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 Wednesday, April 12
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
by at best giving a lower letter for the course
For the in-class part of the exam you are
allowed with 3 sheets of paper (6 pages) of formulas
from the course, in addition
to the tables for the normal, t-distribution, chi-square
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:
-- 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 and the two tailed tests
(when the variance is
known and when the variance is not known) for the mean of a normal
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.
-- 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 p-value(s) of the test.
-- Multiple Logistic Regression. The logit
transformation. The odds ratio OR and a
confidence interval for OR.
Hypothesis testing in multiple logistic regression.
Rank correlation. Ranking procedure. The Spearman
rank-correlation coefficient and
Spearman rank correlation (the p-value of the test).
-- Separable, Linear
first order DE. Exact Equations. The substitution method.
-- Euler, Bernoulli, Riccati
-- Modeling with DE: logistic
model, connected tanks, interacting populations (predator-prey,
-- Linear Second order DE with
constant coefficients. The method of undetermined coefficients
variation of parameters.
-- Existence and uniqueness issues
for linear and nonlinear DEs. Obtaining global existence
-- Slope fields. Phase line analysis and
stability of critical points for DEs. Bifurcation.
-- Systems of DE . Finding
solutions with the eigenvalue-eigenvector method. Phase plane analysis
linear trajectories) and stability of the critical points.
-- Almost linear systems of DEs.
Linearization. The Hartman-Grobman theorem. Nonlinear
-- The Undamped Pendulum and the
conservation of energy. Period, frequency, amplitude.
-- Solving a
linear system of equations with row reduction
transformations. The matrix of a linear transformation
-- Finding eigenvectors and eigenvalues.
Generalized eigenvectors (the case of
duplication for eigenvalues)
-- define functions, plot graphs
differential equations, plot slope fields, solution curves
-- solve systems of differential
equations, phase portraits, trajectories
-- compute eigenvectors and
-- Euler's method and the improved Euler's
method for differential equations and for
systems of differential
equations. Plot the solution and the approximations in the same plot.