Lectures & Schedule Lecture notes and resources will be posted here. Please check this page frequently. DateTopic & NotesRecorded lectureOther resources 8/23/2021Course overview & introduction to python & Jupyter - see syllabusClass overview & syllabus discussion Taylor series reviewIntroduction to Jupyter Notebooks Arrays in python Introductory exercises (download only) 8/25/2021Taylor Series refresher Numerical DifferentiationNumerical derivatives - part 1Discretization notebook 8/30/2021Error Norms Lagrange polynomial examples; vector norms & convergencehomework 1 tips (jupyter notebook) 9/1/2021Convergence; Modified wavenumber analysis 9/8/2021ODE Introduction Boundary value ODEsIntro to ODEs Boundary Value Problems - part 1Example BVP solution notebook 9/13/2021Nonlinear systems of equationsThomas algorithm, Finite Volume methods, intro to nonlinear systems 9/15/2021Nonlinear EquationsBisection demo Newton's method demo 9/20/2021Nonlinear Systems - part 2 Nonlinear BVPs - linearizationNonlinear BVP example 9/23/2021Initial Value ODEsTips on matrices for systems of BVPs Initial Value Problems (part 1) 9/27/2021IVPs part 2 9/29/2021Stability of time integratorsIVP ODEs part 3 StabilityIntegrator demo 10/4/2021Classification of PDEs Elliptic PDEsODE stability (part 2) PDE Classification 10/6/2021Midterm 1 10/18/2021Parabolic PDEsElliptic PDE solution Parabolic PDEs - part 1PDE-Elliptic.ipynb 10/20/2021Hyperbolic PDEsParabolic PDEs - part 2 Hyperbolic PDEs - motivationPDE-Parabolic-Implicit-Linear.ipynb PDE-Hyperbolic.ipynb 10/25/2021Hyperbolic PDEs & Modified Equation Analysis 10/27/2021Parabolic PDE stability analysis Hyperbolic PDEs - Flux Limiters Parabolic PDEs - stability 11/1/2021VerificationVerification 11/3/2021Numeric IntegrationManufactured solutions Numeric Integration 11/8/2021Least Squares RegressionLinear Least Squares Regression 11/10/2021Midterm 2 11/15/2021Other Regression TechniquesNonlinear Least Squares Regression Other Regression approachesKernel regression notebook 11/17/2021OptimizationIntroduction to Optimization 11/24/2021Governing EquationsGoverning equations - part 1 11/29/2021Governing equations - part 2 12/1/2021Governing equations - part 3