Topics of Individual Lectures


   1     1.1, 1.2    Precalculus Review:  Real line, coordinate plane,
                     distance, circles, straight lines.

   2     1.3		 Precalculus Review:  Functions, graphs.
                     Trig review:  Radians, definition of trig functions,
                     graphs of sin, cos, tan, sec.

   3     2.1, 2.2    Limits:  Definition and discussion of intuitive meaning.
                     Rules for limits, computing limits of algebraic functions.
                     One sided limits, squeeze theorem, limits for trig 
                     functions, infinite limits.

   4     2.2         Topics of lecture 3, continued. 

   5     2.3         Continuity, intermediate value theorem, finding  roots.

   6     2.4         Exponentials and logarithms:  Definition of e,
                     properties and inverse relation of exp and ln.
                     Compound interest, future value, exponential
                     population growth.

   7     3.1         Definition of the derivative:  Direct calculation of
                     Relation between the graph of f and  the graph of f'.
                     Continuity and differentiability.

   8     3.2, 3.3    Calculation:  Sum, product and quotient rules.
                     Higher order derivatives.
                     Differentiation of exponential and trig functions.   

   9     3.4         The derivative as a rate of change.  Velocity and acceleration.

  10     Catch up and review.


  12     3.5         Chain rule.

  13     3.6         Implicit differentiation.
                     Derivatives of log and exp to other bases.
                     Derivative of log(|u|).
                     Logarithmic differentiaion

  14     3.7         Related rates.

  15     3.8         Linear approximation.  Differentials.
                     Error and relative error of measurement.
                     Marginal analysis.

  16     4.1         Optimization of a continuous function on a bounded interval.

  17     4.2, 4.3    Mean value theorem.  First and second derivative analysis
                     and curve sketching.

  18     4.3         Topics of lecture 17, continued.

  19     4.4, 4.5    Limits as x approaches plus or minus infinity.
                     Horizontal and vertical asymptotes, L'Hopitals's rule.

  20     4.6         Optimization applications:  Physical problems.

  21     Catch up and review.  


  23     4.7         Optimization applications:  Marginal analysis and profit
                     maximization, inventory problems, physiology problems.

  24     5.1         Antiderivatives.

  25     5.2, 5.3    Riemann sums and the definition of definite integrals.

  26     5.4         Fundamental theorems of calculus.

  27     5.5         Substitution method for both indefinite and definite

  28     Catch up and review.