Page 203 - Postgraduate Catalog 2024-25

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deal with issues relevant to all course Master of Theory, and stochastic
course. Cases, real or simulated, that CIV 509 – Probability, Decision
topics will be discussed and analyzed processes
and students will be asked to report Science in Civil
on them. Credit Hour: 3
Engineering Prerequisite: Graduate Standing

A course that covers advanced
topics in probability and provides an
Core Courses
introduction to Bayesian statistical
decision theory and stochastic
CIV 502 - Advanced Engineering processes. Topics include: The
Mathematics role of uncertainty in engineering
projects. Introduction to sample
Credit Hour: 3 spaces and events; random variables;
axioms of probabilities; simple
Prerequisite: Graduate Standing probabilities of events. Probability of
A course that covers advanced union and intersection; conditional
topics in engineering mathematics probability; combinatorics:
and applications of the material Counting methods; applications
in advanced engineering models. to engineering problems. Total
Topics include: Ordinary differential probability theorem; Bayes theorem;
equations (ODEs): Linear equation of engineering applications. Random
order one and Bernoulli’s equation, variables and distributions:
integrating factors, coefficients discrete and continuous probability
linear in the two variables, linear functions(PMF); cumulative
equations with constant coefficients, distribution function (CDF); histogram
nonhomogeneous equations with and probability distribution models.
undetermined coefficients auxiliary Jointly distributed random variables;
equation and hyperbolic functions, joint PMF; marginal PMF; conditional
and variation of parameters. Partial PMF. Moments and expectation;
differential equations (PDEs): Method engineering applications; common
of separation of variables, boundary probabilistic models: Bernoulli and
value problems, orthogonality of Binomial distributions; Poisson
sines, cosines, solutions of Laplace’s distribution. Geometric and negative
equation, solution inside a rectangle binomial distribution; Time between
and inside a circular disk, vibrating events: exponential distribution;
membranes; numerical methods Gamma distribution; Models from
for solution of ODEs and PDEs, and limiting cases: Normal distribution,
advanced topics in linear algebra central limit theorem; using normal
(matrices, eigenvalue problems, tables; lognormal distribution.
bases, transformations, and Extreme value distribution; Beta,
numerical solutions); linear algebra chi-square, t and F distributions
applications in advanced engineering and tables. Statistical inference:
models: Artificial Neural Networks classical and Bayesian methods;
(ANN), and Linear Programming- hypothesis testing; engineering
Simplex Method. The course applications. Introduction to
concludes with a research-based statistical decision theory; decision
project on applications of the above trees; engineering applications.
material in engineering problems. Bayesian statistical decision theory;
goal function; Bayes risk function;
prior and posterior distributions.
Introduction to stochastic process;
stationarity; ergodicity; Markov
chains; engineering applications. The
course includes a project report and
presentation.

Abu Dhabi University | Postgraduate Catalog 2024 - 2025