Graduate Courses
This course offers an introduction to numerical analysis and various computational techniques for solving complex engineering problems. Topics include mathematical and computational foundations of the numerical approximation; regression and interpolation; integration and differentiation; finite differences method. Students will also work on implementing abstract mathematical constructions into working prototypes of numerical code. Upon completion of this course, you will have an overview of the main ideas of numerical computing and will have a solid foundation for reading up on and working with more advanced numerical needs of your specific subject area.
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Fundamentals of the formulation and application of the finite element method to problems of continuum mechanics, including problems in solid mechanics. Exposure to engineering mathematics (matrix operatoin, differenctial equations) at an undergraduate level is assumed. Knowledge of Matlab programming is an asset.
The course provides the basic concepts and fundamentals of optimization. It covers problems addressed by operations research, and problem formulations in linear programs. It includes the graphical solution of linear programs, simplex method, duality and sensitivity analysis, transportation model, assignment model, network planning, and advanced methods and algorithms for solving optimization problems.
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Topics: Boundary-value problems. Methods of approximation. Time dependent problems. Isoparametric elements. Numerical integration. Computer implementation. Mesh generation and layouts. Two-dimensional finite elements.
- Learning Objectives: Understand the value of statistics and its use in quantitative research methods
- Distinguish among different types of data associated with different outcomes/results
- Appraise statistical methods and tests used in published studies
- Understand the challenges associated with choosing statistical tests and methods
- appropriate to the research question, sampling of populations, level of data collected and data analysis
- Understand the foundations of probability and hypothesis testing
- Understand, create, and interpret graphical summaries
- Understand the importance and mechanisms for sample size calculations
- Perform with confidence one and two samples comparisons and infer their significance and accuracy (p-‐values, confidence intervals) based on the type of outcome/variable.