Lectures & Schedule

Lecture notes and resources will be posted here.  Please check this page frequently.

Date	Topic & Notes	Recorded lecture	Other resources
8/22/2022	Course overview & introduction to python & Jupyter - see syllabus		Introduction to Jupyter Notebooks Arrays in python Introductory exercises (download only) Intro exercises (completed) notebook
8/24/2022	Taylor Series refresher Numerical Differentiation	Taylor Series Numerical Differentiation - Taylor Tables	Discretization notebook
8/29/2022		Lagrange Polynomials & Richardson Extrapolation
8/31/2022	Vector Norms	Convergence, vector norms	notebook with tips for HW1 problem 1
9/7/2022	Introduction to ODEs Boundary Value Problems	ODEs - Overview ODE BVPs 1 - finite difference method
9/12/2022		BVP example, Tridiagonal systems, Finite Volume Method	ODE BVP example notebook
9/14/2022	Newton's Method for Nonlinear Equations	Nonlinear Equations	Bisection demo notebook Newton's method demo notebook
9/19/2022		Nonlinear Systems of Equations Linearization for nonlinear BVPs
9/21/2022		Nonlinear BVPs and systems of BVPs	Linearization example notebook for a single BVP Newton's method example notebook for nonlinear BVP Notebook demonstrating a general matrix (not tridiagona) formulation
9/26/2022	Initial Value ODEs	IVP ODEs - explicit methods	Notebook showing Forward Euler
9/28/2022		IVP ODEs - Backward Euler
10/3/2022	Stability	Implicit Time Integrators Stability - part 1
10/5/2022	Midterm 1
10/17/2022		Stability of ODE Integrators	Stability notebook
10/19/2022	Local & 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
10/24/2022	Parabolic PDEs	Parabolic PDEs	Implicit solution of parabolic PDEs (notebook) Explicit solution of Parabolic PDEs (notebook)
10/26/2022	Hyperbolic PDEs	Nonlinear Parabolic PDE example Hyperbolic PDEs - part 1	Nonlinear parabolic PDE example notebook Hyperbolic PDE notebook
10/31/2022	Stability for Parabolic PDEs	Modified equations & stability analysis - advection Stability for Parabolic PDEs Flux limiters - part 1
11/2/2022	Verification for PDE Solutions	Flux limiters - part 2 Verification for PDEs
11/7/2022	Numeric Integration	Numeric Integration
11/9/2022	Introduction to Optimization	Optimization - part 1	Notebook on optimization
11/14/2022	Midterm 2 review
11/16/2022	Midterm 2
11/21/2022	Least Squares Regression	Least Squares Regression	projectile regression example notebook
11/28/2022	Other regression models	Other Regression Techniques