Tools and methods applied to Chemistry and Geology - Bac géologie [SCHIB209]

Learning outcomes

• 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

Objectives

• Recognize, in real-life problems, differential equations

• Chose and apply a resolution method of first- and second-order ordinary differential equations.

• Familiarize yourself with the notion of transform (Laplace)

Content

1. Introduction

2. First order differential equations

3. Analysis and approximate methods

4. Second order differential equations

5. A few applications of differential equations

Exercises description

Exercise sessions, with a teaching assistant, allow to apply notion seen in the lecture and to prepare the exam. The list of exercises are available on Webcampus.