STANDARD COMPETENCIES:

 

 I.      Solve selected problems involving algebraic expressions.

 II.     Solve and graph linear and non-linear algebraic equations and inequalities.

 III.    Compare the difference between relationships and functions, and be able to work with function notation.

 IV.     Find limits and determine continuity at a point for a variety of algebraic functions.

 V.      Use the appropriate algorithms (including product, chain, and quotient rules) to find derivatives of algebraic functions.

 VI.     Find derivatives of implicitly defined algebraic functions.

 VII.    Use derivatives to find equations of tangent lines, determine the rates of change, and solve applied problems as selected by the instructor.

 VIII.   Use the first and second derivatives of algebraic functions to find extreme, points of inflection, sketch graphs, and solve applied algebraic problems as selected by the instructor.

 IX.     State and use the properties of exponential and logarithmic functions and solve applied problems as selected by the instructor.

 X       Use the appropriate algorithms to find derivatives of exponential and logarithmic functions.

 XI.     Find definite and indefinite integrals of algebraic, exponential, and logarithmic functions.

 XII.    Use definite integrals to evaluate are under curves and other applied problems.

 XIII.   State and use the Fundamental Theorem of Calculus to evaluate integrals.

 XIV.    Use differential equations to solve applied problems as selected by the instructor.

 XV.     Integrate algebraic, exponential, and logarithmic functions using various techniques (such as substitution and integration by parts).

 XVI.    Evaluate various improper integrals as selected by the instructor.

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

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

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

 TOPICAL OUTLINE:

 

 I.      Algebraic Review

 II.     Graphs and Functions

         A.      Inequalities

         B.      Relations and Functions

 III.    The Derivative

         A.      Limits and Continuity

         B.      Tangent Lines and Rates of Change

         C.      Algorithms for Finding Derivatives

         D.      Implicit Differentiation

         E.      Applications

 IV.     Graphing and Optimization

         A.      Curve Sketching

         B.      Optimization

 V.      Exponential and Logarithmic Functions

         A.      Definitions and Properties

         B.      Compound Interest

         C.      Derivatives

 VI.     Integration

         A.      Definite Integrals

         B.      Indefinite Integrals

         C.      Fundamental Theorem of Calculus

         D.      Differential Equations

         E.      Applications

 VII.    Techniques of Integration

         A.      Integration Using Substitution

         B.      Integration by Parts

         C.      Improper Integrals