pt. I. Fitting functions to data. Exact fitting ; Approximate fitting ; Tomographic image reconstruction ; Efficiency and non-linearity
pt. II. Ordinary differential equations. Reduction to first order ; Numerical integration of initial-value problems ; Multidimensional stiff equations : implicit schemes ; Leap-frog schemes
pt. III. Two-point boundary conditions. Examples of two-point problems ; Shooting ; Direct solution ; Conservative differences, finite volumes
pt. IV. Partial differential equations. Examples of partial differential equations ; Classification of partial differential equations ; Finite-difference partial derivatives
pt. V. Diffusion. parabolic partial differential equations. Diffusion equations ; Time-advance choices and stability ; Implicit advancing matrix method ; Multiple space dimensions ; Estimating computational cost
pt. VI. Elliptic problems and iterative matrix solution. Elliptic equations and matrix inversion ; Convergence rate ; Successive over-relaxation ; Iteration and non-linear equations
pt. VII. Fluid dynamics and hyperbolic equations. The fluid momentum equation ; Hyperbolic equations ; Finite differences and stability
pt. VIII. Boltzmann's equation and its solution. The distribution function ; Conservation of particles in phase-space ; Solving the hyperbolic Boltzmann equation ; Collision term
pt. IX. Energy-resolved diffusive transport. Collisions of neutrons ; Reduction to multigroup diffusion equations ; Numerical representation of multigroup equations
pt. X. Atomistic and particle-in-cell simulation. Atomistic simulation ; Particle-in-cell codes
pt. XI. Monte Carlo techniques. Probability and statistics ; Computational random selection ; Flux integration and injection choice
pt. XII. Monte Carlo radiation transport. Transport and collisions ; Tracking, tallying, and statistical uncertainty
pt. XIII. Next steps. Finite-element methods ; Discrete Fourier analysis and spectral methods ; Sparse-matrix iterative Krylov solution ; Fluid evolution schemes
Appendix A. Summary of matrix algebra. Vector and matrix multiplication ; Determinants ; Inverses ; Eigenanalysis.
