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02-02Notes

A working library of the mathematics behind the analysis.

524 notes in 7 areas, from notation to machine learning. Each takes one formula: what it says, a small worked example, and code that runs. Revised in place. Page 13 of 22.

IndexAll notes

02-02-289Constant MultipleCalculus and optimisationRules of integration 02-02-290Integration by PartsCalculus and optimisationRules of integration 02-02-291ReversibilityCalculus and optimisationRules of integration 02-02-292Affine Power RuleCalculus and optimisationStandard integrals 02-02-293CosineCalculus and optimisationStandard integrals 02-02-294ExponentialCalculus and optimisationStandard integrals 02-02-295Exponential Base aCalculus and optimisationStandard integrals 02-02-296Inverse Sine OutputCalculus and optimisationStandard integrals 02-02-297Inverse Tangent OutputCalculus and optimisationStandard integrals 02-02-298Power RuleCalculus and optimisationStandard integrals 02-02-299Quotient-derived lnCalculus and optimisationStandard integrals 02-02-300Reciprocal LogarithmicCalculus and optimisationStandard integrals 02-02-301SineCalculus and optimisationStandard integrals 02-02-302TangentCalculus and optimisationStandard integrals 02-02-303Directional DerivativeCalculus and optimisationDifferential operators: gradients, Jacobians, Hessians 02-02-304Gradient (Row Vector Form)Calculus and optimisationDifferential operators: gradients, Jacobians, Hessians 02-02-305Gradient DirectionCalculus and optimisationDifferential operators: gradients, Jacobians, Hessians 02-02-306Hessian MatrixCalculus and optimisationDifferential operators: gradients, Jacobians, Hessians 02-02-307Jacobian Matrix (f: ℝⁿ → ℝᵐ)Calculus and optimisationDifferential operators: gradients, Jacobians, Hessians 02-02-308Jacobian Matrix (f: ℝⁿ → ℝᵐ)Calculus and optimisationDifferential operators: gradients, Jacobians, Hessians 02-02-309Gradient Flow (vanishing and exploding gradients)Calculus and optimisationMatrix calculus identities and automatic differentiation 02-02-310Gradient of a Linear TransformationCalculus and optimisationMatrix calculus identities and automatic differentiation 02-02-311Gradient of Squared ErrorCalculus and optimisationMatrix calculus identities and automatic differentiation 02-02-312Product RuleCalculus and optimisationMatrix calculus identities and automatic differentiation