## Lectures & Schedule

DateTopic & NotesRecorded lectureOther resources
8/22/2022Course overview & introduction to python & Jupyter - see syllabusIntroduction to Jupyter Notebooks

Arrays in python

Intro exercises (completed) notebook
8/24/2022Taylor Series refresher

Numerical Differentiation
Taylor Series
Numerical Differentiation - Taylor Tables
Discretization 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 Problems
ODEs - 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
10/19/2022Local & Global Truncation Error

PDE Classification

Elliptic PDEs
Stability review

Local & Global Accuracy for time integration

PDE Classification

Elliptic PDEs
Notebook 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 1
Nonlinear 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