Recognize a differential equation in a real-life situation
Recognize and solve separable, exact, homogeneous, or linear type first-order ordinary differential equations by using the appropriate method.
Recognize and solve homogeneous or inhomogeneous type second-order linear ordinary differential equations, by using the appropriate method including Laplace transform.
Find the stability point(s) of first- or second-order homogeneous ordinary differential equation, and discuss their stability.
Use the numerical or graphical methods to solve a initial value problem.
Give the stability interval of a initial value problem involving a first- or second-order linear ordinary differential equation
Recognize and use a set of mutually orthogonal functions
Derive a Fourier series for a simple periodic function and discuss its convergence
Recognize and solve a limiting condition problem involving an homogeneous partial differential equation, by using the separation of variables and Fourier analysis
Recognize, in real-life problems, differential equations
Chose and apply a resolution method of first- and second-order ordinary differential equations.
Familiarize with the notion of transform (Laplace or Fourier)
Derive a function in a Fourier series and use this technique to solve partial differential equations.
Introduction
First order differential equations
Analysis and approximate methods
Second order differential equations
A few applications of differential equations
Introduction to Fourier analysis
Exercise sessions, with a teaching assistant, allow to apply notions seen in the lecture and to prepare the exam. The list of exercises are available on Webcampus.
The content of the exam will be specified at the end of the quadrimester. The lecture is evaluated through a written exam. The student will answer theoretical (about 25% of the exam) and exercises (about 75% of the exam) questions, during about 2h30-3h.
Slideshow of the lectures (available on Webcampus)
List of exercises (available on Webcampus)
Bibliographic references available in the slideshow and/or given during the lectures