# 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)