I. Prerequisite

 
MAT 149 (Elementary Functions, preferred) or both MAT 140 (College Algebra) and MAT 122 (Trigonometry), all with a grade of C or better, or an appropriate score on the Mathematics Assessment Test.

This course focuses on limits, continuity, derivatives, indefinite integrals and definite integrals of algebraic, trigonometric, exponential and logarithmic functions, and applications of differentiation and integration. Use of technology is integrated throughout.

A. Understand the concept of limit.
B. Understand the concept of continuity.
C. Understand the concept of the derivative.
D. Evaluate derivatives of algebraic, trigonometric, exponential and logarithmic functions.
E. Use derivatives to solve optimization problems, motion problems and problems involving rates of change.
F. Use derivatives to analyze functions and their graphs.
G. Understand the concept of indefinite and definite integral.
H. Evaluate indefinite and definite integrals.
I. Use definite integrals to find area, average functional value, distance traveled and total change.
J. Use technology for finding limits, derivatives and integrals.

The very nature of higher education requires that students adhere to accepted standards of academic integrity. Therefore Oakton Community College has adopted a Code of Academic Conduct and a Statement of Student Academic Integrity. These may be found in the Student Handbook. You may also find a summary of the Code of Academic Conduct in the College Catalog. Among the violations of academic integrity listed and defined are: Cheating, plagiarism, falsification and fabrication of records and official documents, personal misrepresentation and proxy, and bribes, favors, and threats.

It is the student’s responsibility to be aware of behaviors that constitute academic dishonesty.

Pursuant to the due process guarantees contained in the Policy and Procedures on Student Academic Integrity, the minimum punishment for the first offense for a student found in violation of the standards of academic integrity is failure in the assignment. In addition, a disciplinary record will be established and kept on file in the office to the Vice-President for Student Affairs for a period of 3 years.

       A. Functions and Limits
 
            1. Functions and their graphs
            2. Operations with functions
            3. Limits
            4. Infinity and limits
            5. Continuity

        B. The Derivative

             1. Definition of the derivative
             2. Differentiation rules for sums, products and quotients of functions
             3. Algebraic, trigonometric, exponential and logarithmic functions and their derivatives
             4. The Chain Rule
             5. Higher order derivatives
             6. Implicit differentiation
             7. Linear approximations of functions

         C. Applications of the Derivative
 
             1. Local extrema of functions
             2. Increasing/decreasing functions and the first derivative
             3. Concavity and the second derivative
             4. Curve sketching
             5. Graph the derivatives to find extrema and inflection points
             6. Optimization problems
             7. Rate of change
             8. Newton’s Method

         D. The Definite Integral
 
              1. Rectangular and trapezoidal approximations for area under curves
              2. Sigma notation
              3. Definition and properties of the definite integral
              4. Evaluating definite integrals
              5. Evaluating antiderivatives
              6. The Fundamental Theorem of Calculus
              7. Evaluating integrals by substitution
 
          E. Applications of the Definite Integral
 
              1. Area under a curve
              2. Average functional value
              3. Distance and velocity
              4. Area between two curves
 
           F. Recommended Technology
 
               1. Graphically, numerically and/or symbolically find limits
               2. Graphically, numerically and/or symbolically find derivatives
               3. Evaluate integrals numerically and/or symbolically