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Articles by Praveen Varghese Thomas
Page 9 of 75
Branches of Mathematics
Introduction Branches of mathematics are Algebra, geometry, arithmetic, number theory, etc. Over time, the scope of mathematics has expanded. There are two types of mathematics: pure mathematics and applied mathematics. The mathematics that can be used to solve real- world problems is known as applied mathematics. Mathematics has evolved over time into a vast and diverse subject. Mathematical advancements continue to make significant contributions. Algebra, Geometry, Arithmetic, Trigonometry, Calculus, and other branches of mathematics exist. In this tutorial, we will discuss branches of mathematics. Mathematics Maths is the science of quantity, pattern, order, structure, and relation, which has evolved over ...
Read MoreArea of Ellipse
Introduction Area of an ellipse is the area or region covered by the ellipse in two dimensions. An ellipse appears to be a regular oval shape, formed when a cone is snipped off by an oblique plane in such a way that a closed curve that does not bisect the base is produced. An ellipse is the locus of all the points in a plane whose distances from two fixed points in the plane are constant. The fixed points, which are surrounded by the curve, are known as foci (singular focus). The constant ratio is the eccentricity of the ellipse ...
Read MoreArea of Isosceles Triangle
Introduction The isosceles triangle area is the amount of surface or space enclosed between the isosceles triangle's sides. The quantity of space encircled by an isosceles triangle in a two-dimensional space is known as its area. Half of the product of the triangle's base and height is the usual formula for calculating its area. Here, to help you better comprehend this subject, a thorough explanation of the isosceles triangle area, its formula, and derivation is provided along with a few solved example problems. Isosceles triangle is one of the types of the triangle based on lengths of the sides. ...
Read MoreArea of Hemisphere
Introduction The area of a hemisphere is of two types: The curved surface area of a hemisphere = 2๐r2 square units. The total surface area of a hemisphere = 3๐r2square units. Two-dimensional geometry is concerned with the x-y plane in mathematics. Three-dimensional geometry is an extension of two-dimensional geometry that deals with three axes in the Cartesian plane, namely x, y, and z. 3D shapes have three dimensions: length, breadth, and height. In most cases, three-dimensional objects are created by rotating two-dimensional objects. Our planet's spherical shape is one of the best examples of 3D shapes. The sphere is formed ...
Read MoreDifference Between Natural and Whole numbers
Introduction Difference between natural and whole numbers is natural number is used to count objects ad whole numbers include 0 and natural numbers. Numerous other types of numbers exist, including whole numbers, natural numbers, integers, rational and irrational numbers, real and complex numbers, and integers. Students may find it puzzling more frequently than not, causing them to mix up one with the other. Particularly in the natural numbers and whole numbers, since both of them resemble one another somewhat. Therefore, it is crucial that the students comprehend both whole numbers and natural numbers in detail. In this tutorial, we ...
Read MoreVariable Definition
Introduction A variable is used to represent an unknown value in an equation. In algebra, we can use the four basic operations addition (+), subtraction (-), multiplication (ร), and division (รท) same as arithmetic. In algebra, terms are mathematical expressions that are made of two different parts: the number part and the variable part. In a term, the number part and variable part are multiplied together and written without a multiplication symbol. Terms can have any number of variables Expressions An expression consisting of one or more terms in which variables may have anything as power, including positive, negative, ...
Read MoreAlgebraic Operations on Complex Numbers
Introduction Algebraic operations on complex numbers are given by arithmetic operations are addition, subtraction, multiplication, and division. Complex numbers make it simpler to find the square root of negative values. The concept of complex numbers was first presented when Hero of Alexandria, a Greek mathematician, attempted to compute the square root of a negative number in the first century. Numerous scientific research, including those involving signal processing, electromagnetism, fluid physics, quantum mechanics, and vibration analysis, have made use of complex numbers. In this tutorial, we will discuss algebraic operations on complex numbers. Complex Numbers Real and imaginary numbers are ...
Read MoreApplication of Integrals
Introduction Application of Integrals is applied in various fields like Mathematics, Science, Engineering etc. The application of integrals is widely seen in both mathematics and physics for various purposes. If integration is applied for an area under a curve or area between two curves it is called the geometrical application of integrals which also includes finding the volume of solid revolution, length of the curve, etc., If the integration is applied to find the centre of gravity, mass, momentum, displacement, the velocity of objects, etc., then it is called the physical application of integrals. In this ...
Read MoreTaylor Series
Introduction Taylor series or Taylor expansion of a function is a finite sum of terms that are expressed in terms of the functions derivatives at a single point The polynomial or function of an infinite sum of terms is the Taylor series. The exponent or degree of each succeeding term will be greater than the exponent or degree of the one before it. $$\mathrm{f(a)\:+\:\frac{f'(a)}{1!}(x\:-\:a)\:+\:\frac{f"(a)}{2!}(x\:-\:a)^{2}\:+\:\frac{f'''(a)}{3!}(x\:-\:a)^{3}\:+\:.......}$$ For a real value function f(x), where f'(a), f"(a), f"'(a), etc., stands for the derivative of the function at point a, the aforementioned Taylor series expansion is provided. The Taylor series is also known as ...
Read MoreCensus
Introduction The census is a process of methodically calculating, gathering, and recording data on a certain population. It is mostly utilized while gathering information on the country's population, housing censuses, and agricultural, business, and supply needs. In this tutorial, we will discuss census, categorical variables, and numerical data. Definition A census is, by definition, the process of carefully computing, compiling, and documenting information on a certain population. It is primarily used to gather data on the population, housing, agricultural, commercial, and supply demands of the nation. This information provided comprehensive details about the occupation, age factors, socioeconomic features, population ...
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