Martin Flashman's Courses
Math 110 Calculus II Fall, '09
MTRF     11:00 -11:50 pm    SH 128
Final Topic Check List for Fall, 2009!

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Differential Equations and Integration  
   Tangent Fields and Integral Curves. 
   Numerical Approximations. 
            Euler's Method
            Trapezoidal Rule. 
            Parabolic (Simpson's) Rule. 
Integration of core functions (from Calc I)
Integration by Substutition
Integration by Parts. 
 Integration of Trigonometric Functions and Elementary Formulas. 
 Trigonometric Substitutions. 
 Integration of Rational Functions. 
            Simple examples. Simple Partial fractions. 
 Separation of Variables. 

Improper Integrals: Extending the Concepts of Integration. 
               Integrals with noncontinuous functions. 
               Integrals with unbounded intervals.
Recognizing sums as the definite integral  
Areas (between curves).  
Volumes (cross sections- discs/rotation).

Average Value of Function



Taylor's Theorem. 
  Taylor Polynomials. Calculus. 
Using Taylor Polynomials to Approximate:  Error  Estimation. 
      Derivative form of the remainder. 
      Approximating known functions, integrals 
      Approximating solutions to diff'l equations using Taylor's theorem.

Sequences and Series: Fundamental Properties. 
  Simple examples and definitions: visualizing sequences. 
         How to find limits. 
         Key theory of convergence. 
             The algebra of convergence. 
             Convergence for monotonic sequences. 
  Geometric series. Harmonic series. Taylor approximations. 
Theory of convergence (series). 
     The divergence test. 
     Positive series. 
          Bounded convergence tests. 
           Integral tests. 
           Ratio test (Part I). 
           Absolute convergence. 
             Absolute convergence implies convergence. 
     Alternating Series Test. 
     Ratio test (Part II). 

Power Series: Polynomials and Series. 
 The radius and interval of convergence. 
 Functions and power series [derivatives and integrals]. 


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