## Lectures & Schedule

DateTopic & NotesRecorded lectureOther resources
8/23/2021Course overview & introduction to python & Jupyter - see syllabusClass overview & syllabus discussion
Taylor series review
Introduction to Jupyter Notebooks

Arrays in python

8/25/2021Taylor Series refresher

Numerical Differentiation
Numerical 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 ODEs
Intro to ODEs
Boundary Value Problems - part 1
Example 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 - linearization
Nonlinear 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

Stability
Integrator demo
10/4/2021Classification of PDEs
Elliptic PDEs
ODE stability (part 2)
PDE Classification
10/6/2021Midterm 1
10/18/2021Parabolic PDEsElliptic PDE solution
Parabolic PDEs - part 1
PDE-Elliptic.ipynb
10/20/2021Hyperbolic PDEsParabolic PDEs - part 2
Hyperbolic PDEs - motivation
PDE-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 approaches
Kernel 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