##### Calculus for Business and Social Science

**I. Course Prefix/Number: **MAT 180

** Course Name: **Calculus for Business and Social Science

** Credits: **4 (4 lecture; 0 lab)

**II. Prerequisite **

MAT 140 with a grade of C or better or an appropriate score on the Mathematics Assessment Test

**III. Course (Catalog) Description **

This course introduces concepts of functions and relations and the basic ideas of differential and integral calculus with applications to the fields of social science and business.

**IV. Learning Objectives **

1. Graph and perform operations with rational, exponential and logarithmic functions.

2. Compute limits of functions.

3. Determine continuity of functions.

4. Use the definition of the derivative to differentiate basic functions.

5. Use differentiation rules to evaluate derivatives of algebraic, exponential and logarithmic functions.

6. Use derivatives to solve optimization problems, motion problems, and problems involving rates of change.

7. Use derivatives to analyze functions and their graphs.

8. Evaluate indefinite and definite integrals using various techniques of integration including substitution and integration by parts.

9. Calculate areas between curves using definite integrals.

10. Calculate partial derivatives of functions of more than one variable.

11. Apply the concepts of differentiation and integration to business and social science models.

12. Use technology to find limits, derivatives, and integrals.

2. Compute limits of functions.

3. Determine continuity of functions.

4. Use the definition of the derivative to differentiate basic functions.

5. Use differentiation rules to evaluate derivatives of algebraic, exponential and logarithmic functions.

6. Use derivatives to solve optimization problems, motion problems, and problems involving rates of change.

7. Use derivatives to analyze functions and their graphs.

8. Evaluate indefinite and definite integrals using various techniques of integration including substitution and integration by parts.

9. Calculate areas between curves using definite integrals.

10. Calculate partial derivatives of functions of more than one variable.

11. Apply the concepts of differentiation and integration to business and social science models.

12. Use technology to find 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.The Derivative

a. Definition of the derivative

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

c. Polynomial, rational and other algebraic functions

d. The Chain Rule

e. Higher order derivatives

f. Imlicit differentiation

3. Further Applications of the Derivative

a. Increasing and decreasing functions

b. Extrema and the First-Derivative Test

c. Concavity and the Second-Derivative Test

d. Optimization Problems

e. Business and economics applications

f. Curve sketching

g. Differentials and marginal analysis

4. Exponential and Logarithmic Functions

a. Derivatives of exponential and logarithmic functions

b. Exponential and logarithmic integrals

c. Exponential growth and decay

5. Integration and Its Applications

a. Definition and properties of the indefinite integral

b. Fundamental Theorem of Calculus

c. The area of a region bounded by two graphs

6. Techniques of Integration

a. Integration by substitution

b. Integration by parts and present value

c. Integration tables and completing the square

7. Functions of More than One Variable

a. Definition

b. Partial derivatives

8. Recommended Technology

a, Graphically, numerically and/or symbolically find limits

b. Graphically, numerically and/or symbolically find derivatives

c. Numerical and symbolic integration

a. Functions and their graphs

b. Operations with functions

c. Limits

d. Infinity and limits

e. Continuity

2.The Derivative

a. Definition of the derivative

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

c. Polynomial, rational and other algebraic functions

d. The Chain Rule

e. Higher order derivatives

f. Imlicit differentiation

3. Further Applications of the Derivative

a. Increasing and decreasing functions

b. Extrema and the First-Derivative Test

c. Concavity and the Second-Derivative Test

d. Optimization Problems

e. Business and economics applications

f. Curve sketching

g. Differentials and marginal analysis

4. Exponential and Logarithmic Functions

a. Derivatives of exponential and logarithmic functions

b. Exponential and logarithmic integrals

c. Exponential growth and decay

5. Integration and Its Applications

a. Definition and properties of the indefinite integral

b. Fundamental Theorem of Calculus

c. The area of a region bounded by two graphs

6. Techniques of Integration

a. Integration by substitution

b. Integration by parts and present value

c. Integration tables and completing the square

7. Functions of More than One Variable

a. Definition

b. Partial derivatives

8. Recommended Technology

a, Graphically, numerically and/or symbolically find limits

b. Graphically, numerically and/or symbolically find derivatives

c. Numerical and symbolic integration

**VII. Methods of Instruction **

(To be completed by instructor)

Methods of presentation can include lectures, discussion, demonstration, experimentation, audiovisual 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, audiovisual 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.

**VIII. Course Practices Required **

(To be completed by instructor)

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

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

**IX. Instructional Materials **

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

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 will be used for instructional purposes.

**X. Methods of Evaluating Student Progress **

(To be completed by instructor)

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

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

**XI. Other Course Information **

Individual instructors will establish and announce specific policies regarding attendance, due dates and make-up work, incomplete grades, etc.

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.