631) 851-6355, contact it via email disabilityG@sunysuffolk.edu, or stop by to make an appointment in Caumsett Hall, Lower Level, Room 20.