Ordinary Differential Equations

Introduction to Ordinary Differential Equations (ODE. Classification of ODEs. First order ODE: separable of variables, homogeneous with respect to x and y, exact ODE, integrating factor, first order linear, Bernoulli and Riccatti. ODE of first order and degree greater than one. Picard's theorem. Theory of linear ODEs second and higher order. Homogeneous ODE with constant coefficients. Non-homogeneous ODE. Euler's equations. Techniques in solving second order linear ODE with non-constant coefficients and certain forms of non-linear ODE.

Objectives

Students will be able to identify, classify first order ODE's and linear ODE's of second order and higher and have the ability to choose the proper method for solving them. Additionally, they will use their knowledge for mathematical modeling simple scientific problems.

Prerequisites

Analysis and integrals of functions of one and two variables

Syllabus

Introduction to Ordinary Differential Equations (ODE. Classification of ODEs. First order ODE: separable of variables, homogeneous with respect to x and y, exact ODE, integrating factor, first order linear, Bernoulli and Riccatti. ODE of first order and degree greater than one. Picard's theorem. Theory of linear ODEs second and higher order. Homogeneous ODE with constant coefficients. Non-homogeneous ODE. Euler's equations. Techniques in solving second order linear ODE with non-constant coefficients and certain forms of non-linear ODE.