Importance of Calculus Mathematics
Calculus is important in every field of science and engineering. Only in geometry, we do not use the concept of calculus. Therefore, fundamentals in calculus need be understood properly at the early state of science students. Calculus is perhaps the study of how things change in daily life. It provides a platform for modeling systems in which there exist change, and a way to deduce the present or future predictions for such models.
We have a notion of calculus to discuss qualitatively and to quantify them on daily based needs. For example the concept of application of force and effect of it or work done by the body under the action of force and which direction the body changes its speed from calculus, though it was found existed long before the calculus did and we know lots about it.
Difficulties faced by a student while solving Calculus problems
The basics of calculus are introduced to students in the high school level. If the teacher handling the subject is not aware of what all the students learn in their curriculum at later part, it is difficult to create concrete idea about the subject. Student start losing the interest in learning the subject as the connectivity is lost during learning. This will affect the confidence and the student start developing dejection about mathematics and his ability to solve problems in physics also starts decreasing. Many a time teachers introduce differentiation and integration without give proper analogy about the need of these concepts. When addition and subtraction yield better results and where it is not. Actually when the variables are changing with constant magnitude, addition and subtraction gives the best result. If the same variable changes exponentially where future is unpredictable or not in control then the use of integration and differentiation gives better result. These fundamental differences must be introduced with sufficient examples. Otherwise, the students will not be able to study the way it should be.
When the student is in the early stage of at lower classes, we may introduce single variable calculus. This may be started with an example of motion of a point object along a straight path. If the motion can take place on a hard surface, or in space, the calculus to be used differs. The teacher handling must understand is that application worth to discuss and single variable or multivariable calculus is good for the situation. If this is clear to the student, the question of bettering the track or engine or the fuel exist later. Like that, there are problems related to gravity and acceleration. Similarly, Keepers law of planetary motion, forces acting on a body in equilibrium condition or non equilibrium. Therefore lots of these topics required are requiring a good analogy to make the student have the grip over the subject. Most of the physics problems are not discussed in the class using calculus. They do with old methods of applying two dimensional variations in Cartesian coordinate system. For a child, imagining the system and learn is a quite difficult task and get lots of doubt on how to remember and apply these concepts to the real time events.
Important Topics in Calculus Mathematics
Projectile motion, vehicles moving in a circular path, aerodynamics, area under the curve to calculate the work done by mechanical engines, electrical devices etc.
We felt many a times that the exponential function is mysteriously defined using calculus. It is the function having its own derivative. It is defined and said to have the value 1 for the argument 0. However it is to be something we have seen all the time. This turns out to bearing on the minds of the student and is a close relation to the trigonometric sine function. We need solutions to these kinds of problems which we the teaching community often tends to make mistakes. They are all very vital in any learning individuals. They must be concentrated to make our life worthy.
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