Consider the real exponential function f (x) = ex (that is, f (x) = exp x). We now extend the definition of this function to define a function f(z) = ez whose domain and codomain are .

We expect complex powers
Author(s): The Open University

We will now discuss complex numbers and their properties. We will show how they can be represented as points in the plane and state the Fundamental Theorem of Algebra: that any polynomial equation with complex coefficients has a solution which is a complex number. We will also define the function exp of a complex variable.

Earlier we mentioned several sets of numbers, including Author(s): The Open University

1. By â€˜containsâ€™, we mean that we can find part of the surface that is homeomorphic to a MÃ¶bius band. The edge of the MÃ¶bius band does not need to correspond to an edge at the surface, so that a surface without boundary can be non-orientable (as we shall shortly see).

2. When seeking MÃ¶bius bands in a surface, it can be helpful to look at all possible closed curves on the surface and thicken these into bands.

3. Remember, fro
Author(s): The Open University

1. This theorem applies to all surfaces and not just to surfaces in space.

2. This theorem tells us that the boundary number is a topological invariant for surfaces, i.e. a property that is invariant under homeomorphisms.

3. It follows from the theorem that two surfaces with different boundary numbers cannot be homeomorphic. It does not follow that two surfaces with the same boundary number are homeomorphic â€“
Author(s): The Open University

Today I woke up thinking that talking about Identity and Access Control and how your strategy around that affects you (web-) app's architecture without going too deeply into the security lingo that usually comes with it. Here's the 40 minute result.

I start with HTTP's "native" authentication model RFC 2617 and how that's universally bad, with both Basic and Digest authentication having issues Digest being, ironically worse for the overall security strategy. Then I d
Author(s): ClemensV

Sir Isaac Newton: Full Biography
Isaac Newton was born December 25, 1642 in Woolsthorpe, Lincolnshire, England, and died March 20, 1727 in London, England. Newton was an English physicist and mathematician, who was also the culminating, figure of the scientific revolution of the 17th century. With discoveries in optics, motion, and mathematics he developed the principles of modern physics. He was the original discoverer of the infinitesimal calculus. Newton's Philosophiae Naturalis Principia Mathematica (Mathematical Principles
Author(s): No creator set

How Did English Evolve?
What is the difference between "a hearty welcome" and "a cordial reception"? In a brief, action-packed history of the English language, Kate Gardoqui explains why these semantically equal phrases evoke such different images.  (05:04)

Author(s): No creator set

Dec 13 - If you are betting on the manufacturing sector creating jobs, you might want to wait till the Markit PMI figures come out Friday - they are not expected to be pretty.
Author(s): No creator set

Results

Author(s): No creator set

SDSU Geological Sciences - Thesis Defense - Shana McCarthy
By: tcarrasc A Geochemical Evaluation of Enhanced In-Situ Bioremediation of Chlorinated Ethenes In Groundwater Shana McCartrhy M.S. Candidate Department of Geological Sciences San Diego State University Advisor Dr. Kathy Thorbjarnarson -------------------------------------------------------------------------------- ABSTRACT Sites impacted with chlorinated solvents present unique technical challenges when compared to most other groundwater contaminants. Chlorinated volatile organic compounds (CV
Author(s): No creator set

Engaging with Detroit
University of Michigan students live, study and work in the Motor City
Author(s): No creator set

A 360 degree view at 322 kilometers an hour
The world's first spherical 360-degree camera made by a Norwegian company is attached to a Formula One car, and could herald a change in the way racing is filmed in the future. Joel Flynn reports.
Author(s): No creator set

Barry Schwartz's 'Practical Wisdom'
Swarthmore professor Barry Schwartz says rules and incentives are an "insurance policy against disaster, but [they don't] produce excellence." In his recent book, Practical Wisdom: The Right Way to Do the Right Thing, Schwartz and co-author Kenneth Sharpe, also a Swarthmore professor, say that what is needed is not more bureaucracy. Instead, society needs the Aristotelian ideal that trumps all others -- practical wisdom. Knowledge@Wharton recently sat down with Schwartz to discuss why individual
Author(s): No creator set

Annabelle's Wish Part 1 Â  Christmas
This is a wonderful fiction story sharing the true meaning of Christmas. This is a wonderful resource for school and home. (15:00)
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Annabelle's Wish Part 4
A poor farmer struggles to raise his orphaned grandson, who was left mute after a raging barnfire. When a beautiful little calf is born on the farm on Christ...
Author(s): No creator set

Reuters Today: No U.S. fiscal cliff just yet
Dec. 18 - A U.S. budget deal may be in sight as the two sides make compromises in talks to curb the deficit. Plus, Japan's new PM Abe puts the squeeze on the BoJ for more stimulus.
Author(s): No creator set

Promo - One Minute Romanian
Hello! My name is Roxana and I'd like to welcome you to One Minute Romanian from the Radio Lingua Network. In this podcast I'm going to be teaching you the basics of Romanian. The great thing about this language course is that you'll be learning all you need to know in just 60 seconds - or thereabouts! Each one minute language lesson will equip you with just enough Romanian to help you get by in lots of situations, either on holiday, or on a business trip to Romania, or just to impress your Roma
Author(s): No creator set

Hepatitis B - what are the symptoms and how can it be prevented.

Author(s): EduTube

La CitÃ© des sciences et de lâ€™industrie
Using the subject of science and technology in France, this unit will show you how to structure arguments, write a summary, use the subjunctive, report numbers and express wishes in French. First published on Fri, 21 Dec 2012 as La CitÃ© des sciences
Author(s): Creator not set

Nani Mine, Nani Nani (Greek) Lullaby from the Lullabies of Europe education project (see http://www.lullabies-of-europe.o

Author(s): acerview54