AMAT 41763: Qualitative and Quantitative Behavior of the Solutions of Ordinary Differential Equations

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Course Code     : AMAT 41763

Title                  : Qualitative and Quantitative Behavior of the Solutions of Ordinary Differential        

                              Equations

Pre-requisites   : PMAT 22572

 

Learning Outcomes:

At the end of this course, the student should be able to obtain the numerical solutions of differential equations and their implementations using appropriate software.

 Course Contents:     

Introduction to Software: Basic procedures in using an appropriate software, Handling numbers and matrices, Control structures, Program design, Script and function files, Plotting.           

Basic Properties of the Solutions of Ordinary Differential Equations: Stability of the solution and State-Space Analysis, Qualitative behavior of the solution of Ordinary Differential Equations.

Numerical Solutions of Ordinary Differential Equations: Concept of consistency, Stability and convergence properties of numerical schemes, Single and multistep methods, Solving Stiff systems, Shooting method, Gear's implementation of automatic ordinary differential equation solver, Finite difference discretizations for second order boundary value problems.                                                                                                                                   

Lab work using appropriate software: Algorithms studied in AMAT 21553, AMAT 22562 and in this unit will be implemented  using an appropriate software.

 Method of Teaching and Learning: A combination of lectures, computer laboratory sessions, tutorial discussions and presentations.

 Assessment: Based on tutorials, tests, presentations and end of course examination.

 Recommended Reading      :

  1. Hanselman, D. & Littlefield, B.R.. Mastering MATLAB, Pearson Education Limited, (2014).
  2. Ferdinand, V. Nonlinear differential equations and dynamical systems, Springer Science & Business Media (2012).
  3. Vanloan, C.F., Introduction to scientific computing: a matrix-vector approach using MATLAB, Prentice Hall, New York. (2000).
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