Applied Mathematics in Chemical Engineering

PART I : Mathematical Modeling

• Modeling procedure
  1- Lumped formulation
  2- Distributed formulation
  3- Mixed lumped and distributed formulation

• Modeling Examples : momentum, heat and mass transfer

PART II : Analytical Methods

• Review of ordinary differential equations
  1- 1st order differential equations
  2- 2nd order differential equations with constant coefficients
  3- Special 2nd order differential equations (trigonometric, Euler, Bessel, Legander, ...)

• Orthogonal functions and Sturm-Liouville problem

• Solution of partial differential equations using separation of variable method
  1- Laplace equation (two dimensional)
  2- Poison equation (two dimensional)
  3- Diffusion equation (one dimensional)

PART III : Numerical Methods

• Introduction to numerical analysis and MATLAB programming

• Solution of ordinary differential equations: initial-value problems
  1- Single-step methods: Euler's, Heun's, and Runge-Kutta methods
  2- Multi-step methods: Adams-Bashforth-Moulton predictor-corrector methods

• Solution of ordinary differential equations: boundary-value problems
  1- Shooting methods: linear and nonlinear (Newton's)
  2- Finite-difference methods: solving linear and nonlinear systems

• Solution of partial differential equations: initial-value problems on finite intervals
  1- Heat equation: explicit, implicit, and Crank-Nicholson difference methods
  2- Stability analysis and errors of finite difference methods