Paths To Knowledge (dot Science)

To understand climate science one must be able to comprehend the jargon based language used by climate scientists. This series of of 20 lectures (of about one hour and 10 minutes each) touches on some math topics used in climate science such as those listed here:

Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, gives an overview of the course, Introduction to Linear Dynamical Systems (EE263).

Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares approximations of over-determined equations and least-norm solutions of under determined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions.

1. Overview
2. Linear functions
3. Linear algebra review
4. Orthonormal sets of vectors and QR factorization
5. Least-squares
6. Least-squares applications
7. Regularized least-squares and Gauss-Newton method
8. Least-norm solutions of under determined equations
9. Autonomous linear dynamical systems
10. Solution via Laplace transform and matrix exponential
11. Eigenvectors and diagonalization
12. Jordan canonical form
13. Linear dynamical systems with inputs and outputs
14. Example: Aircraft dynamics
15. Symmetric matrices, quadratic forms, matrix norm, and SVD
16. SVD applications
17. Example: Quantum mechanics
18. Controllability and state transfer
19. Observability and state estimation
20. Summary and final comments

The lecture slides in one PDF file.

1. Overview

2. Linear functions

3. Linear algebra review

4. Orthonormal sets of vectors and QR factorization

5. Least-squares

6. Least-squares applications

7. Regularized least-squares and Gauss-Newton method

8. Least-norm solutions of under determined equations

9. Autonomous linear dynamical systems

10. Solution via Laplace transform and matrix exponential

11. Eigenvectors and diagonalization

12. Jordan canonical form

13. Linear dynamical systems with inputs and outputs

14. Example: Aircraft dynamics

15. Symmetric matrices, quadratic forms, matrix norm, and SVD

16. SVD applications

17. Example: Quantum mechanics

18. Controllability and state transfer

19. Observability and state estimation

20. Summary and final comments