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Geosci 561: Mathematical Modeling for Geoscientists
Spring, 2003
Week
Jan. 14/16 Course overview; introduction to the Unix computer lab (Kasting)
Solving simple algebraic equations on the computer
Newtons method in 1 dimension: solving a quadratic equation
Jan. 21/23 The carbon cycle and the uptake of fossil fuel CO_{2} (Kasting)
Application of Newtons method to more complex systems: carbonate
equilibria
Jan. 28/30 Solving simultaneous systems of algebraic equations (Kasting)
Newtons method in N dimensions/solving matrix problems numerically
Feb. 4/6 Combined carbon cycle and greenhouse effect (Kasting)
Application: carbonate equilibria revisited
Feb. 11/13 Models of diffusion (Alley)
Ficks laws applied to heat flow
Solving Laplaces equation (steadystate heat conduction): Jacobi
iteration, GaussSeidel iteration, and successive overrelaxation
Feb. 18/20 Ordinary differential equations (ODEs) (Kasting)
Stiff systems of equations
Simple implicit and explicit methods for solving ODES (forward and
reverse Euler method, CrankNicholson method)
Feb. 25/27 Box models of the carbonatesilicate cycle (Kasting)
Application of implicit methods to a stiff, nonlinear system: the BLAG
model
Mar. 1/3 Box modeling of fossil fuel CO_{2} uptake (Kasting)
(No new labcontinue BLAG model)
Mar. 1014 Spring break
Mar. 18/20 Initial conditions and boundary conditions (Alley)
Steadystate heat conduction with gradient boundary conditions and
internal heat generation
Mar. 25/27 Introduction to partial differential equations (PDEs) (Kasting)
Converting PDEs to systems of ODEs by finite differencing
Solving such systems using implicit methods
Lab to be determined
Apr. 1/3 Timedependent heat conduction (Alley)
Nonsteady, 1D heat conduction with sinusoidal surface T and constant
T at depth/tridiagonal matrix solvers
Apr. 8/10 PDE solution methods (cont.) (Kasting)
Lab to be determined
Apr. 15/17 Groundwater flow (Alley)
Numerical solution of simple groundwater flow problems
Apr. 22/24 Groundwater flow cont. (Alley)
A 29/M 1 Course wrapup (Alley, Kasting)
Lab to be determined