# Calculus I

**I. Course Prefix/Number: **
MAT 250

** Course Name: **
Calculus I

** Credits: **
5 (5 lecture; 0 lab)

**II. Prerequisite **

**III. Course (Catalog) Description **

**IV. Learning Objectives **

- Analyze functions in a variety of settings.
- Define, analyze and use limits.
- Compute derivatives.
- Use the derivative in applications.
- Set up, compute and evaluate basic integrals.
- Use technology to compute limits, derivatives and integrals.

**V. Academic Integrity and Student Conduct **

• cheating,

• plagiarism (turning in work not written by you, or lacking proper citation),

• falsification and fabrication (lying or distorting the truth),

• helping others to cheat,

• unauthorized changes on official documents,

• pretending to be someone else or having someone else pretend to be you,

• making or accepting bribes, special favors, or threats, and

• any other behavior that violates academic integrity.

There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.

Please review the Code of Academic Conduct and the Code of Student Conduct, both located online at

www.oakton.edu/studentlife/student-handbook.pdf

**VI. Sequence of Topics **

- Analyze functions in a variety of settings.
- Define and use properties of functions.
- Represent functions through formulas, graphs, tables and words.
- Evaluate exponential and logarithmic functions and to explain the relationship between exponential functions and logarithmic functions.
- Define and graph trigonometric and inverse trigonometric functions and use their properties in algebraic manipulations.
- Use technology to graph functions.

- Define, analyze and use limits.
- Motivate the concept of a limit.
- Define and compute left-sided, right-sided and two-sided limits.
- Evaluate limits analytically.
- Evaluate infinite limits.
- Determine the end behavior of a function.
- Define continuity of a function.
- Use technology to graphically, numerically and/or symbolically find limits.

- To compute derivatives.
- Define the derivative using limits.
- Analyze the relationship between the graph of a function and its derivative.
- Apply the rules of derivatives including the constant, power, constant multiple and sum rules.
- Apply the product and quotient rules.
- Apply the derivative rules for trigonometric functions.
- Interpret the derivative as a rate of change.
- Apply the chain rule in both differential form and Leibniz notation.
- Find the derivative of a function implicitly.
- Apply derivative rules to logarithmic and exponential functions.
- Apply derivative rules to the inverse trigonometric functions.
- Solve related rates problems.
- Use technology to graphically, numerically and/or symbolically find derivatives.

- To use the derivative in applications.
- Define local and absolute maxima and minima.
- Analyze the graph of a function through its first and second derivatives.
- Create an accurate graph of a function through the use of limits and derivatives.
- Solve optimization problems.
- Use linear approximation to approximate the value of a function, and to define the relationship between differentials dy and dx.
- Apply the Mean Value Theorem.
- Apply L’Hopital’s Rul
- Find the anti-derivative of a function.

- To set up, compute and evaluate integrals.
- Approximate the area under the curve using left, right and midpoint Riemann sums.
- Evaluate definite integrals.
- Apply the Fundamental Theorem of Calculus.
- Evaluate definite integrals using symmetry.
- Apply the substitution rule.
- Calculate the position, velocity, displacement and distance travelled by an object as well as the net change and future value of an object.
- Compute the area of a region bounded by two or more curves.
- Use technology to evaluate integrals numerically and/or symbolically.

**VII. Methods of Instruction **

Methods of presentation can include lectures, discussion, demonstration, experimentation, audio-visual aids, group work, and regularly assigned homework. Calculators/computers will be used when appropriate. Use of a computer algebra system is recommended.

*Mathematica*is available for use at the College at no charge.

Course may be taught as face-to-face, hybrid or online course.

**VIII. Course Practices Required **

**IX. Instructional Materials **

**Note:**Current textbook information for each course and section is available on Oakton's Schedule of Classes.

Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words "View Book Information".

Textbooks can also be found at our Mathematics Textbooks page http://www.oakton.edu/academics/academic_departments/math/syllabi

A graphics calculator is required. A TI-83/84 or higher numbered model will be used for instructional purposes.

**X. Methods of Evaluating Student Progress **

(To be determined and announced by the instructor)

Evaluation methods can include graded homework, chapter or major tests, quizzes, individual or group projects, computer/calculator projects, and a final examination.

*The following applies to the online section of this course only:*

This online course requires that students take their exams as directed by their instructor: either on campus at Oakton's Testing Center, at an authorized testing center with a face-to-face monitor, or remotely through a pre-approved testing service. *(To be customized by instructor.)*

**XI. Other Course Information **

If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.

Oakton Community College is committed to maintaining a campus environment emphasizing the dignity and worth of all members of the community, and complies with all federal and state Title IX requirements.

Resources and support for

- pregnancy-related and parenting accommodations; and
- victims of sexual misconduct

Resources and support for LGBTQ+ students can be found at www.oakton.edu/lgbtq.