Course Description

Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems.

Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined 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. Control, reachability, state transfer, and least-norm inputs. Observability and least-squares state estimation.

Prerequisites: Exposure to linear algebra and matrices (as in Math. 103). You should have seen the following topics: matrices and vectors, (introductory) linear algebra; differential equations, Laplace transform, transfer functions. Exposure to topics such as control systems, circuits, signals and systems, or dynamics is not required, but can increase your appreciation.

Courses Index

1 :

Advanced Topics in Circuit Design (Elad Alon / Berkeley)

2 :

Introduction to Digital Integrated Circuits (Jan RABAEY / Berkeley)

3 :

Advanced Analog Integrated Circuits (Elad Alon / Berkeley)

4 :

Introduction to Microelectronic Circuits (Bernhard BOSER / Berkeley)

5 :

The Fourier Transform and its Applications (Brad Osgood / Stanford)

6 :

Convex Optimization I (Stephen Boyd / Stanford)

7 :

Convex Optimization II (Stephen Boyd / Stanford)

8 :

Circuits and Electronics (Anant Agarwal / MIT)

9 :

Computer System Engineering (Samuel Madden / MIT)

10 :

Introduction to Algorithms (Erik Demaine / MIT)

11 :

Principles of Digital Communications I (Lizhong Zheng / MIT)

12 :

Principles of Digital Communication II (David Forney / MIT)

13 :

Understanding Lasers and Fiberoptics (Shaoul Ezekiel / MIT)

14 :

Electromagnetics and Applications (Multiple Instructors / MIT)

15 :

Information and Entropy (Paul Penfield / MIT)

16 :

Fundamentals of Laser (Sabieh Anwar / LUMS)

17 :

Synchrotron Radiation for Materials Science (David Attwood / Berkeley)

18 :

Linear Integrated Circuits (Clark Nguyen / Berkeley)

19 :

Digital Circuit Design (Ken Boyd / University of New South Wales)

20 :

Speech and Audio Processing (Multiple Multiple / University of New South Wales)