BASIC MATHEMATICS
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Matrices and determinants deal with structured arrays of numbers and their properties, including operations like addition, multiplication, and determinant computation, with applications in various mathematical disciplines and practical fields.
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Trigonometric functions relate the angles of a right triangle to the ratios of its sides, providing a mathematical framework for analyzing periodic phenomena, geometry, and waveforms.
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Inverse trigonometry deals with the mathematical functions that provide the angles or values whose trigonometric ratios correspond to a given ratio, enabling the determination of angles and solving trigonometric equations.
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Integrals and their applications involve the mathematical concept of integration, which allows for the calculation of areas, volumes, cumulative quantities, and other quantities of interest, making it a powerful tool in physics, engineering, and other fields.
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Relations and functions examine the connections and associations between sets of elements, defining how inputs relate to outputs and allowing for the representation and analysis of mathematical relationships and mappings.
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Vector algebra deals with mathematical operations and manipulations involving vectors, which are quantities that have both magnitude and direction, allowing for the analysis and calculation of vector quantities in a structured mathematical framework.
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3D geometry deals with the study of spatial relationships and properties of objects in three dimensions, including shapes, sizes, angles, and volumes.
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Permutation and combinations involve the study of different ways to arrange or select objects from a set, exploring the possibilities of ordering and grouping elements, and finding the number of distinct outcomes in various scenarios.
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The binomial theorem states the formula for expanding a binomial raised to a positive integer power, allowing for the efficient calculation of coefficients and terms in the expansion.
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Sequence and series involve the study of ordered lists of numbers and their sums, exploring patterns, convergence, and properties of infinite or finite sequences and their corresponding series.
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Probability and statistics involve the study of uncertainty and data analysis, including the calculation of probabilities, modeling of random events, and drawing meaningful conclusions from data through statistical techniques.
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Complex numbers and quadratic equations are intertwined concepts, where complex numbers extend the number system to include the square root of negative numbers, enabling the solution of quadratic equations with complex roots
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Continuity and differentiability are mathematical properties that describe the smoothness and behavior of functions, with continuity referring to the absence of abrupt changes, and differentiability indicating the existence of derivative and local linearity.
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Differential equations and their applications involve the study of equations that relate rates of change to the variables they depend on, playing a crucial role in modeling and analyzing various phenomena in physics, engineering, and other scientific fields.