Course Description
Modeling and analysis of engineering problems under uncertainty with applications of probability and statistical concepts and methods. Data collection, measurements, simulation, model development, misinformation, validation, and analysis with environmental applications.
Athena Title
MODEL, STAT ANALY
Prerequisite
MATH 2260
Semester Course Offered
Offered every year.
Grading System
A - F (Traditional)
Course Objectives
By the end of this course, students will have an understanding of: (1) The uncertainty inherent to collection of environmental data (2) Simulation and analysis within uncertain environmental problem spaces (3) The principles and concepts of probability and statistics in analyzing and designing environmental engineering systems (4) A systematic technique for describing uncertainty and realizing risk in environmental applications (5) Quantitative methods for describing direct and indirect relationships among environmental variables
Topical Outline
1) Descriptive statistics a) Means, medians, variance, co-variance, percentiles 2) Programming in MATLAB a) MATLAB language b) Vectors and matrices in MATLAB c) Variables, arrays and scripts d) Loops 3) Probability a) Sample spaces b) Assigning probabilities c) Outcomes d) Distributions e) Random variables in environmental applications f) Independent events g) Joint and conditional probabilities h) Repeated trials 4) Combinatorics a) Combinatorial methods b) Combinatorial techniques for evaluating probability 5) Simulation a) Stochastic b) Monte Carlo c) Deterministic d) Probability distributions e) Expectation f) Population mean and variance 6) Evaluating risk within uncertain domains 7) Data fitting 8) Error associated with measurements 9) Error propagation 10) Time series 11) Central Limit Theorem 12) Sampling a) Populations, samples, random sampling b) Error associated with sampling c) Confidence intervals 13) Hypothesis formulation 14) Analysis of variance a) T-test b) Chi-squared c) F statistics d) ANOVA e) Linear regression f) Significance testing
Syllabus