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Mathematics.md

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Mathematics is divided in 3 parts

  • Algebra

    • Permutations and Combinations
    • Binomial Series
    • Sequence and Series
    • Infinite Series
    • Binomial Theorem for any Index
    • Exponential Series
    • Logarithmic Series
  • Mean, Median and Mode

  • Sets and Logic

    • Sets and Relations
    • Functions
    • Reasoning and Logic
    • Knowledge representation
  • Discrete Mathematics

  • Matrices

    • Matrix
    • Types of Matrices
    • Operations on Matrices
    • Transpose of a Matrix
    • Symmetric and Skew Symmetric Matrices
    • Elementary Operation (Transformation) of a Matrix
    • Invertible Matrices
  • Determinants

    • Determinant
    • Properties of Determinants
    • Area of a Triangle
    • Minors and Cofactors
    • Adjoint and Inverse of a Matrix
    • Applications of Determinants and Matrices
  • Probability

    • Events and Random Experiments
    • Conditional Probability
    • Multiplication Theorem on Probability
    • Bayes' Theorem
    • Bernoulli Trials
    • Poission and Binomial Distributions
  • Statistics

    • Mean, Median and Mode
    • Range, Dispersion, Deviation
    • Variance and Standard Deviation
    • T test, F test, Z test, CHI square test
  • Calculus

    • Limits
    • Continuity
    • Differentiability
    • Exponential and Logarithmic Functions
    • Logarithmic Differentiation
    • Derivatives of Functions in Parametric Forms
    • Second Order Derivative
    • Mean Value Theorem
    • Differentiation
    • Rate of Change of Quantities
    • Increasing and Decreasing Functions
    • Tangents and Normals
    • Approximations
    • Maxima and Minima
    • Integration
    • Integration as an Inverse Process of Differentiation
    • Methods of Integration
    • Integrals of some Particular Functions
    • Integration by Partial Fractions
    • Integration by Parts
    • Definite Integral
    • Fundamental Theorem of Calculus
    • Evaluation of Definite Integrals by Substitution
    • Area under Simple Curves
    • Area between Two Curves
    • Differential equations
    • Basic Concepts
    • General and Particular Solutions of a Differential Equation
    • Formation of a Differential Equation whose General Solution is given
    • Methods of Solving First order, First Degree Differential Equations
  • Functions and Equations

    • Quadratic and Cubic equations
    • Complex Numbers
    • Trigonometry
    • Inverse Trigonometric Functions
  • Coordinate Geometry

    • Lines
    • General Equation of a Line
    • Slope
    • Distance of a Point From a Line
    • Conic Sections
    • Sections of a Cone
    • Parabola
    • Ellipse
    • Vector Algebra
    • Types of Vectors
    • Addition of Vectors
    • Multiplication of a Vector by a Scalar
    • Product of Two Vectors
    • Three Dimensional Geometry
    • Coordinate Axes and Coordinate Planes in Three Dimensional Space
    • Section Formula
    • Direction Cosines and Direction Ratios of a Line
    • Equation of a Line in Space
    • Angle between Two Lines
    • Shortest Distance between Two Lines
    • Plane and co-planarity
    • Angle between Two Planes
    • Distance of a Point from a Plane
    • Angle between a Line and a Plane

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