Month: May 2017

Taylor’s polynomials and Maclaurin series in action

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Taylor's polynomial

From the top to the bottom, as I my eyes rides along the gradual descend, I see a series of numbers. Perhaps, Taylor’s polynomials could  describe these better.

Aerial photographs brought it to perspective. Those taken from the front, side, rare or above it, they all depict one thing. The convergence or divergence of series of numbers. Truly, the teacher was right. Mathematics is real. I see a series of numbers.

Up in the planes, it is just a pattern of concentric squares with common center, all vanishing at the center. Oh, I it is true, the series is converging to a point. The point is zero. When I think keenly about it, I see a series of numbers

I had not known what Taylor’s polynomials are. I have neither heard of power series. It is the most abstract one, convergence of series that my sister sings every day. A chorus that their teacher taught them so that they may always remember it. I did not know it could be visualized. Really, I see series of numbers.

I had not known that mathematics could be that beautiful. Marrying tourism and landscaping, or rather, exterior designs. My eyes cannot allow me to move away from it. They, just, want me to see the series of numbers.

Even architects can think along these lines! Bring series, sequences, and convergence into perspective! I am sure that my sister will now understand what Maclaurin series is together with their special case, the mean value theorem and connect all these with Taylor’s polynomials. Moreover, proudly explain it to the fellow students because mathematics is now real, courtesy of seeing the series of numbers.

Yes! I have now realized, as I see the series of numbers, that everybody played his/her part. The architect got it right from the calculus class. The architect’s teacher provided the right materials. The artisans did theirs too: and me? I am challenged. I am must be counted too. As I pass by here every day to admire this building: while, at the back of mind, appreciate Taylor’s work in action, I must get the right person to drive the concept home. This must be the best AP calculus tutor or a calculus tutor. Off course, the cheapest tutor to make me see the series of numbers elsewhere too.

Something sprouts cutesy of a reliable math tutor

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Abstract turned real

From the perceived abstract, mixture of symbols that may look like rubbish cribbed on the board, cryptography, solution of complex problems in engineering, forestry, finance, economics among others, sprouts.

I see green; perhaps it is because of the introduction that my first math tutor made, that appeared in-comprehensive. This looks rubbish, a mixture of logs, dried leaves, and dried branches, name them.

Something is sprouting, I could not imagine. Look at all this rubbish, as some people may take it, yet something beautiful sprouts.

From the dead leaves, tree branches, backs of trees and logs that comprises rubbish, water makes it bring life again; I now see green color almost everywhere. I thought it was the end of it all, yet something beautiful sprouts.

But, where was these water from? It must be from the heavens, I knew no one could water them, because they showed no sense of life, as most people perceived, it must have been from the right source, yet something beautiful sprouts.

I knew it that way; that is all abstract thinking and make up. Teacher scribbling everywhere on the board. Making cabbage from the board and the chalk, yet something beautiful sprouts.

It took the help of the right source, a good math tutor; her approach bathes the rubbish in my head. I saw mathematics in the field, I saw it while eating, pizza became mathematical, and sharing pieces of candies was mathematical too. I saw mathematics while modeling my best first “clay radio” that my friends used to listen to as I sang along with it, yet something beautiful was sprouting.

She was the water, the right source that all math nightmares in my head was longing for. She presses the right button and I developed passion, without realizing, yet something beautiful sprouts.

I knew it was never abstract as people, specially my classmates, though it was. I saw the importance of online tutoring, where every concept was connected to a real life situation. I owned it, I lived it, I spoke it, I testified about it without realizing, it was something beautiful sprouting cutesy of my math tutor.

Understanding calculus

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calculus

Calculus is a wide field. Once you have moved out of the world of Algebra, geometry and trigonometry you enter into a wide domain of Calculus where you can show your algebra, geometry and trigonometry skills. When you step into undergraduate class, you will meet this subject named calculus. You have to make it friend and accept it. Make you mind fresh because you want to meet and know fresh ideas. To master calculus skills you have to understand a number of concepts

Grip on Sets

Calculus uses special algebraic expressions called functions. The functions plays with collection of numbers. For instance, if I show you one, you shout 3, if I show you 2, you shout 6, if I show you 4, you shout 12 and so on. This means, I am playing with counting numbers 1,2, 3,… as you shout 3, 6, 9, 12, …., the multiples of ten. These are collection of numbers are called sets. Thus, functions are defined using sets of numbers. As such, it is very important to understand the features of different sets of numbers and how their relation.

Grip on Limits

If one parks a string, it vibrates covering a large distance. However, as time goes by, this distance reduces. The moment the eye realizes that it is not vibration, in real sense vibrating at within very small distance, the distance is almost zero. Therefore, the distance within which vibrations are done is tending to zero. Thus, the limits of the distance within which vibration takes place is zero after some time. This concept of has a lot of application in calculus, as such, it very important that one understand what it is and how it is applied.

Grip on Differentiation

Differentiation is about determining the slope (gradient) of different types of function. These may be polynomials, rational functions, exponential functions, logarithmic functions, product functions, composite functions, trigonometric functions, power functions and so on. This understand sets you into the real world of calculus so that you may apply the concepts that you would have acquired. Calculus is never fully understand without the getting to know how to describe continuous functions. This is possible courtesy of the two the Rolle’s Theorem, the Mean Value theorem and the first fundamental theorem of Calculus.

Grip on Integration

Integration is the reverse of differentiation, once you have basic command on limits it will lead you to differentiation and this will lead you to integration. Likewise, differentiation you have to learn Different methods of integration such as the , the integration of basic trigonometric and polynomial function. This open a path to understand other methods such as u-substitution, trigonometric substitution, integration by paths, and fractional decomposition among others. The fundamental theorems of calculus come in to provide a guide to definite integration and other applications.

Like other math topics, you have to revise and practice more often to have it readily available.

Algebra, the foundation of mathematics

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Like all things in life, that which is built on a strong foundation lasts. Algebra is probably the most important tool that you will need for excelling in math as it lays done the basics for calculus and many other branches of mathematics. Its concepts will always be applied – even as your studies progress – and hence it is vital to get the edge early and invest in good algebra tutors.

The basic core of algebra is representing relationships between unknown numbers using letters of the alphabet. Algebra, unlike basic arithmetic, is really where logic begins to take hold, and reasoning mathematically starts to take shape. It is not only the principles of algebra that will continue to be implemented as the student progresses, but the scientific way of thinking that algebra starts to teach you as you move away from arithmetic.

It has been noted that students that do dismally in calculus must have done the same in algebra previously. Often times the errors that students make the most in calculus are not elements of calculus at all but those of algebra that the student failed to fully grasp. Sometimes the mistakes are careless, other times the flaws are more deeply rooted – but it always comes down to the student being low performer in algebra.

Similarly, it is also noted that students that do well in algebra go on to have higher grades in calculus and other higher-level mathematics. It is clear that for anyone aiming at excelling in math, excelling in algebra should be the primary focus.

A good Algebra tutor ensure that you get the head start you need by making this core subject simple to understand by connecting mathematical concepts to everyday activities and delivering to the student in a way that is not only tailored to specific needs but also effective too. Thus ensuring a sound knowledge of algebra that leads to a bright future in mathematics.

Preparing to trample calculus underfoot

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preparation for university

For the high school student, and even the university student, mathematics – and more especially calculus – can be a challenging subject. However, for any learner, calculus is an imperative branch of mathematics. Thankfully, the AP calculus tutors can help students grasp their calculus lessons and transition from high school mathematics to university standards smoothly as you learn with the experts.

Students who start preparing for university early on in their studies have an invaluable advantage over their peers. This could not be truer than it is for mathematics, as the difference between school math and the standard of mathematics at university can be frightening.

What is even more shocking is that many high school curricula do not even properly incorporate aspects of pre-calculus and this can be detrimental to the student who takes calculus at the college or university level. The student will find that he or she is miles behind his peers who have learnt calculus, and will not be able to keep up with the pace of the lessons. Having AP calculus tutors ensures that even if your school is not offering the preparation you need for university mathematics, you will still be on par with your peers.

Even if your school does offer calculus, it is easier to bridge the gap to university mathematics by getting in the extra practice while you are still ahead of the game.

AP calculus tutors essentially take what is often a much-feared branch of mathematics (for beginners) and make it simpler to learn, not only at school level but also in such a way that foundations for university are already in place. Calculus does take hard work and dedication – and there is no way around that – but it will be so much less challenging and a lot more rewarding when you learn with the experts and give yourself the head-start you deserve.