Course information

Introductory Concepts: Definitions, Concept of solution and geometric characteristics. Initial-boundary value problems. Well-posed problems. Differential equations with separable variables, linear, homogeneous, exact. First-order differential equations: Riccati, Lagrange, Clairaut. Qualitative Theory: Existence and uniqueness of solution. Picard, Peano Theorems. Linear differential equations: General theory. Linear independence. Wronskian determinant. Homogeneous equations with constant coefficients. Variation of parameters method (Lagrange). Method of undetermined coefficients. Euler equation. Solution by series: Power series. Solution at an ordinary point. Legendre equation. Solution at a regular singular point. Frobenius Theory. Bessel equations. Systems of differential equations: Introduction, solution by elimination. General theory. Systems with constant coefficients, homogeneous and non-homogeneous. Laplace Transform: Definition. Properties. Inverse Laplace transform. Applications. Heaviside function. Dirac delta function. Convolution. Use of computational programs.