Modeling and Simulations in Engineering

Overview and applications of FE theory in linear static and dynamic systems. Review of matrices, strain and stress tensors. Variational and energy principles in FEA. Applications in linear stress analysis; 1D, 2D and 3D. Transient solutions; modal analysis. Modeling concepts. Use of general purpose codes like ANSYS, NISA, ARIES. Project work. Graduate standing or special permission. (3 credits)

The course emphasizes the exact methods used in the solution of the partial differential equations that arise in advanced engineering problems. Examples are taken from heat transfer, fluid dynamics, solid mechanics, electromagnetic theory, vibrations, etc. Linear integral equations, time dependent boundary conditions, nonlinear boundary conditions, and other topics. Graduate standing or special permission. (3 credits)

The course introduces students to the fundamentals of computational fluid dynamics and heat transfer. Classification of partial differential equations and formulation of well-posed problems. Spatial and temporal approximation techniques for partial differential equations: stability, consistency and convergence. Finite volume formulations. Survey of methods for solving hyperbolic, elliptic, and parabolic problems. Formulation of discrete boundary conditions. Application of methods to one- and two-dimensional flow and heat transfer problems. (3 credits)

This course covers fundamental properties of linear dynamic systems. Topics include linear space, linear operators, Eigen-values/vectors, canonical form, representation, solution of state equations, stability, controllability, observability, design of state feedback control and development of observers with application examples in mechanical engineering. (3 credits)

Full Course Title: Battery Systems, Modeling, and Control This course will cover modeling, control, and estimation techniques for battery systems. Students will learn how electrochemical systems work and how they can be mathematically described. A simple phenomenological electrical circuit model and a detailed physics-based model that can capture diffusion dynamics will be covered. The thermal behavior of a battery system and its modeling will be covered as well. Students will learn the basic functions of battery management systems for monitoring state-of-charge, state-of-power, and state-of-health in applications to automotive and consumer electronics. (3 credits)

Review of FE theory in linear static. FEA in dynamics. FEA in heat transfer. FEA in fluid mechanics. FEA in nonlinear problems; material and geometrical nonlinearities, total and updated Lagrangian formulations, solution techniques. Use of FE codes. Graduate standing or special permission. (3 credits)

This course will present the mathematical models and constitutive behavior of engineering materials subjected to mechanical and non-mechanical loads. It will consider both linear and non-linear models to describe elastic, plastic, viscoelastic, viscoplastic, hypo-and hyper-elastic response of materials to mechanical loads. Non-mechanical loads will include thermal and electro-mechanical fields. Micro-scale and multi-scale mechanical modeling will also be introduced. (3 credits)

This course will first introduce systems modeling approach and then develop mathematical models for ride, vibration, handling control, etc. of automobiles. The models will then be used to examine the design and performance of an automobile from a systems point of view. (3 credits)

This course is designed to introduce the applications of finite element method in automotive structure design. It includes specific design examples of vehicle NVH and durability with commercial pre-processor and FEA solver. The course also provides theoretical knowledge of FEA and vehicle design.

This course aims to provide knowledge on vehicle crash mechanics, structutal design to improve crashworthiness and crash energy management. Finite element techniques for vehicle crash analysis are also covered. (3 credits)

This course studies the numerical solution of ordinary and partial differential equations using finite difference methods. Topics include convergence, stability, efficiency, numerical simulation and applications of these methods. (3 credits)

This course will introduce the students to theory and application of wavelets using linear algebra. Topics will include the discrete Fourier transform, the fast Fourier transform, linear transformations, orthogonal decomposition, discrete wavelet analysis, the filter bank, Haar Wavelet family, and applications. Additional reading assignments or projects will distinguish this course from its undergraduate version MATH 458. Students cannot receive credit for both MATH 458 and MATH 558. (3 credits)

The processes of constructing, implementing, and evaluating mathematical models of "real world" phenomena are investigated. Models involving continuous and discrete mathematical constructs are considered. Deterministic and stochastic models are compared. Examples are taken from genetics, epidemiology, queuing theory, and other fields. Additional reading assignments or projects will distinguish this course from its undergraduate version MATH 462. Students cannot receive credit for both MATH 462 and MATH 562. (3 credits)

Solution of linear systems by Gaussian elimination, solution of non-linear equations by iterative methods, numerical solution of ordinary differential equations, data fitting with spline functions, numerical integration, optimization. Additional reading assignments or projects will distinguish this course from its undergraduate version MATH 472. Students cannot receive credit for both MATH 472 and MATH 572. (3 credits)

A study of the most effective methods for finding the numerical solution of problems which can be expressed in terms of matrices, including simultaneous linear equations, orthogonal projections and least squares, eigenvalues and eigenvectors, positive definite matrices, and difference and differential equations. Additional reading assignments or projects will distinguish this course from its undergraduate version MATH 473. Students cannot receive credit for both MATH 473 and MATH 573. (3 credits)

ME 510 Winter

ME 518 Fall, Winter

ME 525 Fall

ME 564 Fall

ME 576 Winter

ME 610 Various semesters

ME 611 Fall

AENG 502 Fall

AENG 551 Winter

AENG 650 Winter

MATH 514 Various semesters

MATH 558 Various semesters

MATH 562 Fall

MATH 572 Fall

MATH 573 Various semesters