SciComp@UNC Courses

1.Undergraduate courses

1.1.Differential equations (MATH383, MATH528)

• Exact differential forms: definition and Mathematica examples

• Direction fields and phase portraits: definition, Maxima examples and plots

• Commented test solutions

• Webinar on differential systems: Infection screening clinics; Susceptible, Infectious, Recovered model; Coupled oscillators

• Homework on first-order differential equations: mathematical typesetting, Maxima verification of solutions

1.2.Linear algebra (MATH547, MATH547DS)

• Matrix spaces

• Least squares: normal equations, polynomial interpolation with Octave examples

• Singular Value Decomposition

• Concept synopsis

1.3.Modeling (MATH564, MATH590)

• Modeling reproduction

• Stochastic model theory

• Topology used in cell type identification

2.Graduate courses

2.1.Scientific computation

• Finite difference formulas: embedded Mathematica generation, analysis

• Gibbs phenomenon in shock propagation

• Eigenvalue problem: theory, webinar showing simple cytoskeleton model construction

2.2.Continuum mechanics

• Tensors

• Large deformation theory

• Elastic media

2.3.Kinetic models

• Theory of lattice Boltzmann methods: Mathematica evaluation of moments, Hermite polynomial expansions