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Last updated:

September 14, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

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Description

This course focuses on the use of modern computational and mathematical techniques in chemical engineering.

Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment.

Course Curriculum

  • Expressing Systems of Linear Algebraic Equations as: Ax=b Unlimited
  • Matrix Addition and Matrix/Vector Multiplication Unlimited
  • Reduction of Ax=b to Triangular Form by Gaussian Elimination Unlimited
  • Gauss-Jordan Elimination Unlimited
  • Pivoting Techniques in Gaussian Elimination Unlimited
  • Multiplication of Matrices/Matrix Transpose Unlimited
  • Basis Sets and Gram-Schmidt Orthogonalization Unlimited
  • Null Space (kernel) and Existence/Uniqueness of Solutions Unlimited
  • The Determinant of a Square Matrix Unlimited
  • The Inverse of a Square Matrix Unlimited
  • LU Decomposition Unlimited
  • Cholesky Decomposition Unlimited
  • MATLAB® Programming Example: TR_1D_model1_SS Unlimited
  • MATLAB® Programming Example: TR_1D_model1_SSmake_file.m Unlimited
  • MATLAB® Programming Example: read_program_input Unlimited
  • MATLAB® Programming Example: read_solver_input Unlimited
  • MATLAB® Programming Example: get_input_scalar Unlimited
  • MATLAB® Programming Example: set_grid_1D Unlimited
  • MATLAB® Programming Example: plot_results Unlimited
  • MATLAB® Programming Example: TR_1D_model1_SS_solver Unlimited
  • MATLAB® Programming Example: calc_epsilon Unlimited
  • MATLAB® Programming Example: stack_state Unlimited
  • MATLAB® Programming Example: unstack_state Unlimited
  • MATLAB® Programming Example: DAE_SS_solver_1 Unlimited
  • MATLAB® Programming Example: TR_1D_model1_func_calc_b_int Unlimited
  • MATLAB® Programming Example: reaction_network_model Unlimited
  • MATLAB® Programming Example: shift_rxn_source_term Unlimited
  • MATLAB® Programming Example: jacket_heat_transfer Unlimited
  • MATLAB® Programming Example: TR_1D_model1_func_calc_A_int Unlimited
  • MATLAB® Programming Example: FinDiff_1D_FirstDeriv Unlimited
  • MATLAB® Programming Example: FinDiff_1D_SecondDeriv Unlimited
  • MATLAB® Programming Example: shift_discretization_matrix Unlimited
  • MATLAB® Programming Example: implement_Dankwert_BC Unlimited
  • MATLAB® Programming Example: discretize_boundary_deriv Unlimited
  • MATLAB® Programming Example: assert_scalar Unlimited
  • MATLAB® Programming Example: assert_vector Unlimited
  • MATLAB® Programming Example: assert_matrix Unlimited
  • MATLAB® Programming Example: assert_structure Unlimited
  • MATLAB® Programming Example: CSTR_SS Unlimited
  • MATLAB® Programming Example: CSTR_ODE Unlimited
  • MATLAB® Programming Example: CSTR_ODE_input1 Unlimited
  • MATLAB® Programming Example: polymer_flow_1D_prog_develop Unlimited
  • MATLAB® Programming Example: polymer_flow_1D_files Unlimited
  • MATLAB® Programming Example: Quasi-Newton Optimization cost_function1.m Unlimited
  • MATLAB® Programming Example: Quasi-Newton Optimization simple_minimizer.m Unlimited
  • MATLAB® Programming Example: Quasi-Newton Optimization plot_2D_Fcost.m Unlimited
  • MATLAB® Programming Example: Linear Least Squares simple_linear_LS.m Unlimited
  • MATLAB® Programming Example: Linear Least Squares simple_LS.m Unlimited
  • MATLAB® Programming Example: Linear Least Squares fit_eta_prime.m Unlimited
  • MATLAB® Programming Example: Linear Least Squares frequency.dat Unlimited
  • MATLAB® Programming Example: Linear Least Squares eta_prime.dat Unlimited
  • MATLAB® Programming Example: Simple Nonlinear Least Squares nlin_fit_kinetics_setup.m Unlimited
  • MATLAB® Programming Example: Simple Nonlinear Least Squares simple_nonlinear_LS.m Unlimited
  • MATLAB® Programming Example: Simple Nonlinear Least Squares nlin_fit_kinetics.m Unlimited
  • MATLAB® Programming Example: Simple Nonlinear Least Squares nlin_fit_kinetics_tdot.m Unlimited
  • Numerical Routines for Solving Non-linear Algebraic Equations Newton_1D_test Unlimited
  • Numerical Routines for Solving Non-linear Algebraic Equations Newton_2D_test1b Unlimited
  • Numerical Routines for Solving Non-linear Algebraic Equations reduced_Newton Unlimited
  • Numerical Routines for Solving Non-linear Algebraic Equations approx_Jacobian_FD Unlimited

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Massachusetts Institute of Technology