Lectures

This page will be updated after class and is meant to serve as a historical record of what has been covered. Also, sample codes presented during lecture will be provided here. Lecture notes will not be posted online.

Topic Material Examples Intro and Basic Concepts Ch 1, Appendix A Intro to Computational Methods 1.1 Numbers and errors 1.2-1.3 precision_test.m, summing.m, aqchem_ex.m MATLAB, Systems of Linear Equations Appendix A, Ch. 4 MATLAB review (scripts, functions, scope, debugging), Intro to linear equations Appendix A, 4.1 fibonacci_example.m Gauss Elimination, Gauss-Jordan, Backsubstitution 4.1 - 4.4 myfunc.m, GEBS_vs_GJ.pdf MATLAB, Systems of Linear Equations Appendix A, Ch. 4 LU decomposition, matrix inverse 2.3, 2.4, 4.5-4.6 Existence, conditioning, and iterative algorithms (Gauss-Seidel, Jacobi) 2.3, 2.4, 4.7, 4.10, 4.11 Iterative Solutions, Nonlinear Equations Ch. 4, Ch. 3 Iterative solutions and programming sqrt_demo.m Nonlinear equations 3.1 - 3.5 bisection.m Nonlinear Equations Ch. 3 Nonlinear equations 3.6 - 3.10 roots_demo.m Linear Regression Intro 6.1 - 6.2 linear_regression.m Midterm and review Ch. 1 - 4 Midterm review Ch. 1 - 4 concept_list.pdf Midterm Regression Ch. 6 Linear transformations, quality of fit (R2, residuals, p-value), multiple linear regression 6.1 - 6.4 linear_regression_race.m, cp.m, cp_data.txt, LagrangeINT.m Midterm review, polynomial regression and interpolation 6.1 - 6.5 see code above from 10/10 Splines and Numerical Differentiation Ch. 6, 8 Spline interpolation 6.6 Finite Difference 8.1 - 8.4 Numerical Differentiation and Integration Ch. 8, 9 FD error scalinng and extrapolation 8.5, 8.8, 8.9 numerical_diff.m Numerical integration Numerical Integration and Review Ch. 6, 8, 9 Numerical integration error 9.9 - 9.10 Midterm Review Ch 6, 8, 9 ODEs and Midterm Ch. 10 Intro to ODEs 10.1 - 10.2 worksheet.pdf Midterm Ch 6, 8, 9 ODEs 10 Euler Methods 10.1 - 10.3 euler_ode.m Accuracy, Stability, and MATLAB ODE solvers predprey_driver.m, predpreyODE.m ODEs 10 Accuracy, Stiffness, Higher-order ODEs 10.9 - 10.14 springs_driver.m, diffeq_springs.m, stiff_driver.m, diffeq_stiff.m Boundary Value Problems: Shooting Method 11.2 shooting_example.m ODEs and PDEs 11 ODE finite difference 11.3 fd_example.m PDEs Advection advection.m PDEs and review Method of Lines heat_equation_pde.m No class - please complete your FCQs online