Exam 2: April 18-19, 2007
Extra Office Hours: Monday, April 16 after class in LN 2233

Exam 2 covers all classes from March 2 through April 13, which includes Sections 3.4, 4.1-4.4, 5.1-5.3, 5.5, 6.3, 7.1-7.3, and 7.5 from the book. In addition, there could be questions on random walks and applications of graph theory.

Concepts you should understand for the exam:

• The modeling process
• Regression, residuals, model verification (Sections 6.3, 3.4)
• Data collection
• Empirical models and the differences between them
• High-order polynomials (but not the lagrangian form)
• Low-order polynomials, difference tables, and divided difference tables
• Splines
• Monte Carlo simulation
• Random and pseudo-random numbers
• Random Walks
• Queuing Model
• Optimization
• Linear programs geometrically: feasible regions, solution sets, sensitivity analysis
• Applications of graph theory to modeling

Things that may be on the Maple part of the exam:

• Plotting data points
• Plotting graphs of functions
• Transforming data points
• Fitting data visually
• Least squares fit (Regression)
• Residual plots
• Empirical model: One term models
• Empirical model: High-order polynomial
• Empirical model: Linear and Cubic splines
• (You will not need to do divided differences in Maple.)
• Simple if statement / for loops
• A simple simulation (perhaps area/volume or similar to rolling a die)
• Linear optimization

Some questions to help you study: 5.3.4, 7.3.1, 7.3.3, 7.5.2, 7.5.3

Exam 1: March 1, 2007
Extra Office Hours: Wednesday, February 28 after class in LN 2233

Exam 1 covers all classes from January 22 through February 26, which includes Sections 1.0-2.4, 3.0-3.4, 6.1-6.2, and 8.0-8.2 from the book.

Concepts you should understand for the exam: (So that you can answer questions about their theory.)

• The modeling process
• A mathematical model
• Types of models and their properties: fidelity, costs, flexibility
• Proportionality
• Difference equations and systems of difference equations
• Markov Chains
• Geometric Similarity
• Dimensionless products
• Dimensional Analysis and Buckingham's Theorem.
• In terms of linear algebra: eigenvalues, eigenvectors, nullspace, matrix multipication
• In terms of probability: independent events, rules for P(E_1 and E_2) and P(E_1 or E_2)
• Model Fitting
• Interpolation / Extrapolation
• Sources of error in the modeling process
• Transformations of the data
• Chebyshev Approximation Criterion
• Minimization of the sum of Absolute deviations
• Least-Squares Criterion

Things you may need to know for the exam:

• You may have to complete some part of the modeling process.
• You may have to create a dynamical system from a word problem.
• You may have to calculate/determine numerical solutions, equilibrium values, etc. for difference equations
• You may have to convert a system of difference equations to a linear algebraic form and then solve using linear algebra.
• I will not ask you to calculate eigenvalues and eigenvectors for a matrix larger than 2x2, but you need to know how to use them for larger sizes.
• You may have to solve a Markov Chain for an equilibrium solution.
• You may have to calculate system reliability given the reliability of the components.
• You may have to determine if proportionality is a reasonable assumption.
• You may have to estimate constants of proportionality visually
• You may have to use geometric similarity or dimensional analysis to predict a relationship between variables.
• You may have to compute dimensionless products of variables.
• You may have to fit a model to data visually.
• You may have to fit a model to data analytically.
• You may have to calculate absolute deviations of data to a given model.
• You may have to do a (simple) transformation of data.
• You may have to determine a best model from a set of possible best models.
• You may have to write out some maple code to show you understand seq and plot.

A couple extra problems to practice

• You haven't had much practice in Sections 3.2, 3.3 and 3.4; try out: 3.2.2 (try all three analytic methods), 3.4.1, 3.4.5, 3.3.1, 3.3.2. (Ordered in order of usefulness.)

Exam Expectations
        The exams are given in the Thursday sections of class, so they are 1:25 long. I plan to make the tests 1:00 long, so that there will be minimal time pressure.
        Of course, you will need to justify all your answers in order to have full credit, just like on the homework. If you use any theorems or methods, state them by name.