#SOLVING QUADRATIC EQUATIONS MATLAB SERIES#

More MOSFETs have been produced than any other object in human history. Although unknown to most people, this tiny device, created in 1959 by an Egyptian-born scientist and Korean-born scientist working in a lab in New Jersey, is the basis for modern electronics. Atalla and Dawon Kahng, for example, invented the MOSFET (metal-oxide-semiconductor field-effect transistor). Our current technological age, the Information Age, builds on all that knowledge and can be traced to critical innovations made by people from all backgrounds working together. This knowledge all stems from physics, whether it's the way a rock would flake when constructing a spear point, the effect of integrating carbon with iron in South Indian and Sri Lankan furnaces to create the earliest high-quality steel, or the proper way to combine perfectly ground and polished pieces of glass to create optical instruments. Successive technological periods (often referred to as the Stone Age, the Bronze Age, the Iron Age, and so on) were marked by our knowledge of the physical properties of certain materials and our ability to manipulate them. Humans have created and manufactured millions of different objects over the history of our species. Through a study of physics, you may gain a greater understanding of the interconnectedness of everything we can see and know in this universe. The forces out there are the same as the ones here on Earth.

Tonight, take a moment to look up at the stars. Although the scale is much different, the interaction of gasses in the Veil Nebula resembles those on Earth and the vibrant color combinations are created by the familiar glows of hydrogen, sulfur, oxygen, and similar elements that make up everything we know. The forces that cause the supernova remnant to act as it does are the same forces we contend with here on Earth, whether we are planning to send a rocket into space or simply heating a new home. Scientists compare newer images, such as the one above, with detailed images taken by the Hubble Space Telescope in 1997 in order to understand nebula expansion and other properties of astronomical objects. The shock wave from the explosion is colliding with a cloud of gas and dust, creating the rope-like filaments and sheet-like appearance. The unique structure is the ongoing result of a supernova that occurred 8,000 years ago. But as you begin your exploration of this broad-ranging subject, you may soon come to realize that physics plays a much larger role in your life than you first thought, no matter your life goals or career choice.Ĭonsider the Veil Nebula, a cloud of heated dust and gas located about 2,400 light years from Earth (a light year is the distance light travels in one year, or approximately 9.5 trillion kilometers).

#SOLVING QUADRATIC EQUATIONS MATLAB SERIES#

Some of the possibilities led to a consistent series of equations whose solutions depended upon the magnitude of the noise (which I called 'delta' when I was solving), but in every one of those cases, the consistent solutions involved expressions divided by delta, so the solutions 'exploded' as the assumed noise was reduced, contradicting the assumption that there was just a little noise in the system.What is your first reaction when you hear the word “physics”? Did you imagine working through difficult equations or memorizing formulas that seem to have no real use in life outside the physics classroom? Many people come to the subject of physics with a bit of fear.

Most of the possibilities just stayed inherently inconsistent. It turns out that with those equations, in every case except perhaps one, the amount that the term would have to be wrong was fairly large compared to what the term actually is, such as -0.05*x^2 needing to be about +0.28*x^2 or -6994.94 needing to be about -15000 for there to be a solution. I did that for each possibility in term, finding out how wrong the stated term would have to be in order for there to be a solution to the equations. For example we could suggest that maybe 12.28 might result in inconsistency but maybe 12.28003582 might allow the equations to be consistent. I would alter a term, and solved to find out what the 'noise' would have to be in the term in order to make the equations consistent. I went through your equations, varying term by term under the assumption that the term had not been given exactly, such a supposing that 12.28 might be (1228/100 + delta) for some unknown delta, or that 0*x*rr might be (0+delta)*x*rr for some unknown delta.

Solving quadratic equations matlab