studiot

My guess would be that the OP is referring to a band matrix where there are terms one or both sides of the main diagonal so the 'diagonal' is more than one term wide. Such matrices are obtained in the solution of certain engineering problems by numerical methods. http://en.wikipedia.org/wiki/Band_matrix https://www.google.co.uk/search?hl=en-GB&source=hp&q=bnaded+matrix&gbv=2&oq=bnaded+matrix&gs_l=heirloom-hp.3..0i13l7j0i13i30l3.1407.3922.0.4079.13.13.0.0.0.0.218.1673.1j11j1.13.0.msedr...0...1ac.1.34.heirloom-hp..0.13.1673.If1_caZx51c

You need to describe what you want to do in more detail.

That mkes no more sense (ie is incomplete) than the OP.

Sorry, studiot, missed your question earlier. That's the change from modern day average ocean temperatures. Gosh if I understand this correctly (and the graph is correct), that graph is utterly amazing. It appears to me to state that, during the last half a million years, there has been a periodic upward jump of around 10oC in the world ocean temperature, with a subsequent relaxation of -10oC over the next 100,000 years. The sawtooth waveform is unmistakable and there are 5 peaks shown over the timescale. This graph really warrants much dicussion.

Is this homework ? And at what level? I guess it is about measuring the solubility of a sparingly soluble salt. At elementary level you could try to dissolve it and see what happens. At a higher level you need to deduce the solubility from EMF or conductivity measurements on the solution.

Is this homework? How can it be? Although this is a dynamic question so not an equilibrium one, you can resolve the forces acting on the balls.

The cynic would say that pure laziness has more to do with it than Occam. Why calculate three things when you only need to work out two? Anyway let us use the xyz coordinates as an example. Let us think of a particle free to roam the galaxy. It can have any x or y or z coordinate quite independently of the other two. We say it has three degrees of freedom. Now let us restrict the particle to the surface of the planet Zog. Zog is perfectly spherical with radius R and the centre of Zog is the centre of the galaxy. So all points on the surface of Zog obey the equation x2 + y2 + z2 = R2 Now all of a sudden if we know x and y we automatically know z. We have reduced the degrees of freedom from 3 to 2 by introducing one equation or condition. Now you asked about energy Remember I said that we distinguish several types of energy. There is no better place to make such a distinction than in Thermodynamics. Here our variables are quantities like, pressure, volume, temperature and yes energy. In fact we have several types of internal energy, Helmholtz free energy, Gibbs free energy, work energy, heat energy, and so on. I mentioned Gibbs and he put forward a formulation of thermodynamics, we call the Gibbs formulation and which Plank later called the canonical equations. Maxwell was so impressed that he made a plaster cast of the graph of the Gibbs formulation and presented it to Gibbs. These days we have CGI to draw such things for us on the screen. However this is a webforum, not a textbook, so I will stop there.

Chicken and egg? Force causes change of motion, including motion in the first place from still or rest. As a result of motion a material body possesses energy. Since we can distinguish several sorts of motion we distinguish several sorts of energy. When a force causes motion it does work on the body, which means energy is transferred to that body from either another body or another store of energy. Another store of energy? There are non material places to store energy eg electric and magnetic fields. It is true that we can plot other quantities than position along an axis on a graph, and that energy is a possibility. Equally clearly when we draw such graphs the axis can be called a dimension and that quantity has a coordinate value relative to its axis. We call these generalised coordinates. In theory we could plot one for every conceivable quantity, but because we can also deduce equations connecting at least some of the quantities we only need to plot some and can obtain the others form the equations. The business of Physics is about finding the minimum number of such axes. We tend to group together suitable and like quantities for example the familiar xyz axes, but there is no justification for calling any one the first or fundamental.

The difference between philosophy (and metaphysics) on the one hand and mathematics (and physics) on the other is that philosophy can question the foundations of the subject. In maths and physics we start with some statements we accept without question (but not without lots of very careful thought) and construct everything from there. If the statements are inadequate out construct will be inadequate (hence the care). Philosophy is the discipline wherein we examine the foundations themselves.

Have you watched Prof Lewin's lecture on Faraday and this stuff? I have linked to google becase there are several presentations of this famous lecture. https://www.google.co.uk/search?hl=en-GB&source=hp&q=Lewin+on+Faraday&gbv=2&oq=Lewin+on+Faraday&gs_l=heirloom-hp.3...1687.7297.0.7906.16.8.0.8.8.0.219.1422.0j5j3.8.0.msedr...0...1ac.1.34.heirloom-hp..7.9.1468.WSnY9qLg1T4

I have no idea what exactly you mean or whether there is a spelling mistake here, But if you are exploring the idea that 'nothing' caould have physical reality and embodyment, the answer is yes. However this is a semi philosophical question on the borders between physics and philosphy. But I don't see how any answer to this question progresses your thread.

Electrical phasors are vectors in the mathematical sense but not in the sense of vector calculus or the grad, div and curl operators. 2D Euclidian vectors do not, for instance, have a cross product, any more than 4D vectors have. The vector double and triple products are special to 3D.

The book by H M Schey is loved by some and hated by others. It is called Div Grad Curl and all that I am noting it here because it is an introduction to vector calculus by an unusual route. It is only a little book, 163 pages all in and easy reading. Although a mathematical book, it takes the electromagnetic field as its working material and develops the subject in terms of EM theory as far as Maxwell's equations. It provides a pretty chatty approach to the subject matter of the relationship between the EM fields, the divergence and the curl and so on, starting from first principles. It might suit you.

Be warned I find this information highly unreliable. Software glitches ensure inconsistencies between the various times presented. You can often see a post attributed to a member who was also recorded as having logged out 3 minutes earlier. If you two (or more) members are shown as viewing a thread at the bottom, this does not change for a long time after one logs out. I have often scrambled to post a reply whilst I thought the other guy was still online, only to find he had logged out a quarter or half an hour before I finally posted.

No the methane pics both represent a 3D picture. Pretend the carbon atom labelled C is a blue ball and the hydrogen atoms, labelled H are red balls and the tapered lines are sticks. Then you have a ball and stick model. I did say to ignore what was inside the atoms and neither of my pics attempt to show the details of the connections in the way the Lewis representations do. None of these are Lewis representations. To understand these would mean going into the structure of the atom and considering some sub atomic 'particles', we call nucleons and electrons. The Wiki article shows some 3D structural (ball and stick) models at the top which is misleading because these are not the Lewis representation. A Lewis example of this appears about halfway down the page with two images of the nitrite ion. Lewis examples are all flattened to 2 dimensions and are used to show the nature of the chemical bonds involved, as well as the electrons not involved in the bonding process. They are, of course, an example of a different model appropriate for a different purpose. We have been talking about structure which, loosly speaking, is about the distribution of things in space and to a lesser extent what is directly connected to what.

What do you mean charges don't cancel? Water is electrically neutral. If you are referring to the eletrical dipole moments please expand as this could be confusing.

It is more like the second one, but you have the general idea. This does not mean the ball and stick model is wrong or redundant. That model is useful for other purposes. Real world molcules are more complicated and unlikely to be symmetric. Many are three dimensional. This fog approach is called the charge cloud representation. Here are the charge cloud representations for oxygen and methane. Compare the ball and stick with the CC for methane.

Be aware of the difference between force and energy. Magnets do not have energy flowing into or out of them. Magnetism is a force. Exerting a force may or may not involve energy. For example the Earth continues to exert a force on you through gravity, but no energy flows into or out of the Earth, unless you fall out of the sky. In the same way a magnet may cause another body to move, doing work in the process. But something moves or holds the magnet. This is like poking something with a stick so it moves or drawing it along with a string. Either way the stick or string exerts a force on the object, but something else has to push or pull the other end. If the object does not move then the force can remain exerted till kingdom come and no work is done, so no energy flows.

My comment about atoms and molecules was meant to be a helpful simplification (particularly as you will meet technical terms as your reading progresses) So I am interested in what you made of it. As to space. Think carefully what how you mentally picture an atom (from a distance, lets leave the inside till later) You must have seen the 'ball and stick' models of molecules (there you go, a technical term) made of coloured balls to represent the atoms making up a mlecule and the sticks to connect them. So when they are close enough to be joined together there are 'connection sticks' in the space between the atoms. These are not solid or other atoms so how do they work? Well instead of picturing the atom as a solid ball, think of a mist or fog. As you walk through the mist some patches seem thicker, more dense than others. The more tenuous parts may even thin out to clear air. Furthermore if you walk far enough you will exit the fog and enter clear air. Now think of an atom as being a clump of particularly dense fog but thinning out towards its edges, and think of two such clumps coming close together. As they appraoch each other the thin edges will touch first, forming a thicker zone between the two clumps. This thicker zone corresponds to the sticks in the ball and stick model. It is formed by overlap of two fuzzy edges of the atoms. How are we doing so far?

For the most part we cannot answer a question "What is XXX ?" The best we can do is create models. We obtain observations and measurements and call the sum of all htis the real world. Clearly since new observations and measurements are continually being made the 'real world' is continually being updated (like Microsoft Windows ) We also create completely abstract constructs with artificial rules and relationships. Many are mathematical. Some of these can be used to model observations and measurements in the real world and even make predictions. But none of these models are exact or perfect. Magnetism is a case in point. We know today that the source of all magnetic effects is electric in origin. But a simple model, That of the separate existence of a magnetic force affecting certain objects for some purposes will make the required prediction easier. On another forum I posed a calculation question about lifting a car in a scapyard with a crane magnet. Members there disputed non electrical explanations and one member with a PhD and many years experience in electrical and magnetic matters finally showed several pages of vector mechanics to calculate the selfsame result I had achieved in three lines. I employed what is known as the method of Virtual Work, and did not need to mention electricity at all. So your question really need lots of context to provide a sensible answer. What are you actually seeking to know?

Well I was referring to the connection between straight lines and geodesics in Newton's First Law. I don't know if Galileo ever referred to the important concept of The Right Line

For static charges or steady current, the statements:- The E field is conservative, has a scalar potential, V (as introduced by imatfaal), has a zero curl, has a line integral around any closed curve equal to zero, are all equivalent statements that are proved by simpler means before Maxwell is introduced. Since these are all mathematically equivalent only one is chosen as the basic and the others follow mathematically. One of the difficulties in replying to this is avoiding a circular argument. So where does your course start? Also where do you stand on vector algebra and vector calculus in 3 dimensions?

Was this a quote from Euclid or Newton Or..............?

I expect that was a simplification imposed by your teacher. What did she have to say about Helium and Avogadro's Hypothesis? Historically the concept of atoms was introduced followed by the concept of elements and finally the concept of compounds. Three laws were enunciated The law of Definite Proportions The Law of Constant Composition The Law of Multiple Proportions These codified the idea of 'pure substances' that could be formed from or reduced to simpler forms of matter (called elements), which could not be reduced further. The natural question arose "If an atom is the basic form of an element, what is the basic form of a pure substance?" This lead to the idea of a molecule, after quite a few false trails and some obstruction by some older scientists, lead by Berzelius. The concept of a bottle or bag of a pure substance containing multiple instances of identical units is simple and alluring and offers a working explanation for many physical observation. But it is only a model and not always reliable. For instance what does a molecule of pure diamond look like? If you are still reading this rather than moving on I was going to discuss your view of the space between atoms with some hopefully helpful comments. Are you still interested?

I'm sorry I didn't make myself clear. I was not asking how the temperature changes were deduced. Your vertical axis plots change of temperature. Change from what temperature? Is the change from a common base, an average or some function of the previous temperatures? Also what about the particulate counts?