System Concept Fundamentals and Linear Vector Spaces Introduction System Classifications and Signal Definition Time Signals and Their Representation System Input-Output Relations Signal representation via Linear Vector Spaces Linear Operators and Matrix Algebra Introduction Introduction to Matrix Algebra - Euclidian Vector Space Systems of Linear Algebraic Equations Diagonalization - Eigenvalue Decomposition of Matrices Multiple Eigenvalues and Jordan Canonical Form Determination of the Co-Efficients of the Characteristic Polynomial of a Matrix Computation of the Polynomial Function of the Matrix A S-N Decomposition of a Non-singular Matrix Computation of An without Eigenvectors Operator Algebra and Related Concepts (Finite and Infinite Dimensions) Addendum Ordinary Differential and Difference Equations Introduction System of Differential and Difference Equations Matrix Formulation and Solution of n-th Order Differential Equations Matrix Formulation of the k-th Order Difference Equation Linear Differential Equations with Variable Coefficients Summary Complex Variables for Transform Methods Introduction Theory of Complex Variables and Contour Integration Poisson''s Integral on Unit Circle (or disk) Positive Real Functions Integral Transform Methods Introduction Fourier Transform Pair Derivation Another Derivation of Fourier Transform Derivation of Bilateral Laplace Transform Lb Another Derivation of the Bilateral Laplace Transform Single-Sided Laplace Transform (Laplace Transform) Summary of Transform Definitions Laplace Transform Properties Recovery of the Original Time Function from the given Single-Sided Laplace Transform Solution of Linear Constant Coefficient Differential Equations via The Laplace Transform Computation of x(t) from X(s) For Causal Processes Inverse of Bilateral (Two-Sided) Laplace Transform Fb(s) Transfer Function Impulse Response Time Convolution for Linear Time Invariant System Frequency Convolution in Laplace Domain Parseval''s Theorem Generation of Orthogonal Signals in Frequency Domain The Fourier Transform Fourier Transform Properties Fourier Transform Inverse Hilbert Transform Application of The Integral Transforms to The Variable Parameter Differential Equations Generalized Error Function Digital Systems, Z-Transforms and Applications Introduction Discrete Systems and Difference Equations Realization of a general Discrete System Z-Transform for the Discrete Systems Fundamental Properties of Z-Transforms Evaluation of f(n), given its Single Sided Z-Transform Solution of Difference Equations using Z-Transforms Computation Algorithm for the Sum of the Squares of the Discrete Signal Sequence Bilateral Z-Transform f(n) Fb(z) Evaluation of some of the Important Series via Z-Transforms Reconstruction of a Continous-Time Band-limited Signal from Uniform Samples State Space Description Of Dynamic Systems Introduction State Space Formulation Selection of The State Variables and Formulation of The State Space Equations Methods of Deriving State Variable Equations for The Physical System State Space Concepts Calculus Of Variations Introduction Calculus of Maxima, Minima and stationary points (Extrema of a Function) Extremal of a Function subject to Multiple Constraints Extremal of a Definite Integral - Derivation of Euler-Lagrange Equations with variable end points Extremal of a Definite Integral with Multiple Constraints Mayer Form Bolza''s Form Variational Principles and Optimal Control Hamilton-Jacobi Formulation of Euler-Lagrange Equations Pontryagin''s Extremum Principle Dynamic Programming Stochastic Processes and Linear Systems Response to Stochastic Inputs Preliminaries Continous Random Variable and probability density function (pdf) Random Walk, Brownian Motion and Wiener Process Markov Chains, Inequalities and Law of Large Numbers Stochastic Hilbert Space Random or Stochastic Processes Wiener Filters Optimal Estimation, Control, Filtering and Prediction - Continuous Kalman Filters putation of An without Eigenvectors Operator Algebra and Related Concepts (Finite and Infinite Dimensions) Addendum Ordinary Differential and Difference Equations Introduction System of Differential and Difference Equations Matrix Formulation and Solution of n-th Order Differential Equations Matrix Formulation of the k-th Order Difference Equation Linear Differential Equations with Variable Coefficients Summary Complex Variables for Transform Methods Introduction Theory of Complex Variables and Contour Integration Poisson''s Integral on Unit Circle (or disk) Positive Real Functions Integral Transform Methods Introduction Fourier Transform Pair Derivation Another Derivation of Fourier Transform Derivation of Bilateral Laplace Transform Lb Another Derivation of the Bilateral Laplace Transform Single-Sided Laplace Transform (Laplace Transform) Summary of Transform Definitions Laplace Transform Properties Recovery of the Original Time Function from the given Single-Sided Laplace Transform Solution of Linear Constant Coefficient Differential Equations via The Laplace Transform Computation of x(t) from X(s) For Causal Processes Inverse of Bilateral (Two-Sided) Laplace Transform Fb(s) Transfer Function Impulse Response Time Convolution for Linear Time Invariant System Frequency Convolution in Laplace Domain Parseval''s Theorem Generation of Orthogonal Signals in Frequency Domain The Fourier Transform Fourier Transform Properties Fourier Transform Inverse Hilbert Transform Application of The Integral Transforms to The Variable Parameter Differential Equations Generalized Error Function Digital Systems, Z-Transforms and Applications Introduction Discrete Systems and Difference Equations Realization of a general Discrete System Z-Transform for the Discrete Systems Fundamental Properties of Z-Transforms Evaluation of f(n), given its Single Sided Z-Transform Solution of Difference Equations using Z-Transforms Computation Algorithm for the Sum of the Squares of the Discrete Signal Sequence Bilateral Z-Transform f(n) Fb(z) Evaluation of some of the Important Series via Z-Transforms Reconstruction of a Continous-Time Band-limited Signal from Uniform Samples State Space Description Of Dynamic Systems Introduction State Space Formulation Selection of The State Variables and Formulation of The State Space Equations Methods of Deriving State Variable Equations for The Physical System State Space Concepts Calculus Of Variations Introduction Calculus of Maxima, Minima and stationary points (Extrema of a Function) Extremal of a Function subject to Multiple Constraints Extremal of a Definite Integral - Derivation of Euler-Lagrange Equations with variable end points Extremal of a Definite Integral with Multiple Constraints Mayer Form Bolza''s Form Variational Principles and Optimal Control Hamilton-Jacobi Formulation of Euler-Lagrange Equations Pontryagin''s Extremum Principle Dynamic Programming Stochastic Processes and Linear Systems Response to Stochastic Inputs Preliminaries Continous Random Variable and probability density function (pdf) Random Walk, Brownian Motion and Wiener Process Markov Chains, Inequalities and Law of Large Numbers Stochastic Hilbert Space Random or Stochastic Processes Wiener Filters Optimal Estimation, Control, Filtering and Prediction - Continuous Kalman Filters mp;lt;/STRONG> Introduction Fourier Transform Pair Derivation Another Derivation of Fourier Transform Derivation of Bilateral Laplace Transform Lb Another Derivation of the Bilateral Laplace Transform Single-Sided Laplace Transform (Laplace Transform) Summary of Transform Definitions Laplace Transform Properties Recovery of the Original Time Function from the given Single-Sided Laplace Transform Solution of Linear Constant Coefficient Differential Equations via The Laplace Transform Computation of x(t) from X(s) For Causal Processes Inverse of Bilateral (Two-Sided) Laplace Transform Fb(s) Transfer Function Impulse Response Time Convolution for Linear Time Invariant System Frequency Convolution in Laplace Domain Parseval''s Theorem Generation of Orthogonal Signals in Frequency Domain The Fourier Transform Fourier Transform Properties Fourier Transform Inverse Hilbert Transform Application of The Integral Transforms to The Variable Parameter Differential Equations Generalized Error Function Digital Systems, Z-Transforms and Applications Introduction Discrete Systems and Difference Equations Realization of a general Discrete System Z-Transform for the Discrete Systems Fundamental Properties of Z-Transforms Evaluation of f.