FINAL EXAM – Tuesday, May 7, KT 216, 10:30-12:30 a.m.

Dr. Peter Dragnev

KT 290, tel. 481-6382

Email: dragnevp@ipfw.edu

OFFICE HOURS: Monday, May 6, 9 a.m. – 12 p.m.

The Final Exam will cover Chapters 5, 6, 7, and 13. It will consist of two parts. For the first part (approx. 30 min) the students will be expected to give definitions of the terms and comment on the topics below (no literature allowed), as well as solve simple problems, not requiring technology. The second part (approx. 90 min) will consist of problem solving, which will involve also writing algorithms and programming on computers. For this part the use of literature, such as book, projects, handouts, and program printouts will be allowed.

**CH. 5 **Model fitting, empirical model, interpolation,
approximation; formulation error, truncation error, round-off error, measurement
error; absolute deviation, data transformation, Chebyshev criterion, residuals,
linear programming; least-squares criterion, deviation of best least-squares
fit of linear curve (y=ax+b).

**CH. 6 **Lagrange interpolation theorem and Lagrange
interpolation formula, advantages and disadvantages of high order polynomial
models, smoothing, differences and divided differences; spline functions,
cubic splines, natural spline, clamped spline.

**CH. 7 **Monte Carlo simulation, probabilistic vs.
deterministic process and behavior; Monte Carlo algorithms and programs
for finding area, volume, experiments involving coins, dice; random numbers,
middle-square and linear congruence methods, cycling; queuing problems
and models (be able to solve simple queuing problems, similar to the 4-ship
problem in the book).

**CH. 13** Dimensionless products, products, dimension,
basic dimensions, dimensional homogeneity, dimensional constant; linear
system, coefficients and constants of linear system, homogeneous system,
trivial solution, linear combination, independent set of solutions, complete
set of solutions; basic products, Buckingham’s theorem.