Textbooks: (free download)

• Introduction to Applied Linear Algebra, Boyd and Vandenberghe, Cambridge University
  Press, 2018 
• Exploring ODEs, Trefethen, Birkisson, and Driscoll, SIAM Publishing, 2018

Course Platforms: MS Teams and Blackboard.

Course Technology Requirements: Computer, internet, microphone and webcam.

Course Overview: The course is divided into two parts. Part I introduces vectors, matrices, and least squares methods, related topics on applied linear algebra that are behind modern data science and other applications, including document classification, prediction model from data, enhanced images, control, state estimation, and portfolio optimization. We will quickly review Part I.1 Vectors and I.2 Matrices in the first two weeks, and then focus on Part I.3 Least Squares and more advanced examples and applications in the following two and half weeks. Part II aims to use Chebfun, an open-source MATLAB package, to explore ODEs and bring new perspectives and insights on topics that are ubiquitous in advanced applications, including heat conduction, chemical reactions, chaos, population dynamics, deformations of a beam, radioactivity, bifurcation theory, stability theory, infectious diseases, nerve signals, vibrations, dynamics of networks, ballistics, planetary dynamics.

Detailed Syllabus (PDF)

Syllabus:  Chapter 1, Chapter 2, Chapter 3, Chapter 4 (4.1-4.4), Chapter 5 (5.1-5.2) (probably not covered)

Course Description: The general theory of Vector Spaces and Linear Transformations will be developed in an axiomatic fashion. Determinants will be covered  to study eigenvalues, eigenvectors and diagonalization.
Grading:  There will be  three  Tests and the Final. I will take the two highest test scores (60%) and the mandatory final (40%). Tests and the Final are based on homework problems and material covered in class.

The instructor will cover Sections 5-7 of the textbook. Topics include: Eigenvalues/Eigenvectors, Cayley-Hamilton Theorem, Inner Products and Norms, Adjoints of Linear Operators, Normal and Self-Adjoint Operators, Orthogonal and Unitary Operators, Jordan Canonical Form, Minimal Polynomials.

TBA