Pre-Calculus Review
Limits
  1.  Definition of Limits
        A.  Right-Hand Limits
        B.  Left -Hand Limits
        C.  Evaluating Limits
                 1.  Substitution
                 2.  Factoring
                 3.  Conjugates
        D.  Finite Limits
        E.  Infinite Limits
 
  2.  Continuity
       A.  Definition of continuity
       B.  Types of continuity
       C.  Rates of change and Limits
       D.  Limits Involving coninuity
       E.  Rates of Change and Tangent lines
 
3.  Derivatives
      A.  Derivative of a Function
      B.  Differentiability
      C.  Rules of Differentiation
      D.  Velocity and Other Rates of Change
      E.  Derivatives of Trigonometric Functions
      F.  Chain Rule
      G.  Implicit Differentiation
      H.  Derivatives of Inverse Trigonometric Functions
      I.  Derivatives of Exponential and Logarithmic Functions
 
4.  Applications of Derivatives
      A.  Extreme Value of Functions
      B.  Mean Value Theorem
      C.  Connecting the first and second derivaties with the function
      D.  Modeling and Optimization
      E.   Related Rates
 
5.  The Definite Integral
      A.  Estimating with Finite Sums
      B.  Definite Integrals
      C.  Definite Integrals and Antiderivatives
      D.  The Fundamental Theorem of Calculus
      E.  Trapezoidal Rule
 
6.  Differential Equations and Mathematical Modeling
      A.  Antiderivatives and Slope Fields
      B.  Integration by Substiution
      C.  Integration by Parts
      D.  Exponential Growth and Decay
 
7.  Applications of Definite Integrals
      A.  Integral as Net Change
      B.  Area in the Plane
      C.  Volumes
      D.  Applications from Science and Statistics