Instructions for the Final Exam


         The final exam will be given in two parts. The first part (which will count as 80% of the total
score on the final exam) will be given in class on Monday, November 27 between 12:30  and 2:30.
The second part (20%) will be take-home and it will cover material from the programming
language Maple. No collaboration is allowed on either part of the exam. Cheating will be penalized
by at best giving a lower letter for the course grade.
  
        For the in-class part of the exam you are allowed with 2 sheets of paper (4 pages) of formulas
from the course, in addition to the tables for the normal, t-distribution, chi-square, and F distributions. 
Also,  you may use calculators, but you have to show your work for every step in your solution
(including integration, substitution, use of identitites, etc.).

       A comprehensive list of subjects on which you may be tested:


  Statistics 
      --
Averages, Variance, Covariance, Correlation coefficient for random variables
      -- T- distribution - definition, the  100 * u percentile of a t-distribution
      -- Confidence interval for the mean of a normal distribution (computing the sem = standard
          error of the mean by using the sample standard deviation).
      -- Chi-square distribution - definition, the 100 * u percentile of a chi-square distribution
      -- Confidence interval for the variance of a distribution
      -- Hypothesis Testing ; definition of H_0 and H_1; One tailed test for the mean of a normal
         distribution (p-values and their significance).
      -- Linear Regression; Total SS, Reg SS, Res SS. The F distribution. The F-test for simple
         linear. The t-test for simple linear regression. The p-value of the test. CIs for the regression
         parameters. Relationship between the Pearson correlation coefficient and the regression
         parameter b.
     -- Multiple Regression. The F-test for assessing if some variables are good predictors for
         the dependent variable ; the p-value of the test. The t-test (or the F-test) for assessing if
         one variable is significant when all the other variables are significant in predicting the
         dependent variable; the p-value(s) of the test.
     -- Multiple Logistic Regression. The logit transformation. The odds ratio OR and its
         interpretation.
     -- Rank correlation. Ranking procedure. The Spearman rank-correlation coefficient and
        the t-test
for Spearman rank correlation (the p-value of the test).

   Traffic Models
     
-- Definition of velocity, density, flow for the continuum model of traffic flow
      -- Flow=density * velocity
      -- the conservation law of traffic; interpretation of terms and derivation
      -- relationship between density and velocity; Fundamental Diagram of Traffic flow
         Light and heavy traffic
      -- solving linear conservation laws; ICs and BCs; characteristics
      -- linearization of nonlinear conservation laws
     
  Matrix Theory  
       --
Solving a linear system of equations with row reduction
       --  Linear dependence and independence
       -- Linear transformations. The matrix of a linear transformation
         --  Finding eigenvectors and eigenvalues. Generalized eigenvectors (the case of
           duplication for eigenvalues)

  Maple
     --
define functions, plot graphs
     -- solve ordinary and partial differential equations, plot solution curves and solution surfaces
     --
compute eigenvectors and eigenvalues
    -- plot curves and surfaces in the same system of coordinates; plot a sequence of ``points" (i.e. disks)
       or curves in the same system of coordinates (for ... from ... do...od; procedure).