Learning outcomes

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.

 

Goals

- 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.


 

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

  6. Introduction to Fourier analysis

 

Table of contents

DIFFERENTIAL EQUATIONS




  1. Reminders
  2. 1st order differential equations
  3. Equations with separable variables: Population models, Chemical kinetics
  4. Exact differential equations
  5. Homogeneous differential equations
  6. Linear differential equations: Integrating factor method, Examination of 2nd member, Variation of constants
  7. Bernouilli-type equations
  8. Stability
  9. Approximations: Series development, Numerical approaches (Euler, Runge-Kutta)
  10. 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
  11. Differential equations of order greater than 2
  12. Laplace transform: Properties, Calculation, Solving differential equations
  13. 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.

 

Exercices

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.

 

 

Teaching methods

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.

 




	 



	 



      




                                                                                                          

                                                        

                  
Assessment method

                                                                                            

    

          
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.
 

      




                                                                      

                                                        

                  
Sources, references and any support material

                                                                                                                                

    

          

	- Exercise syllabus (available on Webcampus)



	- Bibliographical references contained in documents posted on Webcampus and/or announced during the course



	 



      




                                  

                                    

        

      

              

        

            

    
  

          

                                          

                  
Language of instruction

                                                        

    

          
French

      




                                                                                                                                              

                                                                                                                  

        

      

              

        

  
  
  

  
  
  

  

  
  

  

    

      Training
      Study programme
      Block
      Credits
      Mandatory
    

          

        
                      
                              Bachelor in Chemistry
                          
                  
        Standard
        0
        3
        
                      

                  		
      

          

        
                      
                              Bachelor in Chemistry
                          
                  
        Standard
        2
        3