10.34 | Fall 2005 | Graduate

Numerical Methods Applied to Chemical Engineering

Lecture Notes

These lecture notes are from the version of the course taught during Fall 2001.

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

Course Info

Fall 2005
Learning Resource Types
Exams with Solutions
Problem Sets with Solutions