Secret to understanding calculus

A student being taught

Understanding calculus can be tricky because the topic is a bit wide. 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 your 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.

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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 understanding sets you into the real world of calculus so that you may apply the concepts that you would have acquired. Calculus is never fully understood 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 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 understand it fully.

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