Lectures & Schedule Lecture notes and resources will be posted here. Please check this page frequently. DateTopic & NotesRecorded lectureOther resources 8/22/2022Course overview & introduction to python & Jupyter - see syllabusIntroduction to Jupyter Notebooks Arrays in python Introductory exercises (download only) Intro exercises (completed) notebook 8/24/2022Taylor Series refresher Numerical DifferentiationTaylor Series Numerical Differentiation - Taylor TablesDiscretization notebook 8/29/2022Lagrange Polynomials & Richardson Extrapolation 8/31/2022Vector NormsConvergence, vector normsnotebook with tips for HW1 problem 1 9/7/2022Introduction to ODEs Boundary Value ProblemsODEs - Overview ODE BVPs 1 - finite difference method 9/12/2022BVP example, Tridiagonal systems, Finite Volume MethodODE BVP example notebook 9/14/2022Newton's Method for Nonlinear EquationsNonlinear EquationsBisection demo notebook Newton's method demo notebook 9/19/2022Nonlinear Systems of Equations Linearization for nonlinear BVPs 9/21/2022Nonlinear BVPs and systems of BVPsLinearization example notebook for a single BVP Newton's method example notebook for nonlinear BVP Notebook demonstrating a general matrix (not tridiagona) formulation 9/26/2022Initial Value ODEsIVP ODEs - explicit methodsNotebook showing Forward Euler 9/28/2022IVP ODEs - Backward Euler 10/3/2022Stability Implicit Time Integrators Stability - part 1 10/5/2022Midterm 1 10/17/2022Stability of ODE IntegratorsStability notebook 10/19/2022Local & Global Truncation Error PDE Classification Elliptic PDEsStability review Local & Global Accuracy for time integration PDE Classification Elliptic PDEsNotebook on accuracy Notebook on Elliptic PDEs 10/24/2022Parabolic PDEsParabolic PDEsImplicit solution of parabolic PDEs (notebook) Explicit solution of Parabolic PDEs (notebook) 10/26/2022Hyperbolic PDEsNonlinear Parabolic PDE example Hyperbolic PDEs - part 1Nonlinear parabolic PDE example notebook Hyperbolic PDE notebook 10/31/2022Stability for Parabolic PDEsModified equations & stability analysis - advection Stability for Parabolic PDEs Flux limiters - part 1 11/2/2022Verification for PDE SolutionsFlux limiters - part 2 Verification for PDEs 11/7/2022Numeric IntegrationNumeric Integration 11/9/2022Introduction to OptimizationOptimization - part 1Notebook on optimization 11/14/2022Midterm 2 review 11/16/2022Midterm 2 11/21/2022Least Squares RegressionLeast Squares Regressionprojectile regression example notebook 11/28/2022Other regression modelsOther Regression Techniques