Abstract:

Propositional logic: syntax. Semantics, propositional calculus. Interpretations. Deductions systems: L system , Deduction theorem, consistence, soundness and

completeness theorems.

Predicate Logic: syntax: terms and formulas, Semantic predicate calculus.

Abstract:

Sorting differential equations.

First-order differential equations.

Linear differential equations of order n:

homogeneous and non-homogeneous equation, Wronskian homogeneous equations with constant

coefficients. Separation into homogeneous and non-homogeneous problem,

method of unknown coefficients and method of variation of parameters.

Language Problems - Sturm Liouville Theory: Defining a close-knit operator,

finding the operator's self-values and self-func tions and proving their properties.

System of Linear Differential Equations Order 1: Solving the homogeneous

system using eigenvalues and eigenvectors of the matrix.

Abstract:

Derivation of the wave equation.

D’Alembert solution for an infinite string, wave bouncing from a clamped and a free end of a string.

Well-posedness. Classification of second order linear problems.

Canonical forms. Laplace equation.

Solution of the wave equation on a bounded interval by separations of variables.

Uniqueness of the solution using the energy method. The maximum principle.

Separation of variables to Laplace equation in a rectangular and in a circle.

The heat equation. The maximum principle for the heat equation.

Solution of the inhomogeneous problem.

Solution of partial differential equations using Integral transforms.

Abstract:

Interpolation and approximations methods, error analysis.

Numerical integration, differentiation.

Ordinary differential equations solution, Solutions to non-linear equations.