Lectures & Schedule

You can join the zoom lectures by following this link.¬† You’ll need the password that was in the email you received prior to the first day of class, and is also posted on Piazza.

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

DateTopic & NotesRecorded lectureOther resources
8/24/2020Course overview & introduction to python & Jupyter - see syllabusIntroduction to Jupyter Notebooks

Arrays in python

Introductory exercises (download only)
8/26/2020Deriving some common governing equationsGoverning equations - part 1Some notes on the material derivative
Interactive Material Derivatives (download notebook)
8/31/2020Governing equations - part 2 (previous year recording)
9/2/2020Taylor series review

Numeric differentiation
Numeric differentiation - part 1Taylor series notebook

Numeric derivatives notebook
9/9/2020Numeric differentiation - part 2
9/14/2020ODE Intro

Boundary Value ODEs
Intro to ODEs; Finite difference for BVPs
9/16/2020Supplemental notes on vector normsDiscussion of error norm calculations; BVP part 2A notebook on norms

Jupyter notebook to solve the 1D heat equation problem from class notes
9/21/2020Nonlinear systems of equationsFinite Volume; Nonlinear BVP intro
9/23/2020Newton's method demo

Nonlinear equations & Jacobian formation

Linearization BVP example
Bisection notebook

Newton's method notebook

Linearization for BVPs example notebook
9/28/2020Initial Value Problem ODEsTips on matrix setup for BVPs; Explicit IVP techniques (Forward Euler, Runge Kutta)Notebook for Forward Euler
9/30/2020Adams Bashforth, FE example, Backward Euler
Integrator demo notebook
10/5/2020Stability of ODE integratorsImplicit time integrators, stabilityStability notebook
Nonlinear ODE eigenvalues notebook
Stiff ODE Systems stability demo
10/12/2020Stability & systems of ODEs
10/14/2020PDE Classification

Elliptic PDEs

PDE classification; Elliptic PDEsElliptic PDE notebook
10/19/2020Parabolic PDEsParabolic PDEsLinear parabolic PDE example

Nonlinear PDE example
10/21/2020Hyperbolic PDEsParabolic PDEs (part 2), hyperbolic PDEs (part 1)
10/26/2020Hyperbolic PDEs & modified equation analysisHyperbolic PDE notebook
10/28/2020Stability for parabolic systems

Verification & Convergence
Flux limiter review; Stability for Parabolic PDEs; VerificationConvergence notebook
11/2/2020Numeric IntegrationVerification (part 2)

Numeric Integration
11/4/2020Least Squares RegressionLeast Squares RegressionSupplemental "soft-start" summary of linear least squares
11/9/2020Other regression techniques

Review for midterm
Midterm review; non-parametric regression/machine learningKernel regression notebook
11/11/2020Midterm 2
11/16/2020OptimizationOptimization - part 1Optimization notebook
11/18/2020Optimization - part 2