STANDARD COMPETENCIES:

 

 1.   Write and state clearly the definitions and properties, differentiate, and integrate logarithmic and exponential functions.

 2.   Set up and solve applied problems involving logarithmic and exponential functions as selected by the instructor.

 3.   Differentiate and integrate the inverse trigonometric functions.

 4.   Define, differentiate, and integrate hyperbolic functions as selected by the instructor.

 5.   Use the appropriate algorithm(s) (including integration by parts, trigonometric substitutions, partial fractions, numerical methods, etc.)  to integrate algebraic, logarithmic, exponential, trigonometric, and composite functions.

 6.   Use various limit theorems to evaluate improper integrals.

 7.   Determine the convergence or divergence of various sequences and series.

 8.   Use Taylor and Maclaurin series to express selected functions.

 9.   Use Taylor's formula with remainder to approximate selected functions.

 10. Identify and graph equations involving a variety of conic sections.

 11. Convert between Cartesian and polar coordinates.

 12. Graph and determine the area of regions defined by polar equations.

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

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

 TOPICAL OUTLINE:

 

 I.      Logarithms and Exponential Functions

         A.      Definition and Properties of Logarithms

         B.      Definition and Properties of Exponential Functions

         C.      Applications

         D.      Introduction to Differential Equations

 II.     The Calculus of Trigonometric and Hyperbolic Functions

         A.      Derivatives and Integrals

         B.      Inverse Functions

 III.    Techniques of Integration

         A.      Integration by Parts

         B.      Integrating Powers of the Trigonometric Functions

         C.      Trigonometric Substitutions

         D.      Integrals Involving ax2+bx+c

         E.      Partial Fractions

         F.      Numerical Methods of Integration

         G.      Miscellaneous Substitutions

 IV.     Indeterminate Forms and Improper Integrals

         A.      Indeterminate Forms

         B.      Improper Integrals

 V.      Sequences and Series

         A.      Sequences

         B.      Monotonic Sequences

         C.      Infinite Series

         D.      Tests for Convergence

         E.      Taylor Series

         F.      Maclaurin Series

         G.      Binomial Series

         H.      Power Series

         I.      Differentiation and Integration of Series

 VI.     Analytic Geometry

         A.      Conic Sections

         B.      Translation and Rotation Axes

 VII.    Polar Coordinates

         A.      Graphs

         B.      Areas

         C.      Transformation of Polar Expressions to Rectangular Forms and Vice Versa