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BRANCHES OF CALCULUS

Calculus is a mathematical field that is involved in the study of continuous change. It has two traditional branches of calculus which include integral calculus and differential calculus. Differential calculus is concerned with the rates of change and slopes of curves while integral calculus involves the accumulation of quantities and the areas under and between curves.

Applied calculus is just the act of unraveling a problem with calculus. In calculus 2 classes, there is a focus on applied calculus, especially the position-velocity-acceleration relationship, related rates, and optimization.

Differential calculus as one of the Branches of Calculus

This is the study of the definition, properties, and applications of the derivative of a function. It is concerned with finding the rate of change of a function to the variable on which it depends.

It includes calculating derivatives and using them to solve problems that involve non-constant rates of change. The essential objects of studying differential calculus are the derivative of a function and their applications. The derivative of a function illustrates the rate of change of the function near that input value.

The process of finding a derivative is called differentiation. Mathematically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point.

Differentiation has approached in nearly all quantitative disciplines. For instance, in physics, the derivative of the displacement of a moving body concerning time is the velocity of the body and the derivative of velocity concerning time in acceleration.

Integral calculus

This is another branch of calculus that is concerned with the theory and applications of integrals while differential calculus focuses on rates of change, for examples slopes of tangent lines and velocities.

Integral calculus deals with total size or value such as lengths, areas, and volumes. An integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

The principles of integration were formulated by Isaac Newton by G.W. Leibniz in the late 17th century, who considered the integral as an infinite sum of rectangles of infinitesimal width. Bernhard Riemann also gave a rigorous mathematical definition of integrals.

It is based on a limiting procedure that approximates the area of a curvilinear region by breaking the part into thin vertical slabs. We learn different concepts in integral calculus. They include areas of different geometric shapes, the area below the curve using the definite integral, the indefinite integral, and various potential applications.

We also find the most critical calculus theorem dubbed the "Fundamental Calculus Theorem." This theorem expounds on the notion that differentiation and integration are retrograde operations. Integral calculus is closely related to differential calculus, and together they constitute the foundation of mathematical analysis.

Calculus has always been vitally important to the development of many scientific breakthroughs since its invention, particularly in the physics and engineering disciplines. Get in touch with us today for calculus assignment answers.

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