IDC205 Differential Equations for Scientists

Topic outline

• Announcements and updates
  

  Announcements and updates

  • All the students enrolled in this course must go through Rules of the game.
    
  • Assignment 03 (Problem Sheet 03) due on August 23, 2016.
    
  • Report your absence portal : Protect yourself against a possible proxy by someone possibly unknown to you. If you fail to do so before the instructor catches you, it will be assumed that you had arranged the proxy for yourself.

  
  

  Last updated : August 20, 2016 at 13:45 hrs.
  

  • Rules of the game Page
  • Attendance Record File
  • Tutorials Record File
• Lecture 09 : 30/08/2016
  This topic
  

  Lecture 09 : 30/08/2016

  • Reduction of order : New solutions from old ones.
  • Homogeneous linear equations : the case of repeated real roots.
  • Homogeneous linear equations : the case of complex roots.
    
• Lecture 08 : 29/08/2016
  

  Lecture 08 : 29/08/2016

  • Homogeneous differential equations of higher orders.
  • The concept of Wronskian.
    
  • Homogeneous differential equations : the case of distict real roots.
    
• Lecture 07 : 26/08/2016
  

  Lecture 07 : 26/08/2016

  • Linear differential equations of higher order.
  • Solution vector space for homogeneous linear differential equations.
  • Linear independence of solutions.
  • DImension of the solution space.
    

  
  
• Lecture 06 : 19/08/2016
  

  Lecture 06 : 19/08/2016

  • Separable differential forms and their solutions.
  • Homogeneous Equations as a special case of exact equations.
  • Linear differential equations of first order.
    

  
  

  • Problem Sheet 03 File
• Lecture 05 : 16/08/2016
  

  Lecture 05 : 16/08/2016

  • Solving exact equations.
  • Equations reducible to exact equations.
  • Integrating Factor (I. F.) and finding it in some cases.
    
• Lecture 04 : 09/08/2016
  

  Lecture 04 : 09/08/2016

  • The notation of "integral".
  • Differential forms, exact differential forms.
  • A characterisation of exactness.
    

  
  

  • Problem Sheet 02 File
• Lecture 03 : 08/08/2016
  

  Lecture 03 : 08/08/2016

  • Review of Picard's theorem.
  • Solving differential equations using Taylor's series.
  • Importance of concepts from MTH102,
    

  
  
• Lecture 02 : 02/08/2016
  

  Lecture 02 : 02/08/2016

  • Definition of a differential equation.
  • Order of a differential equation.
  • Linear differential equations.
  • Integral curves.

  
  

  • Problem Sheet 01 File
• Lecture 01 : 01/08/2016
  

  Lecture 01 : 01/08/2016

  • Rules of the game.
    
  • What is a differential equation?
  • Ordinary Differential Equations (ODE) vs Partial Differential Equations (PDE).