MARINE SCIENCE (MASC)

MASC 781.  Numerical ODE/PDE, I.  3 Credits.  

Single, multistep methods for ODEs: stability regions, the root condition; stiff systems, backward difference formulas; two-point BVPs; stability theory; finite difference methods for linear advection diffusion equations.

Rules & Requirements  
Requisites: Prerequisites, MATH 661 and 662.  
Grading Status: Letter grade.  
Same as: MATH 761, ENVR 761.  
MASC 782.  Numerical ODE/PDE, II.  3 Credits.  

Elliptic equation methods (finite differences, elements, integral equations); hyperbolic conservation law methods (Lax-Fiedrich, characteristics, entropy condition, shock tracking/capturing); spectral, pseudo-spectral methods; particle methods, fast summation, fast multipole/vortex methods.

Rules & Requirements  
Requisites: Prerequisite, MATH 761.  
Grading Status: Letter grade.  
Same as: MATH 762, ENVR 762.  
MASC 783.  Mathematical Modeling I.  3 Credits.  

Nondimensionalization and identification of leading order physical effects with respect to relevant scales and phenomena; derivation of classical models of fluid mechanics (lubrication, slender filament, thin films, Stokes flow); derivation of weakly nonlinear envelope equations. Fall.

Rules & Requirements  
Requisites: Prerequisites, MATH 661, 662, 668, and 669.  
Grading Status: Letter grade.  
Same as: MATH 768, ENVR 763.  
MASC 784.  Mathematical Modeling II.  3 Credits.  

Current models in science and technology: topics ranging from material science applications (e.g., flow of polymers and LCPs); geophysical applications (e.g., ocean circulation, quasi-geostrophic models, atmospheric vortices).

Rules & Requirements  
Requisites: Prerequisites, MATH 661, 662, 668, and 669.  
Grading Status: Letter grade.  
Same as: MATH 769, ENVR 764.  
MASC 940.  Research in Marine Sciences.  2-21 Credits.  
Rules & Requirements  
Grading Status: Letter grade.  
Same as: BIOL 953.