ME303OVERVIEW.MWS
Physical Problem
Mathematical Formulation
Domain definition
Coordinate system
Physical Laws
Conservation Principles
Boundary Conditions
Initial Conditions
Differential Formulation
Integral Formulation
Solution Methods
Analytical
Numerical
Approximate Analytical
Control of System
Optimization of System
Half-space
Finite Region
Semi-infinite Region
Hooke's Law (Elasticity)
Newton's Law of Viscosity (Fluids)
Fick's Law (Mass Diffusion)
Fourier's Law (Heat Conduction)
Ohm's Law (Current Flow)
Conservation Principles
Conservation of Mass (Continuity)
Conservation of Momentum
Conservation of Energy
Other Conservation Principles
Analytical Methods
Separation of Variables
Similarity
Laplace Transform
Fourier Sine and Cosine Transforms
Hankel Transform
Other Tranforms
Types of Partial Differential Equations
Laplace Equation
Poisson Equations
Diffusion (Heat) Equation
Diffusion Equation with Source Term
Wave Equation
Wave Equation with Damping Term
Helmholtz Equation
Classification of Partial Differential Equations
Elliptic
Hyperbolic
Parabolic
Boundary Conditions
Boundary Condition of First Kind. Dirichlet Condition
Boundary Condition of Second Kind. Neumann Condition
Boundary Condition of Third Kind. Robin Condition
Mixed Condition
Perfect Contact Condition
Numerical Methods
Finite Difference
Finite Element
Boundary Integral Equation
Surface Element
Other Numerical Methods
Boundary Layer Approximations
Momentum Equations
Energy Equation
Special Functions
Gamma function
Bessel functions of first and second kinds of integer and fractional order
Modified Bessel functions of first and second kinds of integer and fractional order
Error and complementary error functions
Elliptic integral of the first and second kinds
Legendre polynomials
Solution Tools
Computer Algebra Systems
Maple
Mathematica
Macsyma
Matlab
Mathcad
Other Computer Algebra Systems
Spreadsheets
Excel
QuattroPro
Lotus 123