Introduction, Definitions, Solution Concept, Initial-Boundary Price Problems, First-Order Linear Equations, Homogeneous Equations, Accurate Equations and Integrating Factors, Linear n-Order, General Theory, Homogeneous with constant coefficients, Method of parameter variation, Coefficient of determination, Euler equation, Solving second-order linear systems with finite series, Solution at smooth point, Legendre equation, Solution to normal zap point, Laplace transform, Definition and properties, Heaviside function, Solving equations with discontinuity, Laplace transformation convolution, Solving special form integral equations, First order linear equation systems, Phase Level for Linear Systems, Autonomous Systems and Stability, Fourier Trigonometric Lines, Convergence Theorem, Sturm-Liouville Boundary Problems, Physical Origin of Diffusion Equation by Fick's Law, Solving Problems of Initial-Boundary Heat Equation by Variable Separation Method for Homogeneous and Non-Homogeneous Boundary Conditions.