Massachusetts Institute of Technology has recorded a series of video lectures on electricity and magnetism from the 8.02 Physics II course that was instructed by Prof. Walter Lewin in the spring of 2002. He is well-known at MIT and beyond for his dynamic and engaging lecture style and have received numerous awards for his excellence in teaching.
There is a total of 36 videos with an average of 50 minutes each. It serves as an invaluable resource for physics undergraduates and the interested general public, allowing users to take part in the same lesson again and again if there were some information or concepts that went past you.
The video lectures are listed by date with links to both the streaming and the full version that can be downloaded. The files below are situated on the MIT servers. RealPlayer is required to view. The videos are also available on Youtube.
Lecture 01: What holds our world together? |Streaming | Full | Lecture 02: Electric Field | Streaming | Full | Lecture 03: Electric Flux and Gauss Law | Streaming | Full | Lecture 04: Electrostatic Potential | Streaming | Full | Lecture 05: Conductors | Streaming | Full | Lecture 06: Lightning and Sparks | Streaming | Full | Lecture 07: Capacitance and Field Energy | Streaming | Full | Lecture 08: Polarization | Streaming | Full | Lecture 09: Resistivity and Ohm’s Law | Streaming | Full | Lecture 10: Batteries and Energy Conservation | Streaming | Full | Lecture 11: Magnetic Fields and Torque | Streaming | Full | Lecture 12: Review Exam 1 | Streaming | Full | Lecture 13: Moving Charges | Streaming | Full | Lecture 14: Gauss’ Law for Magnetic Fields | Streaming | Full | Lecture 15: Ampere’s Law and Solenoids | Streaming | Full | Lecture 16: Electromagnetic Induction | Streaming | Full | Lecture 17: Motional EMF | Streaming | Full | Lecture 18: Displacement Current | Streaming | Full | Lecture 19: How Do Magicians Levitate Women? | Streaming | Full | Lecture 20: How Do Magicians Levitate Women? | Streaming | Full | Lecture 21: Inductance | Streaming | Full | Lecture 22: Hysteresis | Streaming | Full | Lecture 23: Review Exam 2 | Streaming | Full | Lecture 24: Transformers | Streaming | Full | Lecture 25: Driven LRC Circuits | Streaming | Full | Lecture 26: Traveling and Standing Waves | Streaming | Full | Lecture 27: Resonance | Streaming | Full | Lecture 28: Index of Refraction | Streaming | Full | Lecture 29: Snell’s Law | Streaming | Full | Lecture 30: More Polarization | Streaming | Full | Lecture 31: Rainbows | Streaming | Full | Lecture 32: Review Exam 3 | Streaming | Full | Lecture 33: Double-Slit Intereference | Streaming | Full | Lecture 34: Gratings | Streaming | Full | Lecture 35: The Big Bang and Cosmology | Streaming | Full | Lecture 36: Farewell Special | Streaming | Full |
These lectures serve as a great complement to other courses in physics, physics textbooks or as a standalone media experience, exploring many phenomena in classical physics. The course website can be found here.
Vector space is an important concept in areas such as linear algebra, which is frequently used in mathematics, physics and engineering. A vector space is a nonempty set V, containing vectors, on which two operations called vector addition and scalar multiplication are defined and satisfy certain natural axioms listed below that apply for all vectors u, v, w $latex \in$ V and scalars c and d.
Axioms for Vector Spaces
1. For all vectors u and v in V, u + v is also in V 2. For all vectors u in V and all scalars c, cu is also in V. 3. Vector addition is commutative. That is, for all vectors u, v in V, u + v = v + u 4. For all vectors u,v,w in V, (u + v) + w = u + (v + w) 5. For all vectors u in V, u + 0 = u 6. For all vectors u in V, there exists a vector w in V so that u + w = 0, where w = -u 7. For all vectors u in V, 1u = u 8. For all vectors u, v in V and all scalars c, c(u + v) = cu + cv. 9. For all vectors v in V and all scalars c and d, (c + d)v = cv + dv 10. For all vectors v in V and all scalars c and d, c(dv) = (cd)v.
Some Elementary Properties
1. The zero vector, 0 in V is unique.
Let 01 and 02 be zero vectors in V, so that 01 + v = v and 02 + v = v, then 01 + v = 02 + v for all v in V, then 01 = 02 = 0. Q. E. D.
2. The negative of u is unique for each u in V.
Suppose that w satisfies u + w = 0. Adding -u to both sides gives (-u) + [u + w] = (-u) + 0. By axiom 4, we get [(-u) + u] + w = (-u) + 0. By axiom 6, we get 0 + w = (-u) + 0. By axiom 5, we get w = -u. Q.E.D
This is going to be a comprehensive list of books on the religious pseudoscience of creationism and its newest reincarnation, intelligent design from various perspectives, both scientific and religious.
Books on Creationism and Intelligent Design
1.Why Darwin Matters: The Case Against Intelligent Design is a book written by Michael Shermer. It is a great and lucid introduction to intelligent design and its scientific flaws. It also argues that evolution is compatible with religion and that science and religion represents two non-overlapping fields of inquiry and that truth cannot contradict truth.
2.Why Intelligent Design Fails: A Scientific Critique of the New Creationism is a book edited by Matt Young and Taner Edis that contains several different chapters written by different leading scientists in the field responding to claims made by the intelligent design creationists, such as the evolution of the avian flight apparatus, the bacterial flagellum, the origin of genetic information and complexity and so on. This is a slightly technical book, but a must for anyone wanting to get a thorough treatment of the flaws of intelligent design creationism.
3.Creationism’s Trojan Horse: The Wedge of Intelligent Design is a book by Barbara Forrest and Paul Gross examining the intelligent design movement. It is a deep and penetrative analysis that exposes the creationist origin of its new incarnation of intelligent design.
4.God, the Devil, and Darwin: A Critique of Intelligent Design Theory is a book written by Niall Shanks that painstakingly demonstrates the utter intellectual poverty of intelligent design creationism and demolishes their core arguments. It is a close and detailed analysis and is well worth reading.
5.Deception by Design: The Intelligent Design Movement in America is a detailed investigation into the history of the anti-evolution movements in the United States, from the Scopes trial in the 1920s and the rise of “creation science” to intelligent design, the newest reincarnation of creationism. This book includes a copy of Wedge Document, a leaked internal document that spells out the theocratic political goals of the intelligent design creationists. This book is also available online.
6.The Counter-Creationism Handbook contains detailed refutations of several hundred of the most commonly used creationist arguments. The book is written by Mark Isaak, a long-time contributer to the website talkorigins, where the book is also available online. This is a must-read for anyone who is serious about understanding the complete failure of creationism.
7.Scientists Confront Intelligent Design and Creationism is a new edition of an earlier book investigating creationism and it contains mostly new essays and some revised holdovers from the original edition by prominent scientists such as Kevin Padian, Victor Stenger, Eugenie C. Scott and Robert T. Pennock. It covers the relationship between creationism and intelligent design, biological complexity and emergence, the origin of life and more. It works as a great overview of the situation as well as in-depth treatment of selected issues.
8.Intelligent Thought: Science versus the Intelligent Design Movement is another collection of essays from leading scientists such as Richard Dawkins, Daniel Dennett, Steven Pinker, Neil H. Shubin and Lee Smolin, refuting the claims of intelligent design creationism. It describes areas such as human evolution, cosmology and ethics.
9.Unintelligent Design is a book by Mark Perakh that examines the falsehood of creationist mathematics and physics. The first section gives leading creationist such as Dembski and Behe each a chapter, detailing their flawed reasoning. The second section is a critique against religious writers claiming that the bible is compatible with science and the last section deals with bible codes and general creationist misuse of probability. An excellent book for more technical topics.
10.Tower of Babel: The Evidence against the New Creationism is an early book written by philosopher of science Robert T. Pennock, a witness for science in the 2005 Dover trial. The book includes answers to common creationist arguments, describing the history of creationism, the evidence for evolution, the relationship between evolution and ethics as well as various principles in the philosophy of science such as methodological naturalism.
This is going to be a comprehensive list of books on the science of evolution ranging from popular science to technical academic literature as well as criticism of creationism. It is currently a work in progress. The books are ordered by level and required background knowledge.
Books on Evolution
Evolution: The Triumph of An Idea is a book by science writer Carl Zimmer acting as the companion piece for an eight-hour PBS documentary of the same name. It is an introductory book and provide a general and lucid overview of the subject matter. A great place to start.
Evolution: What the Fossils Say and Why It Matters is a book written by the paleontologist Donald R. Prothero presenting a massive amount of evidence for evolution from the fossil record detailing transitional fossils between fish and amphibians, amphibians and reptiles, dinosaurs and birds and reptiles and mammals and more. A key popular science text for understanding the paleontological evidence for evolution.
Taylor’s theorem is a good way of approximating differentiable functions with a polynomial. Such approximations can be used to investigate limits and in numerical calculations. The values of the elementary functions given by computers and calculators is determined with this method.
Taylor’s Theorem
Theorem: The function f that has (n+1) number of continuous derivatives on an interval I that contains a point a. Then f(x) can be written as the following series:
Proof: The following is valid for an arbitrary fixed x in I:
This is Taylor’s Theorem when n = 0. For n ≥ 1, integration by parts is applied:
Where c is an arbitrary constant. So that f’(x) will not exist in the last right hand side, the primitive function where c = -x is selected and it becomes:
Which is the formula when n = 1. For n ≥ 2, integration by parts is yet again applied, which gives:
Which is the formula when n = 2. For n ≥ 3, integration by parts is applied once again, which gives:
Which is equal to:
… and so on until the integrand is no longer continuous, that is, at least until its last term becomes:
In this article, the triangle inequality for two real vectors will be proven. The triangle inequality is useful in analysis for determining upper estimate on the size of the sum of two numbers, in terms of the sizes of the individual numbers.
The Triangle Inequality
Theorem:
The absolute value of the sum of any two vectors x and y is less or equal to the sum of the absolute values of said vectors. The equality happens when x and y are parallel with the same direction.
Proof: The application of the rules for dot products gives:
The application of the Cauchy-Schwarz Inequality, which states that the dot product of two vectors is less or equal to the product of the absolute value of said vectors, gives:
The Cauchy-Schwarz inequality is a useful inequality encountered in many different settings, such as linear algebra applied to vectors. It is also used to derive the triangle inequality.
Cauchy-Schwarz Inequality
Theorem:
The dot product of any vectors in Rn, x and y, is always less or equal to the product of the absolute values of said vectors. The equality happens precisely when x and y are parallel.
Proof: If x is equal to 0, then both sides are equal to 0. If x ≠ 0 the following reasoning is applied. The dot product of a vector by itself is always greater or equal to 0. This means that the following holds (analogous treatment for y):
Where t is an arbitrary real scalar. Factoring |x|2 (which is not equal to zero) gives:
Completing the square gives:
Expansion gives:
Since the inequality is true for all t, it must be true for any particular t. The parenthesis in the right hand side equals zero for an appropriate value of t, namely:
This means that the inequality becomes:
Rearrangement gives the inequality that was suppose to be shown.
In this video, Catholic Cell biologist, Kenneth Miller Ph. D. of Brown University rips apart the claims of intelligent design creationism. He also discusses the massive amount of evidence in favor of evolutionary biology and exposes the creationists tactic to get shoehorned into the American school system.
A question that has puzzled philosophers for thousands of years has recently been solved. Renowned physicist Victor Stenger, author of books including “The Comprehensible Cosmos: Where Do the Laws of Physics Come From?” gives the answer to this in the article Why Is There Something Rather Than Nothing? published in Skeptical Briefs, the Center for Skeptical Inquiry quarterly newsletter in 2006.
Then why is there something rather than nothing? Because something is the more natural state of affairs and is thus more likely than nothing-more than twice as likely according to one calculation. We can infer this from the processes of nature where simple systems tend to be unstable and often spontaneously transform into more complex ones. Theoretical models such as the inflationary model of the early universe bear this out.
In some models of the origin of the universe, the vacuum undergoes a spontaneous phase transition to something more complicated, like a universe containing matter. The transition nothing-to-something is a natural one, not requiring any external agent.
In it, Stenger argues that based on the currently available knowledge of physics that something is more natural than nothing. The solution comes from quantum field theory and has lead scientists to believe that something exists due to the fact that something is a more natural state of affairs than something.
He has written about this at length in the many of his books devoted explaining physics to the general public.
The Royal Society has made an interesting part of the history of science available online for the public and professional to take part of. It is the some of the notes and minutes written by Robert Hooke, considered by some as the world’s first scientist in Europe, during his fellowship of the academy. Hooke was a contemporary with such people as Robert Boyle and Issac Newton and made great contributions to science, such as the famous Hooke’s Law.
Professor Jardine commented: “Hooke’s manuscripts give us an insight into the intellectual wonder and excitement during the sixteenth and seventeenth century. Scientific knowledge and understanding was on the cusp of discovery and Science’ in the modern sense was about to be born.
“The chance discovery of the Hooke folio completed the missing piece in the historical jigsaw puzzle - empty stubs were even left waiting in the binder of secretarial minutes in case the missing records were found.”
The Royal Society has made an interactive feature where you can flip through the notebook yourself. This can be found here. A high-speed connection is required.
A five page historical description and discussion of the Hooke Folio, its history and how it was returned can be found in the article The return of the Hooke folio in the journal Notes and Records of the Royal Society.
The entire 500 page manuscript can be found at the Hooke Folio Online. One can both read and zoom in the original manuscript that has been scanned to the left or read the transcript that is shown at the right. A video presentation on the Hooke Folio is available at Google Video called Rediscovering Robert Hooke.
This fills blanks in the records of the Royal Society and the history of science as well. Hooke was working at the forefront of revolution in science and it is a victory for science to have it freely available online for everyone, professional or the general public.
