Linear Algebra Course From MIT

Course Description
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Lecture Videos

Lecture 1: The geometry of linear equations (Watch Here)
Lecture 2: Elimination with matrices (Watch Here)
Lecture 3: Multiplication and inverse matrices (Watch Here)
Lecture 4: Factorization into A = LU (Watch Here)
Lecture 5: Transposes, permutations, spaces R^n (Watch Here)
Lecture 6: Column space and nullspace (Watch Here)
Lecture 7: Solving Ax = 0: pivot variables, special solutions (Watch Here)
Lecture 8: Solving Ax = b: row reduced form R (Watch Here)
Lecture 9: Independence, basis, and dimension (Watch Here)
Lecture 10: The four fundamental subspaces (Watch Here)
Lecture 11: Matrix spaces; rank 1; small world graphs (Watch Here)
Lecture 12: Graphs, networks, incidence matrices (Watch Here)
Lecture 13: Quiz 1 review (Watch Here)
Lecture 14: Orthogonal vectors and subspaces (Watch Here)
Lecture 15: Projections onto subspaces (Watch Here)
Lecture 16: Projection matrices and least squares (Watch Here)
Lecture 17: Orthogonal matrices and Gram-Schmidt (Watch Here)
Lecture 18: Properties of determinants (Watch Here)
Lecture 19: Determinant formulas and cofactors (Watch Here)
Lecture 20: Cramer's rule, inverse matrix, and volume (Watch Here)
Lecture 21: Eigenvalues and eigenvectors (Watch Here)
Lecture 22: Diagonalization and powers of A (Watch Here)
Lecture 23: Differential equations and exp(At) (Watch Here)
Lecture 24: Markov matrices; fourier series (Watch Here)
Lecture 24b: Quiz 2 review (Watch Here)
Lecture 25: Symmetric matrices and positive definiteness (Watch Here)
Lecture 26: Complex matrices; fast fourier transform (Watch Here)
Lecture 27: Positive definite matrices and minima (Watch Here)
Lecture 28: Similar matrices and jordan form (Watch Here)
Lecture 29: Singular value decomposition (Watch Here)
Lecture 30: Linear transformations and their matrices (Watch Here)
Lecture 31: Change of basis; image compression (Watch Here)
Lecture 32: Quiz 3 review (Watch Here)
Lecture 33: Left and right inverses; pseudoinverse (Watch Here)
Lecture 34: Final course review (Watch Here)


Please feel free to leave a comment if there is a dead link or a problem with the links.

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Introduction to Matlab Video Course

Introduction
By the end of this free course you will be able to get the basic and advanced knowledge of the programming using MATLAB . Starting from introducing the variables and the vectors until you will be able to build your own program like “The Angry Birds” program.

Course Videos

Title	Duration
01 Introduction Desktop, Arithmetic	9 min. 56 sec.
02 Introduction Variables, mathematical functions, vectors, plotting	12 min. 5 sec.
03 Introduction systems of equations, demo, Mexican hat	9 min. 14 sec.
04 Introduction Programs, m files	10 min 23 sec.
05 Variables Scalars and Vectors	11 min. 4 sec.
06 Matrices. Simple Program	10 min. 12 sec.
07 Numbers and Operators	9 min. 25 sec.
08 Operators and Operations on Arrays	12 min. 5 sec.
09 Formula Vectorization, output, format	15 min. 28 sec.
10 Introducing for loops	23 min. 31 sec.
11 Introducing if statements	13 min. 12 sec.
12 Logical operators and if statements	17 min. 57 sec.
13 Complex numbers	6 min. 37 sec.
14 Output with fprintf	5 min. 1 sec.
15 Input function	1 min. 42 sec.
16 Programming Steps	5 min. 13 sec.
17 Angry Birds Program	23 min. 17 sec.
18 Common Functions	9 min. 56 sec.
19 Beam Deflection Problem	5 min. 58 sec.
20 Logical Vectors	8 min. 35 sec.

Please feel free to leave a comment if there is a dead link or a problem with the links.

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Understanding Lasers and Fiberoptics Video Course

Course Description

Lasers are essential to an incredibly large number of applications. Today, they are used in bar code readers, compact discs, medicine, communications, sensors, materials processing, computer printers, data processing, 3D-imaging, spectroscopy, navigation, non-destructive testing, chemical processing, color copiers, laser "shows", and in the military. There is hardly a field untouched by the laser. But what exactly is so unique about lasers that makes them so effective?

This brief video course is designed for engineers, scientists, medical personnel, managers, and others who work with lasers and/or fiberoptics, or who anticipate working with lasers and/or fiberoptics, yet have little or no background in laser or fiberoptic basics. The course focuses on fundamentals and emphasizes a physical intuitive interpretation of laser and fiberoptic phenomena and their applications. Because Prof. Ezekiel keeps mathematics to a minimum, the topics covered are easily understood, without the need for a strong technical background. Prof. Ezekiel uses plain language, graphic illustrations, and video demonstrations to explain the basic characteristics of lasers and fiberoptics.

High quality versions of the videos are also available through Zeelase.
These videos were produced by the MIT Center for Advanced Engineering Study.

Video Lectures
LASER FUNDAMENTALS I
LASER FUNDAMENTALS II
LASER FUNDAMENTALS III
LASER FUNDAMENTALS III (CONT.)
FIBEROPTICS FUNDAMENTALS

Download
You can download the Resource material HERE

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Adaptive Antennas and Phased Arrays Course

Course Description
Adaptive antennas and phased arrays, with rapidly scanned beams or multiple beams, are commonly suggested for radar and communications systems in ground-based, airborne, and spaceborne applications that must function in the presence of jamming and other sources of interference.
This lecture series begins with a discussion of the fundamentals of adaptive antennas pertaining to radar and communications systems, with an emphasis on consumption of adaptive array degrees of freedom from the jammer's viewpoint. Displaced phase center antenna array mutual coupling effects in the problem of adaptive suppression of radar clutter is discussed in Lecture 2. Next, in Lectures 3 through 5 a theoretical foundation for a focused near-field technique that can be used to quantify the far-field adaptive nulling performance of a large aperture adaptive phased array system is described. Simulations of focused near-field and focused far-field nulling performance for adaptive arrays are presented for arrays of isotropic elements in Lecture 3 and for arrays including mutual coupling effects in Lectures 4 and 5. Experimental testing of the focused near-field adaptive nulling technique for phased arrays is described in Lecture 6. An experimental high-resolution multiple-beam adaptive-nulling antenna system is described in Lecture 7.
Lectures 8 through 16 then concentrate on phased array antenna development for a variety of array elements. Lecture 8 provides an introduction to phased array antenna theory. In Lecture 9, finite and infinite array analyses and measurements for periodic phased arrays of monopole elements are presented. Lecture 10 describes the focused near-field polarization characteristics of monopole phased arrays as related to adaptive array testing in the near field. Next, in Lecture 11 a test bed phased array that implements the displaced phase center antenna technique, as related to the analysis presented in Lecture 2, is described along with the planar near field testing technique that is used to assess adaptive clutter cancellation performance. The planar near field scanning method for measuring low-sidelobe radiation patterns of phased arrays is described in Lecture 12. Experimental arrays of horizontally polarized loop-fed slotted cylinder antennas (Lecture 13), dual-polarized dipole arrays (Lecture 14), and ultrawideband dipole arrays (Lecture 15) are described. In Lecture 16, rectangular waveguide arrays are analyzed by the method of moments.


Video lectures and lecture notes

1. Adaptive Antennas and Degrees of Freedom
2. Array Mutual Coupling Effects on Adaptive Radar Clutter Suppression
3. Focused Near-Field Techniques for Evaluating Adaptive Phased Arrays
4. Moment Method Analysis of Focused Near-Field Adaptive Nulling
5. Focused Near-Field Testing of Multiphase-Center Adaptive Array Radar Systems
6. Experimental Testing of Focused Near-Field Adaptive Nulling
7. Experimental Testing of High Resolution Nulling with a Multiple Beam Antenna
8. Phased Array Antennas - An Introduction
9. Monopole Phased Array Antenna Design, Analysis, and Measurements
10. Monopole Phased Array Field Characteristics in the Focused Near-Field Region
11. Displaced Phase Center Antenna Measurements Using Near-Field Scanning
12. Low-Sidelobe Phased Array Antenna Measurements Using Near-Field Scanning
13. Arrays of Horizontally Polarized Omnidirectional Elements
14. Finite Arrays of Crossed V-Dipole Elements
15. Experimental Ultrawideband Dipole Antenna Array
16. Finite Rectangular Waveguide Phased Arrays

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Electromagnetic Fields and Energy Video Lectures

Course Description

Published in 1989 by Prentice-Hall, this book is a useful resource for educators and self-learners alike. The text is aimed at those who have seen Maxwell's equations in integral and differential form and who have been exposed to some integral theorems and differential operators. A hypertext version of this textbook can be found here. An accompanying set of video demonstrations is available below.

These video demonstrations convey electromagnetism concepts. The demonstrations are related to topics covered in the textbook. They were prepared by Markus Zahn, James R. Melcher, and Manuel L. Silva and were produced by the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology.

The purpose of these demonstrations is to make mathematical analysis of electromagnetism take on physical meaning. Based on relatively simple configurations and arrangements of equipment, they make a direct connection between what has been analytically derived and what is observed. They permit the student to observe physically what has been described symbolically. Often presented with a plot of theoretical predictions that are compared to measured data, these demonstrations give the opportunity to test the range of validity of the theory and present a quantitative approach to dealing with the physical world.

The short form of these videos contains the demonstrations only. The long form also presents theory, diagrams, and calculations in support of the demonstrations.

Course Contents

Chapter 1: Maxwell's integral laws in free space (PDF)

1.3.1, 1.5.1: Coulomb's force law and measurements of charge

Demo

- Demo and Theory

1.4.1: Magnetic field of a line current

Demo

- Demo and Theory

1.6.1: Voltmeter reading induced by magnetic induction

Demo

- Demo and Theory

Chapter 2: Maxwell's differential laws in free space (PDF)

Chapter 3: Introduction to electroquasistatics and magnetoquasistatics (PDF)

Chapter 4: Electroquasistatic fields: the superposition integral point of view (PDF)

4.7.1: Charge induced in ground plane by overhead conductor

Demo  -

Demo and Theory

Chapter 5: Electroquasistatic fields from the boundary value point of view (PDF)

5.5.1: Capacitance attenuator

Demo

- Demo and Theory

Chapter 6: Polarization (PDF)

6.6.1: An artificial dielectric

Demo

- Demo and Theory

Chapter 7: Conduction and electroquasistatic charge relaxation (PDF)
7.5.1: Distribution of Unpaired Charge (Courtesy of Education Development Center, Inc. Used with permission.) Demo - Demo and Theory
7.5.2: Rotation of an Insulating Rod in a Steady Current (Courtesy of Education Development Center, Inc. Used with permission.) Demo - Demo and Theory
7.7.1: Relaxation of Charge on Particle in Ohmic Conductor (Courtesy of Education Development Center, Inc. Used with permission.)Demo - Demo and Theory
7.7.1 Supplement: Van de Graaff and Kelvin generators (Courtesy of Education Development Center, Inc. Used with permission.)Demo - Demo and Theory

7.7.2: Electrostatic precipitation

Demo

- Demo and Theory

Chapter 8: Magnetoquasistatic fields: superposition integral and boundary value points of view (PDF)

8.2.1: Field of a circular cylindrical solenoid

Demo

- Demo and Theory

8.2.2: Field of square pair of coils

Demo

- Demo and Theory

8.4.1: Surface used to define the flux linkage

Demo

- Demo and Theory

8.5.1: Field and inductance of a spherical coil

Demo

- Demo and Theory

 8.6.1: Surface currents induced in ground plane by overhead conductor Demo - Demo and Theory

8.6.2: Inductive attenuator

Demo

- Demo and Theory

Chapter 9: Magnetization (PDF)

9.4.1: Measurement of B-H characteristic

Demo

- Demo and Theory

Chapter 10: Magnetoquasistatic relaxation and diffusion (PDF)
 10.0.1: Nonuniqueness of voltage in a magnetoquasistatic (MQS) system Demo - Demo and Theory

10.4.1: Currents induced in a conducting shell

Demo

- Demo and Theory

10.2.1: Edgerton's boomer

Demo

- Demo and Theory

10.4.1: Currents induced in a conducting shell

Demo

- Demo and Theory

Chapter 11: Energy, power flow, and forces (PDF)
11.6.2: Force on a liquid dielectric (Courtesy of Education Development Center, Inc. Used with permission.) Demo - Demo and Theory

11.7.1: Steady state magnetic levitation

Demo

- Demo and Theory

Chapter 12: Electrodynamic fields: the superposition integral point of view (PDF)

Chapter 13: Electrodynamic fields: the boundary value point of view (PDF)

13.1.1: Visualization of standing waves

Demo

- Demo and Theory

Chapter 14: One-dimensional wave dynamics (PDF)

Chapter 15: Overview of electromagnetic fields (PDF)

• Electromagnetic Fields and Energy Solutions Manual. (DOWNLOAD HERE)
• The course materials can be downloaded from the following link. (DOWNLOAD HERE)

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