Tools and methods applied to Chemistry and Geology
- UE code SCHIB209
-
Schedule
22.5 10Quarter 1
- ECTS Credits 3
-
Language
Français
- Teacher Leherte Laurence
- 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 and Fourier analysis.
- 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 and Fourier analysis.
Introduction
First order differential equations
Analysis and approximate methods
Second order differential equations
A few applications of differential equations
Introduction to Fourier analysis
DIFFERENTIAL EQUATIONS
I) Reminders
II) 1st order differential equations
a. Equations with separable variables
b. Exact differential equations
c. Homogeneous differential equations
d. Linear differential equations
e. Numerical approaches
III) 2nd-order differential equations
a. With constant coefficients
b. Coupled differential equations
c. Eigenvalue problems
IV) Differential equations of order greater than 2
V) Laplace transform
a. Properties
b. Calculation
c. Solving differential equations
VI) Some applications of differential equations in Chemistry and Geology
FOURIER SERIES AND TRANSFORMS
I) Introduction and reminders
II) Expression of a Fourier series
III) Fourier transform
IV) Applications
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 exam is compulsory in January. The course is assessed by a written exam (exercises). Questions on theory may also be asked.
- Exercise syllabus (available on Webcampus)
- Bibliographical references contained in documents posted on Webcampus and/or announced during the course
Training | Study programme | Block | Credits | Mandatory |
---|---|---|---|---|
Bachelier en sciences chimiques | Standard | 0 | 3 | |
Bachelier en sciences chimiques | Standard | 2 | 3 |