By the end of the teaching unit, the student will be able to:
- Recognize and solve a separable, exact, homogeneous or linear first-order ordinary differential equation using one or more appropriate methods seen in the course;
- Recognize and solve an ordinary second-order linear homogeneous or inhomogeneous differential equation using the appropriate method, including Laplace transforms.
- Use numerical and graphical methods to solve a problem with initial values.
- Recognize and use a set of mutually orthogonal functions.
- Develop a simple periodic function in Fourier series, and discuss its convergence.
- Recognize and solve a boundary condition problem involving a homogeneous partial differential equation, using separation of variables, Fourier analysis, or Laplace transforms.
-Compute/perform a Fourier transform, demonstrate selected properties, and describe areas of application.
Introduction
First order differential equations
Analysis and approximate methods
Second order differential equations
Partial derivative equations and other applications of differential equations
Introduction to Fourier analysis
DIFFERENTIAL EQUATIONS
Reminders
1st order differential equations
Equations with separable variables: Population models, Chemical kinetics
Exact differential equations
Homogeneous differential equations
Linear differential equations: Integrating factor method, Examination of 2nd member, Variation of constants
Bernouilli-type equations
Stability
Approximations: Series development, Numerical approaches (Euler, Runge-Kutta)
2nd-order differential equations: With constant coefficients (Homogeneous differential equations, Inhomogeneous differential equations: Examination of the 2nd member, Variation of constants, Series development), Coupled differential equations, Eigenvalue problems
Differential equations of order greater than 2
Laplace transform: Properties, Calculation, Solving differential equations
Applications of differential equations in Chemistry and Geology including partial differential equations (heat equation, diffusion equation, consolidation equation, wave equation)
FOURIER SERIES AND TRANSFORMS
Introduction and reminders
Expression of a Fourier series
Fourier transform: Properties, Calculation, Applications
The table of contents is subject to revision during the academic year.
Exercise sessions, supervised by an assistant, enable you to apply the concepts covered in the course and prepare for the exam. Exercises are available on Webcampus.
The Block 1 Chemistry mathematics course is an essential foundation for the course. The concepts and examples associated with the subject are mainly presented on the blackboard. Exercises are solved in class (lectures and tutorials) or at home.
The exam is compulsory in January. The course is assessed by a written exam (exercises). Questions on theory and open questions may also be asked.
- Exercise syllabus (available on Webcampus)
- Bibliographical references contained in documents posted on Webcampus and/or announced during the course
| Training | Block | Credits | Mandatory |
|---|---|---|---|
| Bachelor in Chemistry | 2 | 3 | Yes |