Finite element analysis is now widely used for solving complex static
and dynamic problems encountered in engineering and the sciences.
Differential
Equations are the language in which the laws of nature are expressed.
Understanding properties of solutions of differential equations is
fundamental to much of contemporary science and engineering. Ordinary
differential equations (ODE's) deal with functions of one variable,
which can often be thought of as time.
Principles of Continuum Applied Mathematics covers fundamental concepts
in continuous applied mathematics, including applications from traffic
flow, fluids, elasticity, granular flows, etc. The class also covers
continuum limit; conservation laws, quasi-equilibrium; kinematic waves;
characteristics, simple waves, shocks; diffusion (linear and nonlinear);
numerical solution of wave equations; finite differences, consistency,
stability; discrete and fast Fourier transforms; spectral methods;
transforms and series (Fourier, Laplace). Additional topics may include
sonic booms, Mach cone, caustics, lattices, dispersion, and group
velocity.
This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra.
Introduction to the dynamics and vibrations of lumped-parameter models
of mechanical systems. Kinematics. Force-momentum formulation for
systems of particles and rigid bodies in planar motion. Work-energy
concepts. Virtual displacements and virtual work. Lagrange's equations
for systems of particles and rigid bodies in planar motion.
Linearization of equations of motion. Linear stability analysis of
mechanical systems. Free and forced vibration of linear multi-degree of
freedom models of mechanical systems; matrix eigenvalue problems.
Introduction to numerical methods and MATLAB® to solve dynamics and
vibrations problems.