covers four major algorithm design techniques (greedy algorithms, divide-and-conquer, dynamic programming and network flow)
covers classical algorithm: Gale Shapley Algorithm, interval scheduling and weighted interval scheduling, the Knapsack Problem, Bellman-Ford in DAG (directed acyclic graph), Ford-Fulkerson Algorithm, Max-Flow Min-Cut, Bipartite matching, Edmonds-Karp Algorithm
undecidability and NP-completeness
MAE6810 Methods of Applied Math I
Cartesian tensor
Linear algebra
Complex variable
MAE6820 Methods of Applied Math II
Partial differential equation
Tensor analysis
Calculus of variations
CEE6790 Time Series Data Analysis
Data processing tools and techniques: Fourier transforms, convolution, filtering, autoregressive moving average (ARMA) models
CHEME6800 Computational Optimization
Systems optimization modeling including theory and algorithms of linear, nonlinear, mixed-integer linear, mixed-integer nonlinear optimization;
Stochastic programming, robust optimization, optimization methods for big-data analysis
PHYS6780 Computational Physics
Numerical methods for ordinary and partial differntial equations
Linear algebra and eigenvalue problems, numerical integration
Fast Fourier transforms and spectral method
CS6820 Matrix Computations
Linear systems and Gaussian elimination, structured linear system
Least squares problems
Unsymmetric eigenvalue problems
Symmetric eigenvalue problems
Iterative methods for linear systems and eigenvalue problem
MAE6140 State Variable Modeling
Introduce to the state variable modeling framework, which is used for the representation of a broad range of material behaviors and material systems, including metals, polymers and composites
MAE5730 Intermediate Dynamics and vibration
Used three approaches: Newton Euler method, Lagrangian method and differential algebraic equations (DAE) approach to solve classical dynamics of single- and multi-degree-of-freedom systems, which is made up of particles, rigid-objects in 2 and 3 spatial dimensions
MAE7160 Fracture Mechanics
Mechanics of fracture, including linear elastic and elastic-plastic fracture theory, energy release rate, J integral, experimental methods, computational fracture mechanics and applications;
solving partial differential equation using MATLAB PDE Toolbox
MAE6110 Foundations of Solid Mechanics I
fundamentals of kinematics of deformation, traction and stress, and balance of momentum;
Constitutive theory for linear and nonlinear elastic bodies, including isotropic and orthotropic behaviors;
Boundary conditions, requirements for well-posed problems, and uniqueness.
MAE6120 Foundations of Solid Mechanics II
Dimensional analysis and normalization,Nonlinear beam theory (large deflection and buckling),Linear and von-karman plate theory, buckling of plates, Indentation problems (Hertz and Johnson-Kendall-Roberts theory), Thin film mechanics, Thermal stress and 2D elasticity problems
CEE7780 Continuum Mechanics & Thermodynmaics
kinematics; conservation laws; the entropy inequality; constitutive relations: frame indifference, material symmetry; and finite elasticity, rate-dependent materials, and materials with internal state variables