The photosphere 03/31/16
The photosphere of the sun is so important that if it were to not exist there would be no human life! The photosphere is the spherical surface encapsulating the sun that is thought to emit light. It is situated just above the convection zone of the sun. photosphere blocks certain wavelengths of light. The photosphere is often used to describe a star’s visible surface as it is the part that emits light.
Solar prominence 03/30/16
Solar prominences are one of the most important subjects in modern day astronomy. Solar prominences are Bright, gaseous features that extend out from the surface of the sun. Prominences are anchored to the photosphere of the sun in a loop-like geometry. A prominence can form in as little time as a day, and can last for months on end! Solar prominecnes can break apart and give rise to Coronoal mass ejections
Amorphous solid 03/29/16
Amorphous solids are quite peculiar materials in the natural worlds. An Amorphous solid is a solid with no solid definition of internal molecular structure, instead, everything mostly bounces around. It is said that Amorphous solids are on the border between a solid and a liquid instead of truly being one or another. To be precise, Amorphous solids have no precise GEOMETRIC ordering. Glass and wax are examples of Amorphous solids
One of the most fascinating physical substances known to humanity is one that is probably seen my the majority of the world everyday. This material is known as glass, and we shall examine what makes it so special.
Glass begins it’s life in the form of sand. If one were to raise the temperature of sand to 1700 Centigrades, then it melts and obtains a peculiar internal structure that results in it becoming what material scientists like to refer to as an Amorphous solid. The manufacturing process for glass often begins with such sand being mixed with recycled products and soda ash and limestone in a massive furnace. The soda lowers the amount of energy needed to melt the sand, but an unfortunate side-effect is that the glass that is produced through such means is often of very poor quality, so limestone is often added to prevent this from happening. The resultant glass is termed Soda-lime-silica glass in honor of all of the materials that went into it
Glass is so popular because it has a sublime domain of applications. Glass is chemically inert, so it will react with very little substances making it a prime candidate for use as a material holder such as in glasses Glass is transparent so it is easy to see through and glass is also fairly resistant to thermal expansion so one does not have to worry too much about glass breaking or swelling due to a heat wave. In addition, glass is a highly recyclable material
Glass is truly a most fascinating material. Imagine what human civilization would be like if glass lost one of it’s useful facets, such as chemical inertness or transparentness, then all of society would be simply turned upside down! I want you to ponder how glass and engineering make our world possible
Engineering drafting 03/27/16
One of the most interesting things about Engineering is Engineering drafting. Very simple yet profound question is ‘how can we represent three dimensional machines on a two dimensional plane?” The solution to this is Engineering drafting. First, we take the object in an isometric view. Then, we take a look at it through three planes,the front side, the right side, and the top side. We then make a sketch of what it would look like if we viewed the objects through each of those planes. We use dashed hidden lines to represent parts of the object that are covered by other parts in front of the plane-view.
Black holes 03/26/16
One of the most bewildering and fascinating phenomena of reality is that of black holes. Throughout the Universe there are sections of space that have such a high density that the geometry of the space-time becomes so warped that not even light can escape the gravitational pull of such objects. Black holes are usually created with the collapse of a insurmountably large star. The star has such a great contraction that the equivalent density would be if all of the Earth was shrunk down to a marble. Black holes can be of various sizes. A super massive black hole is thought to exist within the center of the milky way. On February 11th, confirmation was received of gravitational waves originating from a black hole merger.
Applications of derivatives 03/25/16
Derivatives have a myriad of applications in all of science. One of the most practical uses of differential calculus is the evaluation of newtonian mechanics. The most fundamental of facest, kinematics, is simply derivatives. Velocity is the derivative of position in respect to time, or v(t)=dxdt, and acceleration is the derivative of velocity in respect to time, or a(t)=dvdt=d2xdt2. This means that if our function is a defined variable, then we can find all sorts of information about it by applying the fundamental rules of calculus
Another interesting application of differential calculus is the mean value theorem. The mean value theorem states that if we have a function whose graph is continuous on [a,b]and differentiable on (a,b), and that f(a)=f(b), then f(x)’must be equal to 0 at some point in that line. This makes perfect intuitive sense because if a graph goes up then it must come down or vice versa, and if is continuous and differentiable then the sign of the derivative must change and when it changes it hits 0.
A further application includes Linear approximation. If we have a very complicate function to evaluate, then we can take the derivative at a known point and evaluate it further from there. Because the value of derivatives do not change much for close values, we can use a linear tangent from a known variable to make a fairly accurate approximation. The formula for this equation is y=y0 +f(x0)*x.Take for example the function f(x)=x. It is rather difficult to find the numerical value for 1.1off hand, however, it is extremely easy to find f(1)’ as well as f(1). from there, we can evaluate it using our equation which becomes 1+12*1-1/2*0.1=1.05This is extremely close to the true value of 1.0488. In fact, there is only a 0.114%difference! Truly remarkable!
Another useful feature of Differentiation can be used in finding critical points. A critical point is where the derivative of a function f(x)’=0 or f(x)’=undefined When this happens, a graph of a function will either start to decrease or increase. We can find these point using calculus, and then we can determine if it is a maxima or a minima by proceeding with the following steps. If the f(x)” is positive, then it is a minima because the function was decreasing until the point c where it changes signs, and vice versa for a minima
Differentiation is by far the most important topic in a calculus course. Let’s turn the clock back. When you were in algebra, you were able to find the slope of a linear line that contained a rise over a run. Now, you were told that you were unable to find the slope for a line that was not constantly linear in nature. This is where calculus comes in. What you do is that you start out with your simple yxequation (y-y0x → f(x)-f(x0))x→ f(x0+x)-f(x0)x → f(x0+h)-f(x0)h ) and you evaluate it at smaller and smaller increments, until it becomes zero. Mathematically speaking, you are taking the limit as the change in x approaches zero, which can be symbolically analyzed as x0yx. We call this a derivative and we represent this concept with dydx, or the derivative of y in respect to x. Differentiation is a most useful way to find the instantaneous slope of tangent lines.
During one’s study of calculus, Integration will be one of the most fundamental facets learned. To put it simply, integration is the a method used to find the area under the graph of a known function. The basic concept of Integration is to take a Riemann sum and take the limit as xapproaches 0. When this happens, we can have an infinite number of infinitesimal lines, and when summated they will give us the area under the curve. Integration is represented by the ubiquitous symbol. To numerically evaluate an integral, all you need to do is reverse differentiate the function or antiderive it.