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Applied Mathematics for Environmental Engineers

Course Information:

Course ID:ΑΒ-308
Type of Course:Elective
Semester:Fall
ΕCTS:9

Instructors: Associate Professor T. Daras, Associate Professor A. Manoussakis

Recommended Reading:

(Α)   ORDINARY/PARTIAL DIFFERENTIAL EQUATIONS

  • Y.A.Cengel, W.J.Palm III, Differential equations for engineers and scientists, McGraw Hill, 2013.
  • W.E.Boyce – R.C.DiPrima, Elementary differential equations and boundary value problems, Wiley, 10th ed.

(Β)   SIGNALS –SYSTEMS – FOURIER TRANSFORMS

  • Hwei Hsu, Signals and Systems, Schaums outlines, 2nd ed., 2011.

(C)   PROBABILITY – STATISTICS

  • A.Papoulis, Probability, Random variables and Stochastic Processes, international ed, 4th, McGraw Hill, 2012.

(D)   TIME SERIES

  • Chatfield,C. The analysis of time series. An introduction, Chapman & Hall.

Eclass:

  • Registration required

Course objectives:

This is an introductory graduate course on the topics: ordinary and partial differential equations, signals and systems, Laplace and Fourier transforms, simple and multiple linear regression, cluster analysis, time series, knowledge necessary to an Environmental engineer. Using this knowledge he/she can solve, by constructing mathematical models, real life environmental problems. During the lectures, the analytical theory (in each one of the subjects) is given and mathematical models/scenarios for environmental problems are being constructed. SPSS, MINITAB, MATLAB software are also being introduced and implemented.

 

 

Syllabus:

1st WeekOrdinary differential equations. Initial value problems. O.D.E.’ s of first and second order.
2nd Week:Applications of O.D.E.’s to population models, exponential decay, mixing, law of cooling. Introduction to Partial Differential Equations.
3rd WeekLaplace transform. Applications in mechanics, electricity e.t.c. 
4th WeekSignals and systems
5th WeekFourier transform of a signal.  Face recognition.
6th Week:Review of Probability. Conditional probability. Independence. Random variables
7th Week:Simple linear regression. SPSS software
8th Week:Multiple linear regression. Cluster analysis.
9th Week:Normality tests. Chi square test of independence.
10th Week:Introduction to time series (definition, characteristics, stationarity, autocorrelation function). MINITAB software
11th Week:Time series decomposition. Applications of time series.
12th Week:Smoothing methods.  Decomposition & smoothing comparison.
13th Week:Projects presentation

Assessment method:

  • Homework problems (20%)
  • Project (50%)
  • Final exam (30%)

Last modification: 0-10-2019