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In This Chapter
-
Basic Mathematical Calculations for Data
Analytics
- Introduction to Calculation for Data Analytics
- Quadratic Equation
- Overall Mean
- Chebyshev’s Theorem
- Permutations
- Combinations
- Failure
- Probability Distribution
- Probability
- Distribution Function
- Expected Value
- Variance
- Binomial Distribution
- Poisson Distribution
- Mean of a Binomial Distribution
- Variance
- Normal Distribution
- Cumulative Distribution Function
- Population Mean
- Standard Error of the Mean
- t-Distribution
- Chi-Squared Distribution
- Definition of Set and Notation
- Set Terms and Symbols
- Venn Diagrams
- Operations on Sets
- De Morgan’s Laws
- Probability Terminology
- Basic Probability Principles
- Random Variable
- Mean Value x ^ or Expected Value μ
- Series Expansions
- Mathematical Signs and Symbols
- Greek Alphabet
- Algebra
- Laws of Algebraic Operations
- Special Products and Factors
- Powers and Roots
- Proportion
- Arithmetic Mean of n Quantities A
- Geometric Mean of n Quantities G
- Harmonic Mean of n Quantities H
- Generalized Mean
- Solution of Quadratic Equations
- Solution of Cubic Equations
- Trigonometric Solution of the Cubic Equation
- Solution of Quadratic Equations
- Partial Fractions
- Non-repeated Linear Factors
- Repeated Linear Factors
- General Terms
- Repeated Linear Factors
- Factors of Higher Degree
- Geometry
- Triangles
- Right Triangle
- Equilateral Triangle
- General Triangle
- Quadrilaterals
- Rectangle
- Parallelogram
- Rhombus
- Trapezoid
- General Quadrilateral
- Regular Polygon of n Sides Each of Length b
- Regular Polygon of n Sides Inscribed in a Circle of Radius r
- Regular Polygon of n Sides Circumscribing a Circle of Radius r
- Cyclic Quadrilateral
- Prolemy’s Theorem
- Cyclic-Inscriptable Quadrilateral
- Planar Areas by Approximation
- Solids Bounded by Planes
- Prism
- Pyramid
- Prismatoid
- Regular Polyhedra
- Sphere of Radius r
- Right Circular Cylinder of Radius r and Height h
- Circular Cylinder of Radius r and Slant Height l
- Cylinder of Cross-Sectional Area A and Slant Height l
- Right Circular Cone of Radius r and Height h
- Spherical Cap of Radius r and Height h
- Frustum of Right Circular Cone of Radii a, b and Height h
- Zone and Segment of Two Bases
- Lune
- Spherical Sector
- Spherical Triangle and Polygon
- Spheroids
- Formulas from Plane Analytic Geometry
- Distance d between Two Points
- Slope m of Line Joining Two Points
- Equation of Line Joining Two Points
- Equation of Line in Terms of x Intercept a ≠ 0 and y intercept b ≠ 0
- Normal Form for Equation of Line
- General Equation of Line
- Distance from Point ( x 1 , y 1 ) to Line A x + B y + C = 0
- Angle ψ between Two Lines Having Slopes m 1 a n d m 2
- Area of Triangle with Vertices
- Transformation of Coordinates Involving Pure Translation
- Transformation of Coordinates Involving Pure Rotation
- Transformation of Coordinates Involving Translation and Rotation
- Polar Coordinates ( r , θ )
- Plane Curves
- Catenary, Hyperbolic Cosine
- Cardioid
- Circle
- Cassinian Curves
- Cotangent Curve
- Cubical Parabola
- Cosecant Curve
- Cosine Curve
- Ellipse
- Gamma Function
- Hyperbolic Functions
- Inverse Cosine Curve
- Inverse Sine Curve
- Inverse Tangent Curve
- Logarithmic Curve
- Parabola
- Cubical Parabola
- Tangent Curve
- Ellipsoid
- Elliptic Cone
- Elliptic Cylinder
- Hyperboloid of One Sheet
- Elliptic Paraboloid
- Hyperboloid of Two Sheets
- Hyperbolic Paraboloid
- Sphere
- Distance d between Two Points
- Equations of Line Joining P 1 ( x 1 , y 1 , z 1 ) and P 2 ( x 2 , y 2 , z 2 ) in Standard Form
- Equations of Line Joining P 1 ( x 1 , y 1 , z 1 ) and P 2 ( x 2 , y 2 , z 2 ) in Parametric Form
- Angle ϕ between Two Lines with Direction Cosines l 1 , m 1 , n 1 and l 2 , m 2 , n 2
- General Equation of a Plane
- Equation of Plane Passing through Points
- Equation of Plane in Intercept Form
- Equations of Line through ( x 0 , y 0 , z 0 ) and Perpendicular to Plane
- Distance from Point ( x , y , z ) to Plane A x + B y + D = 0
- Normal form for Equation of Plane
- Transformation of Coordinates Involving Pure Translation
- Transformation of Coordinates Involving Pure Rotation
- Transformation of Coordinates Involving Translation and Rotation
- Cylindrical Coordinates ( r , θ , z )
- Spherical Coordinates ( r , θ , ϕ )
- Logarithmic Identities
- Special Values
- Logarithms to General Base
- Series Expansions
- Limiting Values
- Inequalities
- Continued Fractions
- Polynomial Approximations
- Fundamental Properties
- Definition of General Powers
- Logarithmic and Exponential Functions
- Polynomial Approximations
- Slopes
- Trigonometric Ratios
- Sine Law
- Cosine Law
- Algebra
Abstract
This chapter presents a comprehensive collection of basic mathematical calculations that are useful for performing data analytics.
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