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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 14 of 22.

IndexAll notes

02-02-313Reverse Mode BackpropagationCalculus and optimisationMatrix calculus identities and automatic differentiation 02-02-314Sum RuleCalculus and optimisationMatrix calculus identities and automatic differentiation 02-02-315Implicit Differentiation (If F(x,y) = 0)Calculus and optimisationPartial differentiation and total differentials 02-02-316Multivariate Chain Rule (CaseCalculus and optimisationPartial differentiation and total differentials 02-02-317Partial Derivative DefinitionCalculus and optimisationPartial differentiation and total differentials 02-02-318Total DifferentialCalculus and optimisationPartial differentiation and total differentials 02-02-319Arithmetic n-th termCalculus and optimisationArithmetic and geometric progressions 02-02-320Arithmetic n-th termCalculus and optimisationArithmetic and geometric progressions 02-02-321Arithmetic n-th termCalculus and optimisationArithmetic and geometric progressions 02-02-322Arithmetic Sum to nCalculus and optimisationArithmetic and geometric progressions 02-02-323Geometric Infinite SumCalculus and optimisationArithmetic and geometric progressions 02-02-324Geometric n-th termCalculus and optimisationArithmetic and geometric progressions 02-02-325Geometric Sum to nCalculus and optimisationArithmetic and geometric progressions 02-02-326Alternating Series Error BoundCalculus and optimisationConvergence tests for infinite series 02-02-327Alternating Series Test (Leibniz)Calculus and optimisationConvergence tests for infinite series 02-02-328Comparison TestCalculus and optimisationConvergence tests for infinite series 02-02-329Limit Comparison TestCalculus and optimisationConvergence tests for infinite series 02-02-330n-th Term Test for DivergenceCalculus and optimisationConvergence tests for infinite series 02-02-331Ratio TestCalculus and optimisationConvergence tests for infinite series 02-02-332Root TestCalculus and optimisationConvergence tests for infinite series 02-02-333Euler's Forward Approximation (Numerical step)Calculus and optimisationODEs and transforms 02-02-334Fourier SeriesCalculus and optimisationODEs and transforms 02-02-335General ODE formatCalculus and optimisationODEs and transforms 02-02-336Green's Function/Delta Mapping (system behavior jump at t')Calculus and optimisationODEs and transforms