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Equations

Cosine is an even function
Cosine Periodicity
Sine-Cosine equivalence
Sine is an odd function
Even functions
Imaginary Number Relation to Real Numbers
Imaginary Number Definition
Odd functions
Complex Conjugate Definition
Cartesian Form of a Complex Number
Definition of a Derivative
Product Rule
Full cycle cosine idenity
Polar Form of a Complex Number
Derivative of exp(x)
Derivative of Sine
Derivative of Cosine
Cosine quarter cycle zeros identity
Eulers Formula
Angle addition for cosine
Euler Definition of Sine
Euler Definition of Cosine
Angle addition for sine
Pythagorean identity
Pythagorean theorem
Definition of Exponentiation
Exponent Addition
Angle subtraction for sine
Angle subtraction for cosine
Product to sum cosine cosine
Product to sum sine sine
Product to sum sine cosine
Definition of a Quadratic Polynomial
Quadratic Formula
Discrete signal
Radian Frequency
Normalized Radian Frequency
Normalized Frequency
Definition of Sampling Frequency
Definition of a Finite Impulse Response
General form of a Finite Impulse Response Filter
Convolution of a Signal and a Filter
Response of a Linear Time-Invariant Filter
Sinusoidal Response of Finite Impulse Response Filter
General Form for the Equation of a Straight Line
Gradient of a Straight Line
Definition of a Definite Integral
Area of a Rectangle
Definition of an Indefinite Integral
Power Rule for Differentiation
Power Rule for Integration
Fourier Series (Exponential Form)
Integral of a Derivative
Derivative of an Integral
Integral of exp(x)
Integral of exp(ax) wrt x
Integration by Parts
Definition of Product Symbol
Integral of (a exp(ax)) wrt x
Integral Fourier Coefficients(Exponential form)
Z-Transform
Demo Equation
Counting loss
General Form of a Loss Function
Quadratic Loss (L2)
Risk of a Model
Mean Squared Error Loss (MSE)
MSE Minimization
Empirical Risk of a Model
Risk of Optimal Model
Operationalization of Supervised Learning
Loss Minimization with Regularization
General Form of a Regularization Function
Gradient Empirical Risk
Approximation of Performance Landscape
Update rule of the Gradient Descent
L2 Regularization
Goal of Supervised Learning
Polynomial Curve Fitting
RNN Update Equation
Function Estimated by Perceptron
Risk Minimization for MLPs
Gradient of the performance surface
Activation of a neuron
General form of an activation function
Rectified Linear Unit
Activation of a layer
Activation of the output layer
Recurrent Neural Network Update Equations
Gradient Empirical Risk (sum of gradients)
Recurrent Neural Network with Output Feedback
Input neuron of an LSTM
Input gate of an LSTM
Output gate of an LSTM
Forget gate of an LSTM
Update of a memory cell in an LSTM
Recursive Definition of Recurrent Neural Networks
Temporal Evolution of Dynamical System
General Form of an Update Operator
Discrete-Time Update Operator
Stochastic Discrete-Time Update Operator
Continuous-Time Update Operator (ODE)
Discrete-Time System with Input
Discrete-Time Dynamical System
Stochastic Discrete-Time System with Input
Stochastic Discrete-Time Dynamical System
Continuous-Time Dynamical System
Continuous-Time System with Input
Backpropagation - Unit Potential
Markov Property
Markov Transition Matrix Entries
Output of an LSTM
Energy of a state in a Hopfield Network
Activation of a neuron in a Hopfield Network
Weight update of a Hopfield Network
Analytical solution of a Hopfield Network
Delta Equation
Delta Equation by Backpropagation
Neuron Potential to Activation
Weight update of a Heteroassociative Hopfield Network
Energy of a Specific State in a Boltzmann Machine
Boltzmann Normalization Constant/Partition Function
Boltzmann Distribution of Microstates
Boltzmann Acceptance Function
Metropolis Acceptance Function
Boltzmann Normalization Constant/Partition Function (Discrete)
Energy Change When One Unit in Boltzmann Machine Changes
Kullback-Leibler Divergence
Probability of Setting a Unit to 1 in a BM
Division of Exponents
Gradients of KL Divergence with Respect to Weights
Weight Update Rule for Boltzmann Machines
Ratio Metropolis Acceptance Function