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Basic Details:

  • Course Code: EM 216
  • Credits: 3
  • Pre-requisites: None
  • Compulsory/Optional: Compulsory for Mechanical Engineering Specialization

Aim :

To introduce analytical solving techniques of linear ordinary differential equations and interpret the solutions.

Intended Learning Outcomes:

On successful completion of the course, the students should be able to;

  • Identify/derive the mathematical models of many physical problems as differential equations.
  • Solve first order separable, linear and exact differential equations and reducible forms.
  • Solve higher order linear ordinary differential equations analytically and analyze the solution of such second order equations.
  • Apply matrix methods and Laplace transform in solving systems of linear systems of ordinary differential equations.
  • Find and classify the critical points of a first order autonomous equation and use them to describe the qualitative behavior and the stability of the solutions.
  • Obtain analytical solutions of first order and second order linear partial differential equations.

Couse Content:

Differential Equations as a mathematical model and classification.

Separable, Linear, Exact, Reducible forms.

D-operators, method of undetermined coefficients, solution behaviors.

Eigenvalue and eigenvector method, decoupling, matrix exponential method.

Laplace transform of functions and derivatives, solving ordinary differential equations and linear systems, convolution.

Partial differential equations as a mathematical model and Classification, method of characteristics, method of separation of variables, and the d’Alermbert solution.

Time Allocation (Hours):

Lectures
0
Assignments
0

Recommended Texts:

  • R.K. Nagle, E.W. Saff, A.D. Snider, “Fundamentals of Differential Equations”, 8th edition (2012), Pearson Education.
  • E. Kreyszig, “Advanced Engineering Mathematics”, 9th edition (2010), John Wiley & Sons Inc.
  • Philip Franklin, “Differential Equations for Engineers”, 5th edition (1980), Dover Publications.
  • Walter A. Strauss, “Partial Differential Equations”, 2nd edition (2007), John Wiley and Sons Inc.

Assessment:

In - course:

Tutorials/Assignments/Quizzes
10%
Mid Semester Examination
30%

End-semester:

60%