Objectives We study the mechanical behavior of
materials—deformation and stress responses under external
forces—through mathematical modeling. Emphasis is placed
on one-dimensional reductions for common loading cases,
including axial loading, torsion, and bending.
Objectives
Inverse problems provide a mathematical framework for extracting unknown parameters from observational data. This course combines theory and practice through applications in image processing, subsurface characterization, damage detection, and device optimization.
Schedule
Preliminaries
Calculus of Variation
Regularization Theory (Tikhonov regularization, total variation methods)
Adjoint Method
Optimization (line search, steepest descent, Newton method, Gauss-Newton, inexact Newton)
Materials
Lecture notes: TBA
Structural Analysis 1
Objectives
We study mathematical modeling and analysis to understand the behavior (reactions, moments, deformations, etc.) of fundamental civil structures (beams, trusses, frames, arches, etc.) under loads. Topics include freebody diagrams, the principle of virtual work, analysis of indeterminate structures, and influence lines.
Schedule
Preliminaries
Introduction to Structural Analaysis
Reactions and Internal Forces by Freebody Diagrams
chickadee: Python script for 2D frame analysis (under development)
Please be careful when using the software, as it may have many bugs and errors that could lead to incorrect analyses.
Finite Element Method
Objectives This course introduces the mathematical
foundations and numerical methods underlying the Finite
Element Method (FEM). Topics include approximation theory,
variational principles, the Ritz method, discretization
using various shape functions, and numerical integration
techniques.
Schedule
Preliminaries
Introduction to finite element method
One-dimensional model problem
Linear elasticity
Electromagnetism
Shape functions
Time integration
Software implementation (using Petsc, Slepc, and Gmsh)