STANDARD COMPETENCIES:

 

 1.   Solve selected algebraic and trigonometric problems.

 2.   Identify limits of algebraic, trigonometric, and composite functions.

 3.   Solve for the derivatives of algebraic, trigonometry and composite functions.

 4.   Solve for the derivatives of selected functions.

 5.   Use the appropriate algorithm(s) (including product, quotient, and chain rules) to find derivatives of algebraic, trigonometric, and composite function.

 6.   Find derivatives of implicitly defined functions.

 7.   Use the first and second derivatives of functions to find extrema, points of inflection, and sketch the graph of functions.

 8.   Set up and solve applied problems selected by the instructor.

 9.   Find indefinite and definite integralsof algebraic, trigonometric, and composite functions.

 10. Apply definite integrals.

 11. Read, analyze and apply written material to new situations.

 12.  Write and speak clearly and logically in presentations and essays.

 13. Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information.

 TOPICAL OUTLINE:

 

 I.      Pre-calculus Review

 II.     Limits and continuity of Algebraic, Trigonometric, and Composite Functions

         A.      Difference Quotients

         B.      Slope of Tangent Lines

         C.      Limit Theorems

         D.      Continuity

         E.      Intermediate-Value Theorem

 III.    Derivatives of Algebraic, Trigonometric, and Composite Functions

         A.      Definitions of a Derivative

         B.      Algorithms for Finding Derivatives

         C.      Implicit Differentiation

 IV.     Application of Derivatives

         A.      Finding Extrema

         B.      Applications of Derivatives to Curve Sketching

         C.      Problem Solving

 V.      Integration

         A.      Indefinite Integration

         B.      Definite Integration

         C.      Fundamental Theorem of Calculus

 VI.     Applications of the Definite Integral

         A.      Areas and Volumes

         B.      Arc Length

         C.      Physics Applications