# Calculus I

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

** Course Name: **
Calculus I

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

**II. Prerequisite **

MAT 149, or both MAT 140 and MAT 122, all with grades of C or better, or an appropriate score on the OCC Mathematics Assessment Test, or placement by the Mathematics Advisor.

**III. Course (Catalog) Description **

Course is the first in calculus and analytic geometry. Content focuses on limits, continuity, derivatives, indefinite integrals and definite integrals, applied to algebraic, trigonometric, exponential and logarithmic functions, and applications of differentiation and integration. Technology integrated throughout the course.

**IV. Learning Objectives **

1. Calculate limits of functions and give reasons in cases where limits do not exist.

2. Classify functions as continuous or discontinuous at a point or on an interval.

3. Interpret and demonstrate the equivalence of derivatives, rates of change, and slopes of tangent lines.

4. Evaluate derivatives of algebraic, trigonometric, exponential, logarithmic and parametrically defined functions.

5. Use derivatives to solve applications including optimization problems, motion problems, problems involving rates of change, and Hopital’s rule limit problems.

6. Use derivatives to analyze functions and their graphs, including critical points and inflection points.

7. Interpret and demonstrate the equivalence of indefinite integrals and antiderivatives, and of definite integrals, approximation of areas by sums, and total change of a function.

8. Evaluate indefinite and definite integrals, including those requiring substitutions.

9. Use definite integrals to find area, average functional value, distance traveled, and total change.

10. Use technology to help finding limits, derivatives, and integrals.

2. Classify functions as continuous or discontinuous at a point or on an interval.

3. Interpret and demonstrate the equivalence of derivatives, rates of change, and slopes of tangent lines.

4. Evaluate derivatives of algebraic, trigonometric, exponential, logarithmic and parametrically defined functions.

5. Use derivatives to solve applications including optimization problems, motion problems, problems involving rates of change, and Hopital’s rule limit problems.

6. Use derivatives to analyze functions and their graphs, including critical points and inflection points.

7. Interpret and demonstrate the equivalence of indefinite integrals and antiderivatives, and of definite integrals, approximation of areas by sums, and total change of a function.

8. Evaluate indefinite and definite integrals, including those requiring substitutions.

9. Use definite integrals to find area, average functional value, distance traveled, and total change.

10. Use technology to help finding limits, derivatives, and integrals.

**V. Academic Integrity **

Students and employees at Oakton Community College are required to demonstrate academic integrity
and follow Oakton's Code of Academic Conduct. This code prohibits:

• 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.

Details of the Code of Academic Conduct can be found in the Student Handbook.

• 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.

Details of the Code of Academic Conduct can be found in the Student Handbook.

**VI. Sequence of Topics **

1. Functions and Limits

a. Functions and their graphs

b. Operations with functions

c. Limits

d. Infinity and limits

e. Continuity

2. Derivative

a. Definition of the derivative

b. Differentiation rules for sums, products and quotients of functions

c. Algebraic, trigonometric, exponential and logarithmic functions and their derivatives

d. The Chain Rule

e. Parametric equations and their derivatives

f. Higher order derivatives

g. Implicit differentiation

h. Linear approximations of functions

3. Applications of the Derivative

a. Local extrema of functions

b. Increasing/decreasing functions and the first derivative

c. Concavity and the second derivative

d. Curve sketching

e. Graph the derivatives to find local extrema and inflection points

f. Optimization problems

g. Rate of change

h. L’Hopital’s Rule limit problems

4. Definite Integral

a. Rectangular and trapezoidal approximations for area under curve

b. Sigma notation

c. Definition and properties of the definite integral

d. Evaluating of definite integrals

e. Evaluating antiderivates

f. The Fundamental Theorem of Calculus

g. Evaluating integrals by substitution

5. Applications of the Definite Integral

a. Area under curve

b. Average functional value

c. Distance and velocity

d. Area between two curves

6. Recommended Technology

a. Graphically, numerically and/or symbolically find limits

b. Graphically, numerically and/or symbolically find derivatives

c. Evaluate integrals numerically and/or symbolically

a. Functions and their graphs

b. Operations with functions

c. Limits

d. Infinity and limits

e. Continuity

2. Derivative

a. Definition of the derivative

b. Differentiation rules for sums, products and quotients of functions

c. Algebraic, trigonometric, exponential and logarithmic functions and their derivatives

d. The Chain Rule

e. Parametric equations and their derivatives

f. Higher order derivatives

g. Implicit differentiation

h. Linear approximations of functions

3. Applications of the Derivative

a. Local extrema of functions

b. Increasing/decreasing functions and the first derivative

c. Concavity and the second derivative

d. Curve sketching

e. Graph the derivatives to find local extrema and inflection points

f. Optimization problems

g. Rate of change

h. L’Hopital’s Rule limit problems

4. Definite Integral

a. Rectangular and trapezoidal approximations for area under curve

b. Sigma notation

c. Definition and properties of the definite integral

d. Evaluating of definite integrals

e. Evaluating antiderivates

f. The Fundamental Theorem of Calculus

g. Evaluating integrals by substitution

5. Applications of the Definite Integral

a. Area under curve

b. Average functional value

c. Distance and velocity

d. Area between two curves

6. Recommended Technology

a. Graphically, numerically and/or symbolically find limits

b. Graphically, numerically and/or symbolically find derivatives

c. Evaluate integrals numerically and/or symbolically

**VII. Methods of Instruction **

(To be completed by instructor.)

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.

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

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, media-based, hybrid or online course.

**VIII. Course Practices Required **

(To be completed by instructor.)

**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.

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.

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

**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.