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"A little knowledge that acts is worth infinitely more than much knowledge that is idle."
~Kahlil Gibran

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              Links to topics in Math,Physics,and Electrical and Electronic Engineering.


Mathematics

Algebra - In Simplest Terms - a nice set of videos lectures covering Algebra. host Sol Garfunkel explains how algebra is used for solving real-world problems and clearly explains concepts that may baffle many students

Introductory Statistics  - Data Analysis: an applied approach to Statistics with Technology; Macromedia Flash)

Calculus I - Derivatives - A set of video lectures which covers topics in Calculus I: Limits, Derivatives, Applications of Derivatives, Integrals, and Applications of Integrals.

Calculus II - Integrals - A set

of
of video lectures which covers topics
in
in Calculus II: Integration techniques, Applications of Integration, Parametric equations and polar coordinates, Series & Sequences, Vectors, 3D Space.

Calculus III - Differential Equations -  A set of video lectures which covers topics in Calculus III: 3D Space, Partial Derivatives, Applications of partial derivatives, multiple integrals, line integrals, surface integrals.

A Video Introduction to Linear Algebra - These videos were recorded during  Professor Gilbert Strang's Class 18.06 at MIT in the Fall of 1999. They are all approximately 50 min. in length

Elementary Linear Algebra (pdf)

Differential Equations -A full set of Video lectures from MIT's Mathematics department.

Mathematical Methods for Engineers II- This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.

Calculus Videos - A Section of video lectures from University of Houston Department of Mathematics.  Topics a undergrad Calculus I topics. 

Calculus I, II, and III Video Lectures - Calculus for Scientists and Engineers. The full series Calculus I-III.

Mathematical Analysis I- This text carefully leads the student through the basic topics of real analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability.

Mathematical Tools for Physics - provides a one-semester bridge between some of the introductory math courses and the physics courses in which we expect to use the mathematics. This is the course typically called Mathematical Methods in Physics.

Multivariable Calculus - This is a textbook for a course in multivariable calculus. It has been used for the past few years here at Georgia Tech. The notes are available as Adobe Acrobat documents.

Calculusby Gilbert Strang - Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. 

Complex Analysis - This is a textbook for an introductory course in complex analysis. It has been used for our undergraduate complex analysis course here at Georgia Tech

Mathematical Equations - the international scientific-educational website EqWorld presents extensive information on solutions to various classes of ordinary differential, partial differential, integral, functional, and other mathematical equations.

Wolfram Alpha - Wolfram|Alpha is the first step in an ambitious, long-term project to make all systematic knowledge immediately computable by anyone. Enter your question or calculation, and Wolfram|Alpha uses its built-in algorithms and a growing collection of data to compute the answer.

Visual Calculus- A collection of modules that can help you with your Calculus studies.

Understanding Calculus - Understanding Calculus is a complete online introductory book that focuses on concepts. Integrated throughout the e-book are many engineering applications aimed at developing the student's scientific approach towards problem solving.


Mathematical Graphing Software
Discrete Mathematics Video Lectures

Various Math Video Lectures - A set of video lectures on various mathematical topics.

Entropy and Information Theory  - This site provides the current version of the book Entropy and Information Theory by R.M. Gray in the Adobe portable document format (PDF)

Fundamental Numerical Methods and Data Analysis (PDF)

Fundamentals of Model Theory  - Model Theory is the part of mathematics which shows how to apply logic to the study of structures in pure mathematics. On the one hand it is the ultimate abstraction; on the other, it has immediate applications to every-day mathematics. The fundamental tenet of Model Theory is that mathematical truth, like all truth, is relative. A statement may be true or false, depending on how and where it is interpreted. 

Fundamentals of Optimization - This is an introductory course in theory and methods for finite-dimensional continuous optimization. A mathematical optimization problem is one in which a given function is either minimized or maximized relative to some set or range of choices available in a given situation.

Advanced Calculus and Analysis 
The Calculus Bible
Calculus Unlimited
Difference Equations to Differential Equations: An Introduction to Calculus 
Computational Geometry
Differential Geometry
Differential Geometry and General Relativity

Algebraic Topology - This book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject. The viewpoint is quite classical in spirit, and stays well within the confines of pure algebraic topology.

Vector Bundles and K-Theory
Topology
Topology without Tears
Notes on a Variety of Math Topics

Physics


Video Lectures in College Physics with Calculus - This is a video instructional series on physics for college and high school classrooms and adult learners. It is comprised of 52 half-hour video programs that are arranged in the traditional sequence of topics.

Hyper Physics -  An excellent and concise resource to topics in Physics

Physics Notes - Another quick reference to Physics concepts.

Modern Physics

Essential Physics 1  - is an intensive introduction to classical and special relativity, Newtonian dynamics and gravitation, Einsteinian dynamics and gravitation, and wave motion. 

Electricity and Magnetism- In addition to the basic concepts of Electromagnetism, a vast variety of interesting topics are covered in this course: Lightning, Pacemakers, Electric Shock Treatment, Electrocardiograms, Metal Detectors, Musical Instruments, Magnetic Levitation, Bullet Trains, Electric Motors, Radios, TV, Car Coils, Superconductivity, Aurora Borealis, Rainbows, Radio Telescopes, Interferometers, Particle Accelerators (a.k.a. Atom Smashers or Colliders), Mass Spectrometers, Red Sunsets, Blue Skies, Haloes around Sun and Moon, Color Perception, Doppler Effect, Big-Bang Cosmology.

The Elegant Universe (3 hrs of Video)
Classical Mechanics (Video Lectures)

Classical Electromagnetism (Video Lectures)

Vibration and Waves (Video Lectures)

The Mechanical Universe and Beyond - A video instructional series on physics for college and high school classrooms and adult learners; 52 half-hour video programs and coordinated books

Classical Mechanics (video lectures) - is a first-semester freshman physics class in Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory. In addition to the basic concepts of Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory, a variety of interesting topics are covered in this course: Binary Stars, Neutron Stars, Black Holes, Resonance Phenomena, Musical Instruments, Stellar Collapse, Supernovae, Astronomical observations from very high flying balloons (lecture 35), and you will be allowed a peek into the intriguing Quantum World.

The Wonders of Physics (Video Lectures) -  aimed at generating interest in physics among people of all ages and backgrounds. The heart of the program is a fast-paced presentation of physics demonstrations carefully chosen to be entertaining as well as educational.

Physics Video Lectures

Exploring Black Holes: General Relativity & Astrophysics - Study of physical effects in the vicinity of a black hole as a basis for understanding general relativity, astrophysics, and elements of cosmology. Extension to current developments in theory and observation. Energy and momentum in flat spacetime; the metric; curvature of spacetime near rotating and nonrotating centers of attraction; trajectories and orbits of particles and light; elementary models of the Cosmos. Weekly meetings include an evening seminar and recitation. The last third of the semester is reserved for collaborative research projects on topics such as the Global Positioning System, solar system tests of relativity, descending into a black hole, gravitational lensing, gravitational waves, Gravity Probe B, and more advanced models of the Cosmos.


States of Matter  - John Murrell discusses the basic physical principles relating to the gaseous, liquid and solid states with the aid of models and demonstrations. Attention is drawn to phase changes and subtle features involving intermediate phases such as liquid crystals, supercritical fluids and pseudosolids. These aspects are developed further in interactive discussions.

Electricity, Magnetism and the Body - Anthony Barker.  The controlled ways that electricity and magnetism can stimulate the body are demonstrated and how the resulting responses can aid diagnosis discussed.

The Birth and Death of Stars  - We know that some stars exist because we can see them with our own eyes. In this lecture Walter Lewin provides illuminating evidence of stars we cannot see. Birth and death of stars; dwarves are just a few of the topics covered.

Introduction to Plasma Physics - A complete set of lecture notes for a graduate plasma physics course. Topics covered include particle orbit theory, fluid theory, wave theory, MHD theory, and kinetic theory.

An Introduction to Feynman Path Integrals
Classical Electrodynamics and Theory of Relativity
Conservation Laws - An interesting read in all things conservation
Electricity and Magnetism 

Electromagnetism and Optics - A complete set of lecture notes for a lower-division undergraduate electromagnetism and optics course. Topics covered include electric fields, Gauss' law, electric potential, capacitance, electric current, magnetism, magnetic induction, inductance, electromagnetic waves, geometric optics, paraxial optics, and wave optics. 

Fluid Dynamics
Introduction to Computational Physics - A complete set of lecture notes for an upper-division undergraduate computational physics course. Topics covered include scientific programming in C, the numerical solution of ordinary and partial differential equations, particle-in-cell codes, and Montecarlo methods. 

Introduction to Superstring Theory - In these lecture notes, an introduction to superstring theory is presented. Classical strings, covariant and light-cone quantization, supersymmetric strings, anomaly cancelation, compactification, T-duality, supersymmetry breaking, and threshold corrections to low-energy couplings are discussed. A brief introduction to non-perturbative duality symmetries is also included.

Newtonian Physics
Optical Physics and Quantum Electronics
Optics

Quantum Mechanics - A complete set of lecture notes for a graduate quantum mechanics course. Topics covered include fundamentals of quantum mechanics, angular momentum, perturbation theory, and scattering.

Quantum Principles and Particles
Relativistic Quantum Field Theory
Relativistic Quantum Fields
Special Relativity
Thermal and Statistical Physics - Topics in Thermal and Statistical Physics.

Thermodynamics and Statistical Mechanics - A complete set of lecture notes for an upper-division undergraduate thermodynamics and statistical mechanics course. Topics covered include elementary probability theory, classical thermodynamics, the thermodynamics of the atmosphere, heat engines, specific heat capacities of gases and solids, the Maxwell velocity distribution, paramagnetism, black-body radiation and the Stephan-Bolzmann law, conduction electrons in metals, and degeneracy pressure in white-dwarfs and neutron stars.

The Origin of Mass and the Feebleness of Gravity  - .Lecture by Frank Wilczek. This lecture proves the point, as Wilczek goes after one of the deepest questions in science: What is the origin of mass? Rewriting Einstein’s famous equation as m=E / c2 dramatizes that energy is the source of mass; energetic but massless quarks and gluons, Wilczek argues, give rise to mass by finding quasi-stable equilibrium states, better know as protons and neutrons. 

Bose-Einstein Condensates: The Coldest Matter in the Universe - Video Lecture. What happens when a gas is cooled to absolute zero? A new door to the quantum world opens up because all the atoms start "marching in lockstep", forming one giant matter wave . the Bose-Einstein condensate. This was predicted by Einstein in 1925, but only realized in 1995 in laboratories at JILA in Boulder and at MIT. Since then, many properties of this mysterious form of matter have been revealed, including matter wave amplification and quantized vortices. Bose condensates have been used to realize a basic atom laser, an intense source of coherent matter waves

The Age of Einstein - a brief introduction to Einstein's Theories of Special and General Relativity. It is a book for the inquisitive general reader who wishes to gain an understanding of the key ideas put forward by the greatest scientist of the 20th-century. No more than a modest grasp of High School Mathematics is required to follow the arguments.

Calculus-Based Physics - Calculus-Based Physics is an introductory physics textbook designed for use in the two-semester introductory physics course typically taken by science and engineering students.

Fields
Dyson's 1951 Lectures on Advanced Quantum Mechanics Second Edition
Superconductors For Beginners





Electrical Engineering


Lessons in Electric Circuits - A free set of books covering undergraduate topic in Electrical Engineering.

Discover Circuits - 25,000+ schematics. They also have great links to other tutorials.

Electronics Lab Projects - Tons of great projects
Sam Electronic Circuits- The best way to gain experience in EE is to build projects. This site has many hobbyist projects.

Circuit Exchange International- Another electronics hobbyist site.

Circuits and Electronics (Video Lectures) - The course introduces the fundamentals of the lumped circuit abstraction. Topics covered include: resistive elements and networks; independent and dependent sources; switches and MOS transistors; digital abstraction; amplifiers; energy storage elements; dynamics of first- and second-order networks; design in the time and frequency domains; and analog and digital circuits and applications. Design and lab exercises are also significant components of the course. 6.002 is worth 4 Engineering Design Points. The 6.002 content was created collaboratively by Profs. Anant Agarwal and Jeffrey H. Lang.

Principles of Digital Communications II (Video Lectures)    

Linear Integrated Circuits (Video Lecture)   

Digital Integrated Circuits (Video lectures) 

Signals and Systems (Video Lectures)  - Fourier Transforms, Laplace Transforms, Filters, etc.

Digital Signal Processing (Video Lectures) - Covers topics in DSP such as FIR, IIR, DFT, and FFT.

BASIC Stamp on GNU/Linux (pdf)
Transistors, LEDS, and Semiconducotrs - covers the operational theory, circuits, and configuration.

Basic Circuit Theory
Basic Soldering Guide - An EE should know how to solder (properly)
Capacitors - What are They Good For - the many uses of the capacitor.
Communications Electronics
DC Circuits
Dictionary of Electronics
Digital Logic - Basic introduction to digital logic.
Digital Logic Tutorial - Play Hookey
Electrical Engineering Circuits Archive
Electronics - Wikibooks
Fundamentals of Power Electronics
Introduction to Power Supplies - PDF - Talks about the different types of power supplies. Switching or Linear? hmmmm....
Electrical Circuit Formulas - All the formulae  you will need in circuit analysis classes.
Basic Electrical Laws and Circuit Theory